Estimates parameters of non-linear regression models for DIF detection using either non-linear least squares or maximum likelihood method with various algorithms.
Usage
estimNLR(y, match, group, formula, method, lower, upper, start)
# S3 method for class 'estimNLR'
logLik(object, ...)
# S3 method for class 'estimNLR'
coef(object, ...)
# S3 method for class 'estimNLR'
fitted(object, ...)
# S3 method for class 'estimNLR'
residuals(object, ...)
# S3 method for class 'estimNLR'
print(x, ...)
# S3 method for class 'estimNLR'
vcov(object, sandwich = FALSE, ...)Arguments
- y
numeric: a binary vector of responses (
"1"correct,"0"incorrect).- match
numeric: a numeric vector describing the matching criterion.
- group
numeric: a binary vector of a group membership (
"0"for the reference group,"1"for the focal group).- formula
formula: specification of the model. It can be obtained by the
formulaNLR()function.- method
character: an estimation method to be applied. The options are
"nls"for non-linear least squares (default),"mle"for the maximum likelihood method using the"L-BFGS-B"algorithm with constraints,"em"for the maximum likelihood estimation with the EM algorithm,"plf"for the maximum likelihood estimation with the algorithm based on parametric link function, and"irls"for the maximum likelihood estimation with the iteratively reweighted least squares algorithm (available for the"2PL"model only). See Details.- lower
numeric: lower bounds for item parameters of the model specified in the
formula.- upper
numeric: upper bounds for item parameters of the model specified in the
formula.- start
numeric: initial values of item parameters. They can be obtained by the
startNLR()function.- object
an object of the
"estimNLR"class.- ...
other generic parameters for S3 methods.
- x
an object of the
"estimNLR"class.- sandwich
logical: should the sandwich estimator be applied for computation of the covariance matrix of item parameters when using
method = "nls"? (the default isFALSE).
Details
The function offers either the non-linear least squares estimation via the
nls function (Drabinova & Martinkova, 2017; Hladka &
Martinkova, 2020), the maximum likelihood method with the "L-BFGS-B"
algorithm with constraints via the optim function (Hladka &
Martinkova, 2020), the maximum likelihood method with the EM algorithm (Hladka,
Martinkova, & Brabec, 2025), the maximum likelihood method with the algorithm
based on parametric link function (PLF; Hladka, Martinkova, & Brabec, 2025), or
the maximum likelihood method with the iteratively reweighted least squares
algorithm via the glm function.
References
Drabinova, A. & Martinkova, P. (2017). Detection of differential item functioning with nonlinear regression: A non-IRT approach accounting for guessing. Journal of Educational Measurement, 54(4), 498–517, doi:10.1111/jedm.12158 .
Hladka, A. & Martinkova, P. (2020). difNLR: Generalized logistic regression models for DIF and DDF detection. The R Journal, 12(1), 300–323, doi:10.32614/RJ-2020-014 .
Hladka, A. (2021). Statistical models for detection of differential item functioning. Dissertation thesis. Faculty of Mathematics and Physics, Charles University.
Hladka, A., Martinkova, P., & Brabec, M. (2025). New iterative algorithms for estimation of item functioning. Journal of Educational and Behavioral Statistics. Online first, doi:10.3102/10769986241312354 .
Author
Adela Hladka (nee Drabinova)
Institute of Computer Science of the Czech Academy of Sciences
hladka@cs.cas.cz
Patricia Martinkova
Institute of Computer Science of the Czech Academy of Sciences
martinkova@cs.cas.cz
Examples
# loading data
data(GMAT)
y <- GMAT[, 1] # item 1
match <- scale(rowSums(GMAT[, 1:20])) # standardized total score
group <- GMAT[, "group"] # group membership variable
# formula for 3PL model with the same guessing for both groups,
# IRT parameterization
M <- formulaNLR(model = "3PLcg", type = "both", parameterization = "irt")
# starting values for 3PL model with the same guessing for item 1
start <- startNLR(GMAT[, 1:20], group, model = "3PLcg", parameterization = "irt")
start <- start[[1]][M$M1$parameters]
# nonlinear least squares
(fit_nls <- estimNLR(
y = y, match = match, group = group,
formula = M$M1$formula, method = "nls",
lower = M$M1$lower, upper = M$M1$upper, start = start
))
#> Nonlinear regression model
#>
#> Model: y ~ c + (1 - c)/(1 + exp(-(a + aDif * g) * (x - (b + bDif * g))))
#>
#> Coefficients:
#> a b c aDif bDif
#> 1.1211 -0.3037 0.1106 -0.0645 0.9497
#>
#> Nonlinear least squares estimation
#> Converged after 8 iterations
coef(fit_nls)
#> a b c aDif bDif
#> 1.12111002 -0.30366987 0.11055294 -0.06452584 0.94969524
logLik(fit_nls)
#> 'log Lik.' -1252.515 (df=5)
vcov(fit_nls)
#> a b c aDif bDif
#> a 0.022431664 0.016929831 6.457960e-03 -0.007351992 -1.727466e-03
#> b 0.016929831 0.029611668 1.033136e-02 0.007194420 -5.291136e-03
#> c 0.006457960 0.010331355 4.384449e-03 0.003779956 -1.014112e-05
#> aDif -0.007351992 0.007194420 3.779956e-03 0.029190088 -2.220439e-03
#> bDif -0.001727466 -0.005291136 -1.014112e-05 -0.002220439 1.235827e-02
vcov(fit_nls, sandwich = TRUE)
#> a b c aDif bDif
#> a 0.018614638 0.017218187 0.0064071814 -1.145073e-03 -1.203845e-03
#> b 0.017218187 0.034356847 0.0120786688 1.546893e-02 -4.325496e-03
#> c 0.006407181 0.012078669 0.0050928509 7.394285e-03 5.961622e-04
#> aDif -0.001145073 0.015468934 0.0073942854 3.290892e-02 -3.919505e-05
#> bDif -0.001203845 -0.004325496 0.0005961622 -3.919505e-05 1.291965e-02
fitted(fit_nls)
#> [1] 0.4364812 0.7866565 0.8870283 0.2254449 0.7950140 0.2979030 0.5093386
#> [8] 0.4258949 0.7950140 0.7866565 0.8463985 0.7267632 0.4364812 0.5025620
#> [15] 0.7326843 0.3567994 0.5825445 0.7267632 0.4364812 0.3120549 0.4258949
#> [22] 0.8368962 0.8870283 0.8463985 0.6607947 0.5025620 0.7866565 0.5025620
#> [29] 0.7267632 0.2639710 0.5025620 0.6585474 0.7950140 0.3120549 0.4364812
#> [36] 0.5093386 0.6607947 0.8463985 0.5025620 0.5847767 0.2639710 0.5025620
#> [43] 0.5025620 0.7950140 0.7950140 0.4364812 0.3120549 0.5025620 0.2254449
#> [50] 0.5093386 0.5093386 0.2639710 0.1726989 0.5093386 0.3120549 0.5825445
#> [57] 0.3120549 0.5093386 0.5093386 0.5093386 0.9091806 0.6607947 0.3120549
#> [64] 0.2254449 0.6585474 0.7326843 0.2254449 0.7326843 0.1431491 0.9412824
#> [71] 0.4258949 0.2254449 0.4364812 0.5825445 0.5025620 0.2254449 0.6585474
#> [78] 0.2500384 0.3120549 0.5025620 0.5093386 0.5825445 0.2254449 0.3567994
#> [85] 0.5025620 0.6585474 0.2979030 0.3567994 0.4364812 0.7326843 0.2979030
#> [92] 0.7267632 0.4364812 0.7267632 0.2639710 0.2254449 0.3698990 0.8463985
#> [99] 0.2639710 0.8774495 0.9582385 0.5093386 0.5093386 0.6607947 0.3698990
#> [106] 0.2126246 0.7950140 0.7950140 0.6607947 0.1726989 0.6585474 0.4364812
#> [113] 0.3698990 0.8463985 0.3120549 0.5825445 0.3120549 0.8870283 0.2254449
#> [120] 0.4364812 0.7866565 0.4364812 0.2639710 0.8463985 0.2639710 0.5025620
#> [127] 0.2639710 0.2500384 0.2639710 0.2979030 0.4364812 0.4258949 0.4258949
#> [134] 0.8463985 0.3698990 0.3698990 0.1842599 0.5847767 0.7326843 0.8463985
#> [141] 0.3698990 0.1954772 0.2979030 0.7950140 0.5025620 0.6607947 0.9181070
#> [148] 0.7326843 0.2254449 0.3120549 0.2639710 0.2254449 0.6607947 0.4364812
#> [155] 0.8463985 0.3567994 0.2254449 0.9181070 0.9412824 0.3698990 0.4258949
#> [162] 0.5093386 0.9181070 0.1726989 0.4258949 0.4364812 0.6607947 0.9181070
#> [169] 0.2639710 0.7950140 0.2979030 0.6607947 0.5847767 0.5825445 0.7326843
#> [176] 0.4258949 0.4364812 0.7866565 0.8870283 0.1954772 0.3698990 0.8870283
#> [183] 0.9181070 0.8368962 0.5847767 0.5025620 0.8870283 0.3567994 0.1556874
#> [190] 0.7326843 0.3120549 0.5025620 0.7326843 0.1726989 0.9181070 0.5825445
#> [197] 0.5825445 0.6607947 0.7950140 0.4364812 0.3120549 0.5825445 0.2500384
#> [204] 0.7950140 0.8870283 0.7326843 0.7326843 0.4364812 0.7950140 0.3698990
#> [211] 0.5847767 0.3698990 0.2500384 0.5093386 0.1954772 0.2979030 0.7326843
#> [218] 0.7950140 0.9412824 0.7326843 0.5847767 0.3698990 0.3698990 0.7326843
#> [225] 0.3698990 0.4258949 0.7326843 0.5025620 0.5825445 0.5093386 0.3567994
#> [232] 0.9181070 0.8870283 0.3567994 0.8463985 0.7326843 0.5825445 0.9412824
#> [239] 0.3120549 0.9181070 0.7326843 0.6585474 0.6607947 0.4364812 0.5025620
#> [246] 0.3120549 0.4364812 0.5825445 0.5847767 0.3120549 0.8463985 0.5025620
#> [253] 0.7950140 0.6607947 0.5847767 0.5847767 0.6607947 0.4364812 0.7267632
#> [260] 0.7950140 0.1431491 0.6585474 0.3567994 0.2639710 0.6607947 0.5825445
#> [267] 0.8463985 0.4364812 0.7866565 0.1726989 0.4364812 0.6607947 0.7950140
#> [274] 0.3567994 0.9181070 0.3120549 0.5093386 0.1954772 0.3567994 0.5093386
#> [281] 0.2639710 0.7326843 0.5825445 0.4258949 0.5847767 0.7866565 0.5025620
#> [288] 0.7950140 0.9412824 0.4258949 0.4258949 0.2639710 0.3120549 0.5825445
#> [295] 0.4364812 0.8463985 0.5847767 0.5025620 0.5847767 0.8463985 0.5847767
#> [302] 0.3698990 0.3567994 0.2500384 0.6607947 0.9181070 0.7950140 0.9181070
#> [309] 0.4258949 0.3698990 0.6607947 0.2639710 0.4364812 0.5093386 0.8774495
#> [316] 0.7950140 0.5093386 0.6585474 0.5825445 0.3120549 0.2639710 0.5093386
#> [323] 0.7326843 0.1339972 0.6585474 0.7326843 0.3567994 0.7950140 0.7326843
#> [330] 0.1726989 0.3120549 0.3698990 0.4364812 0.2639710 0.8870283 0.5025620
#> [337] 0.5825445 0.4364812 0.6607947 0.3698990 0.6607947 0.5847767 0.7950140
#> [344] 0.7326843 0.5025620 0.5025620 0.4364812 0.4258949 0.8463985 0.2639710
#> [351] 0.1954772 0.8463985 0.5825445 0.6607947 0.2979030 0.8463985 0.5093386
#> [358] 0.2639710 0.2979030 0.4258949 0.7866565 0.2639710 0.5093386 0.2979030
#> [365] 0.8870283 0.4364812 0.3567994 0.3120549 0.2639710 0.5847767 0.3567994
#> [372] 0.5093386 0.2254449 0.4258949 0.5825445 0.3120549 0.1726989 0.7326843
#> [379] 0.5025620 0.7950140 0.8463985 0.5093386 0.4258949 0.5825445 0.6607947
#> [386] 0.9412824 0.5025620 0.9704721 0.3567994 0.1556874 0.3120549 0.3698990
#> [393] 0.7267632 0.5093386 0.5025620 0.3698990 0.4258949 0.8368962 0.8368962
#> [400] 0.8463985 0.2500384 0.3120549 0.4364812 0.8463985 0.9181070 0.3698990
#> [407] 0.5093386 0.5847767 0.4364812 0.8368962 0.6585474 0.4364812 0.7950140
#> [414] 0.4258949 0.5825445 0.1954772 0.5093386 0.2979030 0.4258949 0.1556874
#> [421] 0.3120549 0.6585474 0.4364812 0.4364812 0.5093386 0.3567994 0.6585474
#> [428] 0.6585474 0.5093386 0.5025620 0.3698990 0.4364812 0.5025620 0.8463985
#> [435] 0.3120549 0.7866565 0.7950140 0.2639710 0.2500384 0.5093386 0.5847767
#> [442] 0.5093386 0.7326843 0.2254449 0.3120549 0.7950140 0.6585474 0.6585474
#> [449] 0.1954772 0.3120549 0.5847767 0.1726989 0.8368962 0.5093386 0.5025620
#> [456] 0.7267632 0.5093386 0.5847767 0.3120549 0.7326843 0.5093386 0.5847767
#> [463] 0.7267632 0.7950140 0.2126246 0.2639710 0.5093386 0.7326843 0.5847767
#> [470] 0.6585474 0.5825445 0.6607947 0.3120549 0.5025620 0.7950140 0.7326843
#> [477] 0.3567994 0.5093386 0.5093386 0.7326843 0.8463985 0.5847767 0.7950140
#> [484] 0.7326843 0.5025620 0.3120549 0.7950140 0.6607947 0.4364812 0.6585474
#> [491] 0.7326843 0.2254449 0.2254449 0.3120549 0.5025620 0.1954772 0.2979030
#> [498] 0.5847767 0.5025620 0.7866565 0.8463985 0.2500384 0.3698990 0.3120549
#> [505] 0.5025620 0.4258949 0.3120549 0.4364812 0.3120549 0.3120549 0.3120549
#> [512] 0.1842599 0.2126246 0.6607947 0.7267632 0.2979030 0.3698990 0.4258949
#> [519] 0.2639710 0.5093386 0.5825445 0.5093386 0.9091806 0.7866565 0.5093386
#> [526] 0.6585474 0.8870283 0.5847767 0.2639710 0.8463985 0.8463985 0.5847767
#> [533] 0.3698990 0.4258949 0.3120549 0.6607947 0.6607947 0.7326843 0.5025620
#> [540] 0.5093386 0.2639710 0.3698990 0.6585474 0.3567994 0.5025620 0.7326843
#> [547] 0.5093386 0.4364812 0.3698990 0.2254449 0.4364812 0.2254449 0.7326843
#> [554] 0.4364812 0.3567994 0.4364812 0.6585474 0.2639710 0.6607947 0.5093386
#> [561] 0.8463985 0.2500384 0.5025620 0.7950140 0.4364812 0.5847767 0.2639710
#> [568] 0.7326843 0.9181070 0.4258949 0.5025620 0.7267632 0.3698990 0.4364812
#> [575] 0.5025620 0.5093386 0.3698990 0.7326843 0.1726989 0.3698990 0.4258949
#> [582] 0.1954772 0.5025620 0.5025620 0.5093386 0.2639710 0.4364812 0.1556874
#> [589] 0.7950140 0.4364812 0.8870283 0.2126246 0.3567994 0.5825445 0.5025620
#> [596] 0.5025620 0.4364812 0.2254449 0.5847767 0.6607947 0.2639710 0.2500384
#> [603] 0.3698990 0.2639710 0.3120549 0.7326843 0.8463985 0.7326843 0.7866565
#> [610] 0.5847767 0.6607947 0.5847767 0.5825445 0.7866565 0.4364812 0.1556874
#> [617] 0.5025620 0.1556874 0.7326843 0.2979030 0.4364812 0.1954772 0.4364812
#> [624] 0.4364812 0.3698990 0.1954772 0.7950140 0.4258949 0.8870283 0.7326843
#> [631] 0.2254449 0.6607947 0.5825445 0.7950140 0.7326843 0.8463985 0.6607947
#> [638] 0.7326843 0.5825445 0.8870283 0.4258949 0.5825445 0.5825445 0.5847767
#> [645] 0.2254449 0.3567994 0.3120549 0.3567994 0.4258949 0.5025620 0.8774495
#> [652] 0.4258949 0.7326843 0.7326843 0.6607947 0.4364812 0.7950140 0.7326843
#> [659] 0.1954772 0.7326843 0.3120549 0.7950140 0.2639710 0.3120549 0.3120549
#> [666] 0.9704721 0.5825445 0.6607947 0.2979030 0.2254449 0.3698990 0.5847767
#> [673] 0.4364812 0.3120549 0.7326843 0.5847767 0.1954772 0.4364812 0.3120549
#> [680] 0.4364812 0.1726989 0.4258949 0.3120549 0.1556874 0.6607947 0.8870283
#> [687] 0.4364812 0.8368962 0.3120549 0.3698990 0.8463985 0.5093386 0.5025620
#> [694] 0.5093386 0.2500384 0.7950140 0.7950140 0.5025620 0.2639710 0.7950140
#> [701] 0.2500384 0.2639710 0.9181070 0.2639710 0.3698990 0.2979030 0.7950140
#> [708] 0.4258949 0.4258949 0.3120549 0.1556874 0.8870283 0.7950140 0.5825445
#> [715] 0.5093386 0.5093386 0.5825445 0.1954772 0.3120549 0.5025620 0.5093386
#> [722] 0.4258949 0.5025620 0.5825445 0.8463985 0.7267632 0.1954772 0.3698990
#> [729] 0.5093386 0.6607947 0.3698990 0.7326843 0.5825445 0.3698990 0.6585474
#> [736] 0.3698990 0.7326843 0.2254449 0.3567994 0.8368962 0.5093386 0.5847767
#> [743] 0.8368962 0.7326843 0.3120549 0.5093386 0.2500384 0.8870283 0.7267632
#> [750] 0.2979030 0.7267632 0.5847767 0.5847767 0.6607947 0.5025620 0.7326843
#> [757] 0.4258949 0.3698990 0.6607947 0.9412824 0.2254449 0.3698990 0.6585474
#> [764] 0.1726989 0.2639710 0.3120549 0.5025620 0.5825445 0.5025620 0.3567994
#> [771] 0.3567994 0.8870283 0.7326843 0.5093386 0.3120549 0.3567994 0.6585474
#> [778] 0.7326843 0.3698990 0.8463985 0.6607947 0.3567994 0.7950140 0.3698990
#> [785] 0.4258949 0.3120549 0.2639710 0.5025620 0.5025620 0.5847767 0.2979030
#> [792] 0.8463985 0.5025620 0.7326843 0.1954772 0.5025620 0.4364812 0.5825445
#> [799] 0.3567994 0.2639710 0.5825445 0.5825445 0.7950140 0.8368962 0.7267632
#> [806] 0.7326843 0.3120549 0.4258949 0.2639710 0.8368962 0.8463985 0.5093386
#> [813] 0.7267632 0.7950140 0.2639710 0.4258949 0.2254449 0.5093386 0.4364812
#> [820] 0.1954772 0.7950140 0.7326843 0.7950140 0.8870283 0.8870283 0.3698990
#> [827] 0.4258949 0.1954772 0.5025620 0.4364812 0.2254449 0.2500384 0.5093386
#> [834] 0.5093386 0.3120549 0.2254449 0.4364812 0.3567994 0.8463985 0.5847767
#> [841] 0.6607947 0.4258949 0.7326843 0.2979030 0.5847767 0.3698990 0.2639710
#> [848] 0.2639710 0.7326843 0.1726989 0.5025620 0.4258949 0.5825445 0.2500384
#> [855] 0.5825445 0.3698990 0.5093386 0.5825445 0.5093386 0.7326843 0.5093386
#> [862] 0.7326843 0.6585474 0.7866565 0.4364812 0.5847767 0.8368962 0.5093386
#> [869] 0.5825445 0.2639710 0.5825445 0.8870283 0.6607947 0.3698990 0.9181070
#> [876] 0.7326843 0.5825445 0.3567994 0.4364812 0.6585474 0.3698990 0.1954772
#> [883] 0.5025620 0.8870283 0.5825445 0.4364812 0.6607947 0.5825445 0.3698990
#> [890] 0.7950140 0.4258949 0.1954772 0.4258949 0.6585474 0.5847767 0.4364812
#> [897] 0.3120549 0.8368962 0.6585474 0.6607947 0.5825445 0.3120549 0.7866565
#> [904] 0.3120549 0.7326843 0.2639710 0.7326843 0.5847767 0.3120549 0.7950140
#> [911] 0.6607947 0.3698990 0.5847767 0.5825445 0.3698990 0.7950140 0.3698990
#> [918] 0.4364812 0.5847767 0.8870283 0.5847767 0.3567994 0.4258949 0.5025620
#> [925] 0.6607947 0.1954772 0.5825445 0.5847767 0.5025620 0.5847767 0.7326843
#> [932] 0.7866565 0.5825445 0.4258949 0.5825445 0.3698990 0.5847767 0.7267632
#> [939] 0.1954772 0.7326843 0.5093386 0.4258949 0.3698990 0.8870283 0.3120549
#> [946] 0.5847767 0.1954772 0.2500384 0.5825445 0.5025620 0.5847767 0.5093386
#> [953] 0.3698990 0.8870283 0.6607947 0.1954772 0.5025620 0.5093386 0.2254449
#> [960] 0.8463985 0.7866565 0.2639710 0.1954772 0.6607947 0.2254449 0.2254449
#> [967] 0.4364812 0.6585474 0.4364812 0.2639710 0.3698990 0.1726989 0.5825445
#> [974] 0.7267632 0.3698990 0.6607947 0.7267632 0.7267632 0.6607947 0.7326843
#> [981] 0.6585474 0.9181070 0.5825445 0.7950140 0.2254449 0.6607947 0.5825445
#> [988] 0.2639710 0.5093386 0.5847767 0.1339972 0.5847767 0.5093386 0.3698990
#> [995] 0.7326843 0.3567994 0.9181070 0.3698990 0.8870283 0.6607947
#> [ reached 'max' / getOption("max.print") -- omitted 1000 entries ]
#> attr(,"label")
#> [1] "Fitted values"
residuals(fit_nls)
#> [1] -0.43648118 0.21334351 0.11297170 -0.22544492 0.20498604 -0.29790303
#> [7] 0.49066141 0.57410507 0.20498604 0.21334351 0.15360150 0.27323680
#> [13] -0.43648118 -0.50256204 -0.73268430 -0.35679942 0.41745551 0.27323680
#> [19] -0.43648118 -0.31205490 0.57410507 0.16310381 0.11297170 0.15360150
#> [25] 0.33920535 0.49743796 0.21334351 -0.50256204 0.27323680 -0.26397097
#> [31] -0.50256204 -0.65854737 -0.79501396 -0.31205490 0.56351882 -0.50933859
#> [37] -0.66079465 0.15360150 0.49743796 -0.58477673 -0.26397097 0.49743796
#> [43] -0.50256204 0.20498604 0.20498604 -0.43648118 -0.31205490 0.49743796
#> [49] 0.77455508 -0.50933859 0.49066141 -0.26397097 0.82730110 -0.50933859
#> [55] 0.68794510 0.41745551 -0.31205490 0.49066141 -0.50933859 0.49066141
#> [61] 0.09081937 -0.66079465 0.68794510 -0.22544492 0.34145263 -0.73268430
#> [67] -0.22544492 0.26731570 -0.14314911 0.05871756 -0.42589493 -0.22544492
#> [73] 0.56351882 0.41745551 -0.50256204 0.77455508 0.34145263 -0.25003843
#> [79] -0.31205490 0.49743796 0.49066141 -0.58254449 -0.22544492 -0.35679942
#> [85] -0.50256204 -0.65854737 0.70209697 -0.35679942 -0.43648118 -0.73268430
#> [91] -0.29790303 0.27323680 -0.43648118 0.27323680 0.73602903 -0.22544492
#> [97] 0.63010098 0.15360150 -0.26397097 0.12255046 0.04176152 0.49066141
#> [103] 0.49066141 0.33920535 -0.36989902 -0.21262457 0.20498604 -0.79501396
#> [109] 0.33920535 -0.17269890 0.34145263 -0.43648118 0.63010098 0.15360150
#> [115] -0.31205490 -0.58254449 0.68794510 0.11297170 -0.22544492 0.56351882
#> [121] 0.21334351 -0.43648118 -0.26397097 0.15360150 -0.26397097 0.49743796
#> [127] 0.73602903 -0.25003843 -0.26397097 -0.29790303 0.56351882 -0.42589493
#> [133] -0.42589493 0.15360150 -0.36989902 -0.36989902 -0.18425986 0.41522327
#> [139] 0.26731570 0.15360150 -0.36989902 0.80452281 -0.29790303 0.20498604
#> [145] 0.49743796 -0.66079465 0.08189300 0.26731570 -0.22544492 0.68794510
#> [151] -0.26397097 -0.22544492 0.33920535 -0.43648118 0.15360150 -0.35679942
#> [157] -0.22544492 0.08189300 0.05871756 0.63010098 0.57410507 0.49066141
#> [163] -0.91810700 -0.17269890 0.57410507 -0.43648118 0.33920535 -0.91810700
#> [169] -0.26397097 0.20498604 -0.29790303 0.33920535 -0.58477673 0.41745551
#> [175] -0.73268430 0.57410507 -0.43648118 0.21334351 0.11297170 -0.19547719
#> [181] 0.63010098 0.11297170 0.08189300 0.16310381 -0.58477673 -0.50256204
#> [187] 0.11297170 -0.35679942 -0.15568743 0.26731570 -0.31205490 0.49743796
#> [193] 0.26731570 -0.17269890 0.08189300 0.41745551 -0.58254449 -0.66079465
#> [199] 0.20498604 0.56351882 -0.31205490 0.41745551 -0.25003843 0.20498604
#> [205] 0.11297170 -0.73268430 0.26731570 -0.43648118 0.20498604 -0.36989902
#> [211] -0.58477673 0.63010098 0.74996157 -0.50933859 -0.19547719 -0.29790303
#> [217] 0.26731570 0.20498604 0.05871756 0.26731570 0.41522327 -0.36989902
#> [223] -0.36989902 -0.73268430 -0.36989902 0.57410507 0.26731570 0.49743796
#> [229] 0.41745551 -0.50933859 0.64320058 0.08189300 0.11297170 0.64320058
#> [235] 0.15360150 -0.73268430 0.41745551 -0.94128244 -0.31205490 0.08189300
#> [241] 0.26731570 -0.65854737 0.33920535 0.56351882 0.49743796 -0.31205490
#> [247] -0.43648118 -0.58254449 0.41522327 -0.31205490 0.15360150 0.49743796
#> [253] 0.20498604 -0.66079465 -0.58477673 -0.58477673 0.33920535 0.56351882
#> [259] 0.27323680 0.20498604 -0.14314911 0.34145263 -0.35679942 -0.26397097
#> [265] 0.33920535 -0.58254449 0.15360150 -0.43648118 0.21334351 -0.17269890
#> [271] -0.43648118 -0.66079465 0.20498604 -0.35679942 0.08189300 -0.31205490
#> [277] -0.50933859 -0.19547719 0.64320058 -0.50933859 -0.26397097 0.26731570
#> [283] 0.41745551 -0.42589493 -0.58477673 -0.78665649 0.49743796 -0.79501396
#> [289] 0.05871756 -0.42589493 -0.42589493 -0.26397097 0.68794510 -0.58254449
#> [295] 0.56351882 0.15360150 0.41522327 -0.50256204 0.41522327 0.15360150
#> [301] 0.41522327 -0.36989902 -0.35679942 -0.25003843 -0.66079465 0.08189300
#> [307] 0.20498604 0.08189300 0.57410507 -0.36989902 -0.66079465 -0.26397097
#> [313] -0.43648118 -0.50933859 0.12255046 0.20498604 -0.50933859 -0.65854737
#> [319] 0.41745551 -0.31205490 0.73602903 0.49066141 0.26731570 -0.13399720
#> [325] 0.34145263 0.26731570 -0.35679942 0.20498604 0.26731570 -0.17269890
#> [331] -0.31205490 -0.36989902 -0.43648118 0.73602903 0.11297170 0.49743796
#> [337] -0.58254449 0.56351882 0.33920535 -0.36989902 -0.66079465 0.41522327
#> [343] 0.20498604 -0.73268430 0.49743796 0.49743796 0.56351882 0.57410507
#> [349] 0.15360150 -0.26397097 -0.19547719 0.15360150 -0.58254449 0.33920535
#> [355] -0.29790303 0.15360150 -0.50933859 -0.26397097 -0.29790303 0.57410507
#> [361] 0.21334351 0.73602903 -0.50933859 -0.29790303 0.11297170 -0.43648118
#> [367] -0.35679942 -0.31205490 -0.26397097 -0.58477673 -0.35679942 -0.50933859
#> [373] 0.77455508 -0.42589493 0.41745551 0.68794510 -0.17269890 -0.73268430
#> [379] 0.49743796 0.20498604 0.15360150 -0.50933859 0.57410507 -0.58254449
#> [385] -0.66079465 0.05871756 -0.50256204 0.02952789 -0.35679942 -0.15568743
#> [391] -0.31205490 -0.36989902 0.27323680 -0.50933859 -0.50256204 0.63010098
#> [397] -0.42589493 0.16310381 -0.83689619 0.15360150 -0.25003843 -0.31205490
#> [403] -0.43648118 -0.84639850 0.08189300 -0.36989902 0.49066141 0.41522327
#> [409] 0.56351882 0.16310381 0.34145263 0.56351882 0.20498604 -0.42589493
#> [415] -0.58254449 -0.19547719 0.49066141 -0.29790303 0.57410507 0.84431257
#> [421] -0.31205490 0.34145263 -0.43648118 -0.43648118 0.49066141 -0.35679942
#> [427] -0.65854737 0.34145263 -0.50933859 0.49743796 -0.36989902 0.56351882
#> [433] 0.49743796 0.15360150 -0.31205490 0.21334351 0.20498604 0.73602903
#> [439] 0.74996157 -0.50933859 0.41522327 0.49066141 0.26731570 -0.22544492
#> [445] -0.31205490 0.20498604 -0.65854737 -0.65854737 -0.19547719 -0.31205490
#> [451] 0.41522327 -0.17269890 0.16310381 0.49066141 0.49743796 0.27323680
#> [457] 0.49066141 0.41522327 0.68794510 0.26731570 0.49066141 0.41522327
#> [463] -0.72676320 -0.79501396 0.78737543 0.73602903 -0.50933859 0.26731570
#> [469] -0.58477673 0.34145263 -0.58254449 0.33920535 -0.31205490 -0.50256204
#> [475] 0.20498604 0.26731570 -0.35679942 -0.50933859 -0.50933859 0.26731570
#> [481] 0.15360150 -0.58477673 0.20498604 0.26731570 0.49743796 -0.31205490
#> [487] 0.20498604 -0.66079465 -0.43648118 0.34145263 -0.73268430 -0.22544492
#> [493] 0.77455508 -0.31205490 -0.50256204 0.80452281 0.70209697 0.41522327
#> [499] -0.50256204 0.21334351 -0.84639850 -0.25003843 -0.36989902 0.68794510
#> [505] -0.50256204 0.57410507 0.68794510 -0.43648118 0.68794510 0.68794510
#> [511] -0.31205490 -0.18425986 -0.21262457 0.33920535 -0.72676320 -0.29790303
#> [517] -0.36989902 0.57410507 -0.26397097 0.49066141 0.41745551 0.49066141
#> [523] 0.09081937 -0.78665649 0.49066141 0.34145263 0.11297170 -0.58477673
#> [529] -0.26397097 -0.84639850 0.15360150 -0.58477673 -0.36989902 0.57410507
#> [535] 0.68794510 0.33920535 0.33920535 0.26731570 0.49743796 0.49066141
#> [541] -0.26397097 -0.36989902 0.34145263 -0.35679942 0.49743796 0.26731570
#> [547] -0.50933859 -0.43648118 -0.36989902 0.77455508 -0.43648118 -0.22544492
#> [553] 0.26731570 0.56351882 0.64320058 -0.43648118 0.34145263 -0.26397097
#> [559] 0.33920535 0.49066141 0.15360150 -0.25003843 0.49743796 0.20498604
#> [565] 0.56351882 0.41522327 -0.26397097 -0.73268430 0.08189300 0.57410507
#> [571] -0.50256204 -0.72676320 -0.36989902 0.56351882 0.49743796 -0.50933859
#> [577] -0.36989902 0.26731570 0.82730110 -0.36989902 0.57410507 -0.19547719
#> [583] 0.49743796 -0.50256204 0.49066141 -0.26397097 -0.43648118 -0.15568743
#> [589] -0.79501396 0.56351882 0.11297170 -0.21262457 0.64320058 0.41745551
#> [595] -0.50256204 0.49743796 0.56351882 -0.22544492 0.41522327 -0.66079465
#> [601] 0.73602903 -0.25003843 0.63010098 0.73602903 -0.31205490 0.26731570
#> [607] -0.84639850 -0.73268430 0.21334351 0.41522327 0.33920535 -0.58477673
#> [613] -0.58254449 0.21334351 0.56351882 -0.15568743 -0.50256204 -0.15568743
#> [619] -0.73268430 -0.29790303 -0.43648118 0.80452281 -0.43648118 -0.43648118
#> [625] -0.36989902 -0.19547719 -0.79501396 0.57410507 0.11297170 0.26731570
#> [631] -0.22544492 -0.66079465 0.41745551 0.20498604 0.26731570 0.15360150
#> [637] 0.33920535 0.26731570 0.41745551 0.11297170 -0.42589493 -0.58254449
#> [643] 0.41745551 -0.58477673 0.77455508 -0.35679942 0.68794510 0.64320058
#> [649] -0.42589493 0.49743796 -0.87744954 -0.42589493 0.26731570 0.26731570
#> [655] -0.66079465 -0.43648118 -0.79501396 0.26731570 -0.19547719 0.26731570
#> [661] -0.31205490 0.20498604 -0.26397097 -0.31205490 0.68794510 0.02952789
#> [667] -0.58254449 0.33920535 0.70209697 -0.22544492 -0.36989902 0.41522327
#> [673] -0.43648118 -0.31205490 0.26731570 -0.58477673 -0.19547719 -0.43648118
#> [679] -0.31205490 0.56351882 -0.17269890 -0.42589493 -0.31205490 -0.15568743
#> [685] 0.33920535 -0.88702830 -0.43648118 0.16310381 -0.31205490 0.63010098
#> [691] 0.15360150 -0.50933859 0.49743796 -0.50933859 -0.25003843 0.20498604
#> [697] 0.20498604 0.49743796 0.73602903 0.20498604 0.74996157 0.73602903
#> [703] 0.08189300 -0.26397097 0.63010098 0.70209697 -0.79501396 -0.42589493
#> [709] 0.57410507 0.68794510 0.84431257 0.11297170 0.20498604 0.41745551
#> [715] -0.50933859 -0.50933859 0.41745551 -0.19547719 -0.31205490 -0.50256204
#> [721] 0.49066141 0.57410507 -0.50256204 -0.58254449 -0.84639850 -0.72676320
#> [727] -0.19547719 -0.36989902 -0.50933859 0.33920535 -0.36989902 -0.73268430
#> [733] -0.58254449 0.63010098 -0.65854737 0.63010098 0.26731570 -0.22544492
#> [739] -0.35679942 0.16310381 -0.50933859 -0.58477673 0.16310381 0.26731570
#> [745] -0.31205490 0.49066141 -0.25003843 -0.88702830 0.27323680 -0.29790303
#> [751] 0.27323680 -0.58477673 -0.58477673 0.33920535 -0.50256204 0.26731570
#> [757] -0.42589493 0.63010098 -0.66079465 0.05871756 -0.22544492 0.63010098
#> [763] 0.34145263 -0.17269890 0.73602903 -0.31205490 -0.50256204 -0.58254449
#> [769] -0.50256204 -0.35679942 -0.35679942 0.11297170 0.26731570 -0.50933859
#> [775] -0.31205490 -0.35679942 0.34145263 0.26731570 -0.36989902 0.15360150
#> [781] 0.33920535 0.64320058 0.20498604 -0.36989902 -0.42589493 0.68794510
#> [787] -0.26397097 0.49743796 0.49743796 0.41522327 0.70209697 0.15360150
#> [793] -0.50256204 0.26731570 -0.19547719 0.49743796 0.56351882 -0.58254449
#> [799] -0.35679942 -0.26397097 0.41745551 -0.58254449 0.20498604 0.16310381
#> [805] 0.27323680 -0.73268430 -0.31205490 -0.42589493 -0.26397097 0.16310381
#> [811] 0.15360150 -0.50933859 -0.72676320 0.20498604 -0.26397097 -0.42589493
#> [817] -0.22544492 -0.50933859 -0.43648118 -0.19547719 -0.79501396 0.26731570
#> [823] 0.20498604 0.11297170 0.11297170 0.63010098 0.57410507 -0.19547719
#> [829] -0.50256204 -0.43648118 -0.22544492 -0.25003843 -0.50933859 0.49066141
#> [835] -0.31205490 -0.22544492 0.56351882 -0.35679942 -0.84639850 0.41522327
#> [841] 0.33920535 0.57410507 -0.73268430 -0.29790303 -0.58477673 -0.36989902
#> [847] -0.26397097 -0.26397097 0.26731570 -0.17269890 -0.50256204 0.57410507
#> [853] -0.58254449 -0.25003843 0.41745551 -0.36989902 -0.50933859 0.41745551
#> [859] 0.49066141 -0.73268430 0.49066141 0.26731570 -0.65854737 0.21334351
#> [865] 0.56351882 -0.58477673 0.16310381 0.49066141 0.41745551 -0.26397097
#> [871] 0.41745551 0.11297170 0.33920535 0.63010098 0.08189300 0.26731570
#> [877] 0.41745551 0.64320058 0.56351882 0.34145263 -0.36989902 -0.19547719
#> [883] 0.49743796 0.11297170 0.41745551 0.56351882 0.33920535 0.41745551
#> [889] -0.36989902 0.20498604 0.57410507 -0.19547719 0.57410507 0.34145263
#> [895] 0.41522327 0.56351882 -0.31205490 0.16310381 -0.65854737 0.33920535
#> [901] -0.58254449 -0.31205490 0.21334351 0.68794510 0.26731570 -0.26397097
#> [907] 0.26731570 0.41522327 0.68794510 0.20498604 0.33920535 -0.36989902
#> [913] -0.58477673 0.41745551 -0.36989902 0.20498604 0.63010098 0.56351882
#> [919] 0.41522327 0.11297170 -0.58477673 0.64320058 -0.42589493 -0.50256204
#> [925] 0.33920535 -0.19547719 0.41745551 0.41522327 0.49743796 -0.58477673
#> [931] 0.26731570 0.21334351 0.41745551 -0.42589493 -0.58254449 -0.36989902
#> [937] -0.58477673 -0.72676320 -0.19547719 -0.73268430 -0.50933859 -0.42589493
#> [943] -0.36989902 0.11297170 -0.31205490 -0.58477673 -0.19547719 -0.25003843
#> [949] 0.41745551 0.49743796 0.41522327 0.49066141 -0.36989902 0.11297170
#> [955] 0.33920535 0.80452281 -0.50256204 -0.50933859 0.77455508 0.15360150
#> [961] 0.21334351 -0.26397097 0.80452281 -0.66079465 -0.22544492 -0.22544492
#> [967] -0.43648118 0.34145263 0.56351882 0.73602903 0.63010098 -0.17269890
#> [973] -0.58254449 -0.72676320 -0.36989902 0.33920535 -0.72676320 0.27323680
#> [979] 0.33920535 -0.73268430 0.34145263 0.08189300 -0.58254449 -0.79501396
#> [985] 0.77455508 -0.66079465 -0.58254449 -0.26397097 0.49066141 0.41522327
#> [991] -0.13399720 0.41522327 0.49066141 -0.36989902 0.26731570 -0.35679942
#> [997] -0.91810700 -0.36989902 0.11297170 0.33920535
#> [ reached 'max' / getOption("max.print") -- omitted 1000 entries ]
#> attr(,"label")
#> [1] "Residuals"
# maximum likelihood method
(fit_mle <- estimNLR(
y = y, match = match, group = group,
formula = M$M1$formula, method = "mle",
lower = M$M1$lower, upper = M$M1$upper, start = start
))
#> Nonlinear regression model
#>
#> Model: y ~ c + (1 - c)/(1 + exp(-(a + aDif * g) * (x - (b + bDif * g))))
#>
#> Coefficients:
#> a b c aDif bDif
#> 1.0779 -0.3469 0.0893 -0.0626 0.9235
#>
#> Maximum likelihood estimation using the L-BFGS-B algorithm
#> Converged after 23 iterations
coef(fit_mle)
#> a b c aDif bDif
#> 1.07785356 -0.34693642 0.08925326 -0.06260473 0.92348995
logLik(fit_mle)
#> 'log Lik.' -1191.904 (df=5)
vcov(fit_mle)
#> a b c aDif bDif
#> a 0.015987675 0.017897665 0.0066068809 -0.0000986350 -0.0013822815
#> b 0.017897665 0.040677309 0.0148394967 0.0177901835 -0.0035826532
#> c 0.006606881 0.014839497 0.0063269453 0.0086089359 0.0009761246
#> aDif -0.000098635 0.017790183 0.0086089359 0.0311452397 0.0007864552
#> bDif -0.001382282 -0.003582653 0.0009761246 0.0007864552 0.0132645725
fitted(fit_mle)
#> [1] 0.48169035 0.75898307 0.82965505 0.25930609 0.74378849 0.32185597
#> [7] 0.54259783 0.44328898 0.74378849 0.75898307 0.78992426 0.71157291
#> [13] 0.48169035 0.50772217 0.69147792 0.38070900 0.57189984 0.71157291
#> [19] 0.48169035 0.36321785 0.44328898 0.80078200 0.82965505 0.78992426
#> [25] 0.63374625 0.50772217 0.75898307 0.50772217 0.71157291 0.30884991
#> [31] 0.50772217 0.65902646 0.74378849 0.36321785 0.48169035 0.54259783
#> [37] 0.63374625 0.78992426 0.50772217 0.60225793 0.30884991 0.50772217
#> [43] 0.50772217 0.74378849 0.74378849 0.48169035 0.36321785 0.50772217
#> [49] 0.25930609 0.54259783 0.54259783 0.30884991 0.17686525 0.54259783
#> [55] 0.36321785 0.57189984 0.36321785 0.54259783 0.54259783 0.54259783
#> [61] 0.86753558 0.63374625 0.36321785 0.25930609 0.65902646 0.69147792
#> [67] 0.25930609 0.69147792 0.11651182 0.89096300 0.44328898 0.25930609
#> [73] 0.48169035 0.57189984 0.50772217 0.25930609 0.65902646 0.26816137
#> [79] 0.36321785 0.50772217 0.54259783 0.57189984 0.25930609 0.38070900
#> [85] 0.50772217 0.65902646 0.32185597 0.38070900 0.48169035 0.69147792
#> [91] 0.32185597 0.71157291 0.48169035 0.71157291 0.30884991 0.25930609
#> [97] 0.42132217 0.78992426 0.30884991 0.83688972 0.91367307 0.54259783
#> [103] 0.54259783 0.63374625 0.42132217 0.22051175 0.74378849 0.74378849
#> [109] 0.63374625 0.17686525 0.65902646 0.48169035 0.42132217 0.78992426
#> [115] 0.36321785 0.57189984 0.36321785 0.82965505 0.25930609 0.48169035
#> [121] 0.75898307 0.48169035 0.30884991 0.78992426 0.30884991 0.50772217
#> [127] 0.30884991 0.26816137 0.30884991 0.32185597 0.48169035 0.44328898
#> [133] 0.44328898 0.78992426 0.42132217 0.42132217 0.17925513 0.60225793
#> [139] 0.69147792 0.78992426 0.42132217 0.21523480 0.32185597 0.74378849
#> [145] 0.50772217 0.63374625 0.86317327 0.69147792 0.25930609 0.36321785
#> [151] 0.30884991 0.25930609 0.63374625 0.48169035 0.78992426 0.38070900
#> [157] 0.25930609 0.86317327 0.89096300 0.42132217 0.44328898 0.54259783
#> [163] 0.86317327 0.17686525 0.44328898 0.48169035 0.63374625 0.86317327
#> [169] 0.30884991 0.74378849 0.32185597 0.63374625 0.60225793 0.57189984
#> [175] 0.69147792 0.44328898 0.48169035 0.75898307 0.82965505 0.21523480
#> [181] 0.42132217 0.82965505 0.86317327 0.80078200 0.60225793 0.50772217
#> [187] 0.82965505 0.38070900 0.14407997 0.69147792 0.36321785 0.50772217
#> [193] 0.69147792 0.17686525 0.86317327 0.57189984 0.57189984 0.63374625
#> [199] 0.74378849 0.48169035 0.36321785 0.57189984 0.26816137 0.74378849
#> [205] 0.82965505 0.69147792 0.69147792 0.48169035 0.74378849 0.42132217
#> [211] 0.60225793 0.42132217 0.26816137 0.54259783 0.21523480 0.32185597
#> [217] 0.69147792 0.74378849 0.89096300 0.69147792 0.60225793 0.42132217
#> [223] 0.42132217 0.69147792 0.42132217 0.44328898 0.69147792 0.50772217
#> [229] 0.57189984 0.54259783 0.38070900 0.86317327 0.82965505 0.38070900
#> [235] 0.78992426 0.69147792 0.57189984 0.89096300 0.36321785 0.86317327
#> [241] 0.69147792 0.65902646 0.63374625 0.48169035 0.50772217 0.36321785
#> [247] 0.48169035 0.57189984 0.60225793 0.36321785 0.78992426 0.50772217
#> [253] 0.74378849 0.63374625 0.60225793 0.60225793 0.63374625 0.48169035
#> [259] 0.71157291 0.74378849 0.11651182 0.65902646 0.38070900 0.30884991
#> [265] 0.63374625 0.57189984 0.78992426 0.48169035 0.75898307 0.17686525
#> [271] 0.48169035 0.63374625 0.74378849 0.38070900 0.86317327 0.36321785
#> [277] 0.54259783 0.21523480 0.38070900 0.54259783 0.30884991 0.69147792
#> [283] 0.57189984 0.44328898 0.60225793 0.75898307 0.50772217 0.74378849
#> [289] 0.89096300 0.44328898 0.44328898 0.30884991 0.36321785 0.57189984
#> [295] 0.48169035 0.78992426 0.60225793 0.50772217 0.60225793 0.78992426
#> [301] 0.60225793 0.42132217 0.38070900 0.26816137 0.63374625 0.86317327
#> [307] 0.74378849 0.86317327 0.44328898 0.42132217 0.63374625 0.30884991
#> [313] 0.48169035 0.54259783 0.83688972 0.74378849 0.54259783 0.65902646
#> [319] 0.57189984 0.36321785 0.30884991 0.54259783 0.69147792 0.09364144
#> [325] 0.65902646 0.69147792 0.38070900 0.74378849 0.69147792 0.17686525
#> [331] 0.36321785 0.42132217 0.48169035 0.30884991 0.82965505 0.50772217
#> [337] 0.57189984 0.48169035 0.63374625 0.42132217 0.63374625 0.60225793
#> [343] 0.74378849 0.69147792 0.50772217 0.50772217 0.48169035 0.44328898
#> [349] 0.78992426 0.30884991 0.21523480 0.78992426 0.57189984 0.63374625
#> [355] 0.32185597 0.78992426 0.54259783 0.30884991 0.32185597 0.44328898
#> [361] 0.75898307 0.30884991 0.54259783 0.32185597 0.82965505 0.48169035
#> [367] 0.38070900 0.36321785 0.30884991 0.60225793 0.38070900 0.54259783
#> [373] 0.25930609 0.44328898 0.57189984 0.36321785 0.17686525 0.69147792
#> [379] 0.50772217 0.74378849 0.78992426 0.54259783 0.44328898 0.57189984
#> [385] 0.63374625 0.89096300 0.50772217 0.93201404 0.38070900 0.14407997
#> [391] 0.36321785 0.42132217 0.71157291 0.54259783 0.50772217 0.42132217
#> [397] 0.44328898 0.80078200 0.80078200 0.78992426 0.26816137 0.36321785
#> [403] 0.48169035 0.78992426 0.86317327 0.42132217 0.54259783 0.60225793
#> [409] 0.48169035 0.80078200 0.65902646 0.48169035 0.74378849 0.44328898
#> [415] 0.57189984 0.21523480 0.54259783 0.32185597 0.44328898 0.14407997
#> [421] 0.36321785 0.65902646 0.48169035 0.48169035 0.54259783 0.38070900
#> [427] 0.65902646 0.65902646 0.54259783 0.50772217 0.42132217 0.48169035
#> [433] 0.50772217 0.78992426 0.36321785 0.75898307 0.74378849 0.30884991
#> [439] 0.26816137 0.54259783 0.60225793 0.54259783 0.69147792 0.25930609
#> [445] 0.36321785 0.74378849 0.65902646 0.65902646 0.21523480 0.36321785
#> [451] 0.60225793 0.17686525 0.80078200 0.54259783 0.50772217 0.71157291
#> [457] 0.54259783 0.60225793 0.36321785 0.69147792 0.54259783 0.60225793
#> [463] 0.71157291 0.74378849 0.22051175 0.30884991 0.54259783 0.69147792
#> [469] 0.60225793 0.65902646 0.57189984 0.63374625 0.36321785 0.50772217
#> [475] 0.74378849 0.69147792 0.38070900 0.54259783 0.54259783 0.69147792
#> [481] 0.78992426 0.60225793 0.74378849 0.69147792 0.50772217 0.36321785
#> [487] 0.74378849 0.63374625 0.48169035 0.65902646 0.69147792 0.25930609
#> [493] 0.25930609 0.36321785 0.50772217 0.21523480 0.32185597 0.60225793
#> [499] 0.50772217 0.75898307 0.78992426 0.26816137 0.42132217 0.36321785
#> [505] 0.50772217 0.44328898 0.36321785 0.48169035 0.36321785 0.36321785
#> [511] 0.36321785 0.17925513 0.22051175 0.63374625 0.71157291 0.32185597
#> [517] 0.42132217 0.44328898 0.30884991 0.54259783 0.57189984 0.54259783
#> [523] 0.86753558 0.75898307 0.54259783 0.65902646 0.82965505 0.60225793
#> [529] 0.30884991 0.78992426 0.78992426 0.60225793 0.42132217 0.44328898
#> [535] 0.36321785 0.63374625 0.63374625 0.69147792 0.50772217 0.54259783
#> [541] 0.30884991 0.42132217 0.65902646 0.38070900 0.50772217 0.69147792
#> [547] 0.54259783 0.48169035 0.42132217 0.25930609 0.48169035 0.25930609
#> [553] 0.69147792 0.48169035 0.38070900 0.48169035 0.65902646 0.30884991
#> [559] 0.63374625 0.54259783 0.78992426 0.26816137 0.50772217 0.74378849
#> [565] 0.48169035 0.60225793 0.30884991 0.69147792 0.86317327 0.44328898
#> [571] 0.50772217 0.71157291 0.42132217 0.48169035 0.50772217 0.54259783
#> [577] 0.42132217 0.69147792 0.17686525 0.42132217 0.44328898 0.21523480
#> [583] 0.50772217 0.50772217 0.54259783 0.30884991 0.48169035 0.14407997
#> [589] 0.74378849 0.48169035 0.82965505 0.22051175 0.38070900 0.57189984
#> [595] 0.50772217 0.50772217 0.48169035 0.25930609 0.60225793 0.63374625
#> [601] 0.30884991 0.26816137 0.42132217 0.30884991 0.36321785 0.69147792
#> [607] 0.78992426 0.69147792 0.75898307 0.60225793 0.63374625 0.60225793
#> [613] 0.57189984 0.75898307 0.48169035 0.14407997 0.50772217 0.14407997
#> [619] 0.69147792 0.32185597 0.48169035 0.21523480 0.48169035 0.48169035
#> [625] 0.42132217 0.21523480 0.74378849 0.44328898 0.82965505 0.69147792
#> [631] 0.25930609 0.63374625 0.57189984 0.74378849 0.69147792 0.78992426
#> [637] 0.63374625 0.69147792 0.57189984 0.82965505 0.44328898 0.57189984
#> [643] 0.57189984 0.60225793 0.25930609 0.38070900 0.36321785 0.38070900
#> [649] 0.44328898 0.50772217 0.83688972 0.44328898 0.69147792 0.69147792
#> [655] 0.63374625 0.48169035 0.74378849 0.69147792 0.21523480 0.69147792
#> [661] 0.36321785 0.74378849 0.30884991 0.36321785 0.36321785 0.93201404
#> [667] 0.57189984 0.63374625 0.32185597 0.25930609 0.42132217 0.60225793
#> [673] 0.48169035 0.36321785 0.69147792 0.60225793 0.21523480 0.48169035
#> [679] 0.36321785 0.48169035 0.17686525 0.44328898 0.36321785 0.14407997
#> [685] 0.63374625 0.82965505 0.48169035 0.80078200 0.36321785 0.42132217
#> [691] 0.78992426 0.54259783 0.50772217 0.54259783 0.26816137 0.74378849
#> [697] 0.74378849 0.50772217 0.30884991 0.74378849 0.26816137 0.30884991
#> [703] 0.86317327 0.30884991 0.42132217 0.32185597 0.74378849 0.44328898
#> [709] 0.44328898 0.36321785 0.14407997 0.82965505 0.74378849 0.57189984
#> [715] 0.54259783 0.54259783 0.57189984 0.21523480 0.36321785 0.50772217
#> [721] 0.54259783 0.44328898 0.50772217 0.57189984 0.78992426 0.71157291
#> [727] 0.21523480 0.42132217 0.54259783 0.63374625 0.42132217 0.69147792
#> [733] 0.57189984 0.42132217 0.65902646 0.42132217 0.69147792 0.25930609
#> [739] 0.38070900 0.80078200 0.54259783 0.60225793 0.80078200 0.69147792
#> [745] 0.36321785 0.54259783 0.26816137 0.82965505 0.71157291 0.32185597
#> [751] 0.71157291 0.60225793 0.60225793 0.63374625 0.50772217 0.69147792
#> [757] 0.44328898 0.42132217 0.63374625 0.89096300 0.25930609 0.42132217
#> [763] 0.65902646 0.17686525 0.30884991 0.36321785 0.50772217 0.57189984
#> [769] 0.50772217 0.38070900 0.38070900 0.82965505 0.69147792 0.54259783
#> [775] 0.36321785 0.38070900 0.65902646 0.69147792 0.42132217 0.78992426
#> [781] 0.63374625 0.38070900 0.74378849 0.42132217 0.44328898 0.36321785
#> [787] 0.30884991 0.50772217 0.50772217 0.60225793 0.32185597 0.78992426
#> [793] 0.50772217 0.69147792 0.21523480 0.50772217 0.48169035 0.57189984
#> [799] 0.38070900 0.30884991 0.57189984 0.57189984 0.74378849 0.80078200
#> [805] 0.71157291 0.69147792 0.36321785 0.44328898 0.30884991 0.80078200
#> [811] 0.78992426 0.54259783 0.71157291 0.74378849 0.30884991 0.44328898
#> [817] 0.25930609 0.54259783 0.48169035 0.21523480 0.74378849 0.69147792
#> [823] 0.74378849 0.82965505 0.82965505 0.42132217 0.44328898 0.21523480
#> [829] 0.50772217 0.48169035 0.25930609 0.26816137 0.54259783 0.54259783
#> [835] 0.36321785 0.25930609 0.48169035 0.38070900 0.78992426 0.60225793
#> [841] 0.63374625 0.44328898 0.69147792 0.32185597 0.60225793 0.42132217
#> [847] 0.30884991 0.30884991 0.69147792 0.17686525 0.50772217 0.44328898
#> [853] 0.57189984 0.26816137 0.57189984 0.42132217 0.54259783 0.57189984
#> [859] 0.54259783 0.69147792 0.54259783 0.69147792 0.65902646 0.75898307
#> [865] 0.48169035 0.60225793 0.80078200 0.54259783 0.57189984 0.30884991
#> [871] 0.57189984 0.82965505 0.63374625 0.42132217 0.86317327 0.69147792
#> [877] 0.57189984 0.38070900 0.48169035 0.65902646 0.42132217 0.21523480
#> [883] 0.50772217 0.82965505 0.57189984 0.48169035 0.63374625 0.57189984
#> [889] 0.42132217 0.74378849 0.44328898 0.21523480 0.44328898 0.65902646
#> [895] 0.60225793 0.48169035 0.36321785 0.80078200 0.65902646 0.63374625
#> [901] 0.57189984 0.36321785 0.75898307 0.36321785 0.69147792 0.30884991
#> [907] 0.69147792 0.60225793 0.36321785 0.74378849 0.63374625 0.42132217
#> [913] 0.60225793 0.57189984 0.42132217 0.74378849 0.42132217 0.48169035
#> [919] 0.60225793 0.82965505 0.60225793 0.38070900 0.44328898 0.50772217
#> [925] 0.63374625 0.21523480 0.57189984 0.60225793 0.50772217 0.60225793
#> [931] 0.69147792 0.75898307 0.57189984 0.44328898 0.57189984 0.42132217
#> [937] 0.60225793 0.71157291 0.21523480 0.69147792 0.54259783 0.44328898
#> [943] 0.42132217 0.82965505 0.36321785 0.60225793 0.21523480 0.26816137
#> [949] 0.57189984 0.50772217 0.60225793 0.54259783 0.42132217 0.82965505
#> [955] 0.63374625 0.21523480 0.50772217 0.54259783 0.25930609 0.78992426
#> [961] 0.75898307 0.30884991 0.21523480 0.63374625 0.25930609 0.25930609
#> [967] 0.48169035 0.65902646 0.48169035 0.30884991 0.42132217 0.17686525
#> [973] 0.57189984 0.71157291 0.42132217 0.63374625 0.71157291 0.71157291
#> [979] 0.63374625 0.69147792 0.65902646 0.86317327 0.57189984 0.74378849
#> [985] 0.25930609 0.63374625 0.57189984 0.30884991 0.54259783 0.60225793
#> [991] 0.09364144 0.60225793 0.54259783 0.42132217 0.69147792 0.38070900
#> [997] 0.86317327 0.42132217 0.82965505 0.63374625
#> [ reached 'max' / getOption("max.print") -- omitted 1000 entries ]
#> attr(,"label")
#> [1] "Fitted values"
residuals(fit_mle)
#> [1] -0.48169035 0.24101693 0.17034495 -0.25930609 0.25621151 -0.32185597
#> [7] 0.45740217 0.55671102 0.25621151 0.24101693 0.21007574 0.28842709
#> [13] -0.48169035 -0.50772217 -0.69147792 -0.38070900 0.42810016 0.28842709
#> [19] -0.48169035 -0.36321785 0.55671102 0.19921800 0.17034495 0.21007574
#> [25] 0.36625375 0.49227783 0.24101693 -0.50772217 0.28842709 -0.30884991
#> [31] -0.50772217 -0.65902646 -0.74378849 -0.36321785 0.51830965 -0.54259783
#> [37] -0.63374625 0.21007574 0.49227783 -0.60225793 -0.30884991 0.49227783
#> [43] -0.50772217 0.25621151 0.25621151 -0.48169035 -0.36321785 0.49227783
#> [49] 0.74069391 -0.54259783 0.45740217 -0.30884991 0.82313475 -0.54259783
#> [55] 0.63678215 0.42810016 -0.36321785 0.45740217 -0.54259783 0.45740217
#> [61] 0.13246442 -0.63374625 0.63678215 -0.25930609 0.34097354 -0.69147792
#> [67] -0.25930609 0.30852208 -0.11651182 0.10903700 -0.44328898 -0.25930609
#> [73] 0.51830965 0.42810016 -0.50772217 0.74069391 0.34097354 -0.26816137
#> [79] -0.36321785 0.49227783 0.45740217 -0.57189984 -0.25930609 -0.38070900
#> [85] -0.50772217 -0.65902646 0.67814403 -0.38070900 -0.48169035 -0.69147792
#> [91] -0.32185597 0.28842709 -0.48169035 0.28842709 0.69115009 -0.25930609
#> [97] 0.57867783 0.21007574 -0.30884991 0.16311028 0.08632693 0.45740217
#> [103] 0.45740217 0.36625375 -0.42132217 -0.22051175 0.25621151 -0.74378849
#> [109] 0.36625375 -0.17686525 0.34097354 -0.48169035 0.57867783 0.21007574
#> [115] -0.36321785 -0.57189984 0.63678215 0.17034495 -0.25930609 0.51830965
#> [121] 0.24101693 -0.48169035 -0.30884991 0.21007574 -0.30884991 0.49227783
#> [127] 0.69115009 -0.26816137 -0.30884991 -0.32185597 0.51830965 -0.44328898
#> [133] -0.44328898 0.21007574 -0.42132217 -0.42132217 -0.17925513 0.39774207
#> [139] 0.30852208 0.21007574 -0.42132217 0.78476520 -0.32185597 0.25621151
#> [145] 0.49227783 -0.63374625 0.13682673 0.30852208 -0.25930609 0.63678215
#> [151] -0.30884991 -0.25930609 0.36625375 -0.48169035 0.21007574 -0.38070900
#> [157] -0.25930609 0.13682673 0.10903700 0.57867783 0.55671102 0.45740217
#> [163] -0.86317327 -0.17686525 0.55671102 -0.48169035 0.36625375 -0.86317327
#> [169] -0.30884991 0.25621151 -0.32185597 0.36625375 -0.60225793 0.42810016
#> [175] -0.69147792 0.55671102 -0.48169035 0.24101693 0.17034495 -0.21523480
#> [181] 0.57867783 0.17034495 0.13682673 0.19921800 -0.60225793 -0.50772217
#> [187] 0.17034495 -0.38070900 -0.14407997 0.30852208 -0.36321785 0.49227783
#> [193] 0.30852208 -0.17686525 0.13682673 0.42810016 -0.57189984 -0.63374625
#> [199] 0.25621151 0.51830965 -0.36321785 0.42810016 -0.26816137 0.25621151
#> [205] 0.17034495 -0.69147792 0.30852208 -0.48169035 0.25621151 -0.42132217
#> [211] -0.60225793 0.57867783 0.73183863 -0.54259783 -0.21523480 -0.32185597
#> [217] 0.30852208 0.25621151 0.10903700 0.30852208 0.39774207 -0.42132217
#> [223] -0.42132217 -0.69147792 -0.42132217 0.55671102 0.30852208 0.49227783
#> [229] 0.42810016 -0.54259783 0.61929100 0.13682673 0.17034495 0.61929100
#> [235] 0.21007574 -0.69147792 0.42810016 -0.89096300 -0.36321785 0.13682673
#> [241] 0.30852208 -0.65902646 0.36625375 0.51830965 0.49227783 -0.36321785
#> [247] -0.48169035 -0.57189984 0.39774207 -0.36321785 0.21007574 0.49227783
#> [253] 0.25621151 -0.63374625 -0.60225793 -0.60225793 0.36625375 0.51830965
#> [259] 0.28842709 0.25621151 -0.11651182 0.34097354 -0.38070900 -0.30884991
#> [265] 0.36625375 -0.57189984 0.21007574 -0.48169035 0.24101693 -0.17686525
#> [271] -0.48169035 -0.63374625 0.25621151 -0.38070900 0.13682673 -0.36321785
#> [277] -0.54259783 -0.21523480 0.61929100 -0.54259783 -0.30884991 0.30852208
#> [283] 0.42810016 -0.44328898 -0.60225793 -0.75898307 0.49227783 -0.74378849
#> [289] 0.10903700 -0.44328898 -0.44328898 -0.30884991 0.63678215 -0.57189984
#> [295] 0.51830965 0.21007574 0.39774207 -0.50772217 0.39774207 0.21007574
#> [301] 0.39774207 -0.42132217 -0.38070900 -0.26816137 -0.63374625 0.13682673
#> [307] 0.25621151 0.13682673 0.55671102 -0.42132217 -0.63374625 -0.30884991
#> [313] -0.48169035 -0.54259783 0.16311028 0.25621151 -0.54259783 -0.65902646
#> [319] 0.42810016 -0.36321785 0.69115009 0.45740217 0.30852208 -0.09364144
#> [325] 0.34097354 0.30852208 -0.38070900 0.25621151 0.30852208 -0.17686525
#> [331] -0.36321785 -0.42132217 -0.48169035 0.69115009 0.17034495 0.49227783
#> [337] -0.57189984 0.51830965 0.36625375 -0.42132217 -0.63374625 0.39774207
#> [343] 0.25621151 -0.69147792 0.49227783 0.49227783 0.51830965 0.55671102
#> [349] 0.21007574 -0.30884991 -0.21523480 0.21007574 -0.57189984 0.36625375
#> [355] -0.32185597 0.21007574 -0.54259783 -0.30884991 -0.32185597 0.55671102
#> [361] 0.24101693 0.69115009 -0.54259783 -0.32185597 0.17034495 -0.48169035
#> [367] -0.38070900 -0.36321785 -0.30884991 -0.60225793 -0.38070900 -0.54259783
#> [373] 0.74069391 -0.44328898 0.42810016 0.63678215 -0.17686525 -0.69147792
#> [379] 0.49227783 0.25621151 0.21007574 -0.54259783 0.55671102 -0.57189984
#> [385] -0.63374625 0.10903700 -0.50772217 0.06798596 -0.38070900 -0.14407997
#> [391] -0.36321785 -0.42132217 0.28842709 -0.54259783 -0.50772217 0.57867783
#> [397] -0.44328898 0.19921800 -0.80078200 0.21007574 -0.26816137 -0.36321785
#> [403] -0.48169035 -0.78992426 0.13682673 -0.42132217 0.45740217 0.39774207
#> [409] 0.51830965 0.19921800 0.34097354 0.51830965 0.25621151 -0.44328898
#> [415] -0.57189984 -0.21523480 0.45740217 -0.32185597 0.55671102 0.85592003
#> [421] -0.36321785 0.34097354 -0.48169035 -0.48169035 0.45740217 -0.38070900
#> [427] -0.65902646 0.34097354 -0.54259783 0.49227783 -0.42132217 0.51830965
#> [433] 0.49227783 0.21007574 -0.36321785 0.24101693 0.25621151 0.69115009
#> [439] 0.73183863 -0.54259783 0.39774207 0.45740217 0.30852208 -0.25930609
#> [445] -0.36321785 0.25621151 -0.65902646 -0.65902646 -0.21523480 -0.36321785
#> [451] 0.39774207 -0.17686525 0.19921800 0.45740217 0.49227783 0.28842709
#> [457] 0.45740217 0.39774207 0.63678215 0.30852208 0.45740217 0.39774207
#> [463] -0.71157291 -0.74378849 0.77948825 0.69115009 -0.54259783 0.30852208
#> [469] -0.60225793 0.34097354 -0.57189984 0.36625375 -0.36321785 -0.50772217
#> [475] 0.25621151 0.30852208 -0.38070900 -0.54259783 -0.54259783 0.30852208
#> [481] 0.21007574 -0.60225793 0.25621151 0.30852208 0.49227783 -0.36321785
#> [487] 0.25621151 -0.63374625 -0.48169035 0.34097354 -0.69147792 -0.25930609
#> [493] 0.74069391 -0.36321785 -0.50772217 0.78476520 0.67814403 0.39774207
#> [499] -0.50772217 0.24101693 -0.78992426 -0.26816137 -0.42132217 0.63678215
#> [505] -0.50772217 0.55671102 0.63678215 -0.48169035 0.63678215 0.63678215
#> [511] -0.36321785 -0.17925513 -0.22051175 0.36625375 -0.71157291 -0.32185597
#> [517] -0.42132217 0.55671102 -0.30884991 0.45740217 0.42810016 0.45740217
#> [523] 0.13246442 -0.75898307 0.45740217 0.34097354 0.17034495 -0.60225793
#> [529] -0.30884991 -0.78992426 0.21007574 -0.60225793 -0.42132217 0.55671102
#> [535] 0.63678215 0.36625375 0.36625375 0.30852208 0.49227783 0.45740217
#> [541] -0.30884991 -0.42132217 0.34097354 -0.38070900 0.49227783 0.30852208
#> [547] -0.54259783 -0.48169035 -0.42132217 0.74069391 -0.48169035 -0.25930609
#> [553] 0.30852208 0.51830965 0.61929100 -0.48169035 0.34097354 -0.30884991
#> [559] 0.36625375 0.45740217 0.21007574 -0.26816137 0.49227783 0.25621151
#> [565] 0.51830965 0.39774207 -0.30884991 -0.69147792 0.13682673 0.55671102
#> [571] -0.50772217 -0.71157291 -0.42132217 0.51830965 0.49227783 -0.54259783
#> [577] -0.42132217 0.30852208 0.82313475 -0.42132217 0.55671102 -0.21523480
#> [583] 0.49227783 -0.50772217 0.45740217 -0.30884991 -0.48169035 -0.14407997
#> [589] -0.74378849 0.51830965 0.17034495 -0.22051175 0.61929100 0.42810016
#> [595] -0.50772217 0.49227783 0.51830965 -0.25930609 0.39774207 -0.63374625
#> [601] 0.69115009 -0.26816137 0.57867783 0.69115009 -0.36321785 0.30852208
#> [607] -0.78992426 -0.69147792 0.24101693 0.39774207 0.36625375 -0.60225793
#> [613] -0.57189984 0.24101693 0.51830965 -0.14407997 -0.50772217 -0.14407997
#> [619] -0.69147792 -0.32185597 -0.48169035 0.78476520 -0.48169035 -0.48169035
#> [625] -0.42132217 -0.21523480 -0.74378849 0.55671102 0.17034495 0.30852208
#> [631] -0.25930609 -0.63374625 0.42810016 0.25621151 0.30852208 0.21007574
#> [637] 0.36625375 0.30852208 0.42810016 0.17034495 -0.44328898 -0.57189984
#> [643] 0.42810016 -0.60225793 0.74069391 -0.38070900 0.63678215 0.61929100
#> [649] -0.44328898 0.49227783 -0.83688972 -0.44328898 0.30852208 0.30852208
#> [655] -0.63374625 -0.48169035 -0.74378849 0.30852208 -0.21523480 0.30852208
#> [661] -0.36321785 0.25621151 -0.30884991 -0.36321785 0.63678215 0.06798596
#> [667] -0.57189984 0.36625375 0.67814403 -0.25930609 -0.42132217 0.39774207
#> [673] -0.48169035 -0.36321785 0.30852208 -0.60225793 -0.21523480 -0.48169035
#> [679] -0.36321785 0.51830965 -0.17686525 -0.44328898 -0.36321785 -0.14407997
#> [685] 0.36625375 -0.82965505 -0.48169035 0.19921800 -0.36321785 0.57867783
#> [691] 0.21007574 -0.54259783 0.49227783 -0.54259783 -0.26816137 0.25621151
#> [697] 0.25621151 0.49227783 0.69115009 0.25621151 0.73183863 0.69115009
#> [703] 0.13682673 -0.30884991 0.57867783 0.67814403 -0.74378849 -0.44328898
#> [709] 0.55671102 0.63678215 0.85592003 0.17034495 0.25621151 0.42810016
#> [715] -0.54259783 -0.54259783 0.42810016 -0.21523480 -0.36321785 -0.50772217
#> [721] 0.45740217 0.55671102 -0.50772217 -0.57189984 -0.78992426 -0.71157291
#> [727] -0.21523480 -0.42132217 -0.54259783 0.36625375 -0.42132217 -0.69147792
#> [733] -0.57189984 0.57867783 -0.65902646 0.57867783 0.30852208 -0.25930609
#> [739] -0.38070900 0.19921800 -0.54259783 -0.60225793 0.19921800 0.30852208
#> [745] -0.36321785 0.45740217 -0.26816137 -0.82965505 0.28842709 -0.32185597
#> [751] 0.28842709 -0.60225793 -0.60225793 0.36625375 -0.50772217 0.30852208
#> [757] -0.44328898 0.57867783 -0.63374625 0.10903700 -0.25930609 0.57867783
#> [763] 0.34097354 -0.17686525 0.69115009 -0.36321785 -0.50772217 -0.57189984
#> [769] -0.50772217 -0.38070900 -0.38070900 0.17034495 0.30852208 -0.54259783
#> [775] -0.36321785 -0.38070900 0.34097354 0.30852208 -0.42132217 0.21007574
#> [781] 0.36625375 0.61929100 0.25621151 -0.42132217 -0.44328898 0.63678215
#> [787] -0.30884991 0.49227783 0.49227783 0.39774207 0.67814403 0.21007574
#> [793] -0.50772217 0.30852208 -0.21523480 0.49227783 0.51830965 -0.57189984
#> [799] -0.38070900 -0.30884991 0.42810016 -0.57189984 0.25621151 0.19921800
#> [805] 0.28842709 -0.69147792 -0.36321785 -0.44328898 -0.30884991 0.19921800
#> [811] 0.21007574 -0.54259783 -0.71157291 0.25621151 -0.30884991 -0.44328898
#> [817] -0.25930609 -0.54259783 -0.48169035 -0.21523480 -0.74378849 0.30852208
#> [823] 0.25621151 0.17034495 0.17034495 0.57867783 0.55671102 -0.21523480
#> [829] -0.50772217 -0.48169035 -0.25930609 -0.26816137 -0.54259783 0.45740217
#> [835] -0.36321785 -0.25930609 0.51830965 -0.38070900 -0.78992426 0.39774207
#> [841] 0.36625375 0.55671102 -0.69147792 -0.32185597 -0.60225793 -0.42132217
#> [847] -0.30884991 -0.30884991 0.30852208 -0.17686525 -0.50772217 0.55671102
#> [853] -0.57189984 -0.26816137 0.42810016 -0.42132217 -0.54259783 0.42810016
#> [859] 0.45740217 -0.69147792 0.45740217 0.30852208 -0.65902646 0.24101693
#> [865] 0.51830965 -0.60225793 0.19921800 0.45740217 0.42810016 -0.30884991
#> [871] 0.42810016 0.17034495 0.36625375 0.57867783 0.13682673 0.30852208
#> [877] 0.42810016 0.61929100 0.51830965 0.34097354 -0.42132217 -0.21523480
#> [883] 0.49227783 0.17034495 0.42810016 0.51830965 0.36625375 0.42810016
#> [889] -0.42132217 0.25621151 0.55671102 -0.21523480 0.55671102 0.34097354
#> [895] 0.39774207 0.51830965 -0.36321785 0.19921800 -0.65902646 0.36625375
#> [901] -0.57189984 -0.36321785 0.24101693 0.63678215 0.30852208 -0.30884991
#> [907] 0.30852208 0.39774207 0.63678215 0.25621151 0.36625375 -0.42132217
#> [913] -0.60225793 0.42810016 -0.42132217 0.25621151 0.57867783 0.51830965
#> [919] 0.39774207 0.17034495 -0.60225793 0.61929100 -0.44328898 -0.50772217
#> [925] 0.36625375 -0.21523480 0.42810016 0.39774207 0.49227783 -0.60225793
#> [931] 0.30852208 0.24101693 0.42810016 -0.44328898 -0.57189984 -0.42132217
#> [937] -0.60225793 -0.71157291 -0.21523480 -0.69147792 -0.54259783 -0.44328898
#> [943] -0.42132217 0.17034495 -0.36321785 -0.60225793 -0.21523480 -0.26816137
#> [949] 0.42810016 0.49227783 0.39774207 0.45740217 -0.42132217 0.17034495
#> [955] 0.36625375 0.78476520 -0.50772217 -0.54259783 0.74069391 0.21007574
#> [961] 0.24101693 -0.30884991 0.78476520 -0.63374625 -0.25930609 -0.25930609
#> [967] -0.48169035 0.34097354 0.51830965 0.69115009 0.57867783 -0.17686525
#> [973] -0.57189984 -0.71157291 -0.42132217 0.36625375 -0.71157291 0.28842709
#> [979] 0.36625375 -0.69147792 0.34097354 0.13682673 -0.57189984 -0.74378849
#> [985] 0.74069391 -0.63374625 -0.57189984 -0.30884991 0.45740217 0.39774207
#> [991] -0.09364144 0.39774207 0.45740217 -0.42132217 0.30852208 -0.38070900
#> [997] -0.86317327 -0.42132217 0.17034495 0.36625375
#> [ reached 'max' / getOption("max.print") -- omitted 1000 entries ]
#> attr(,"label")
#> [1] "Residuals"
# formula for 3PL model with the same guessing for both groups
# intercept-slope parameterization
M <- formulaNLR(model = "3PLcg", type = "both", parameterization = "is")
# starting values for 3PL model with the same guessing for item 1,
start <- startNLR(GMAT[, 1:20], group, model = "3PLcg", parameterization = "is")
start <- start[[1]][M$M1$parameters]
# EM algorithm
(fit_em <- estimNLR(
y = y, match = match, group = group,
formula = M$M1$formula, method = "em",
lower = M$M1$lower, upper = M$M1$upper, start = start
))
#> Nonlinear regression model
#>
#> Model: y ~ c + (1 - c)/(1 + exp(-(b0 + b1 * x + b2 * g + b3 * x * g)))
#>
#> Coefficients:
#> b0 b1 b2 b3 c
#> 0.5503 0.9941 -0.8388 -0.1536 0.0000
#>
#> Maximum likelihood estimation using the EM algorithm
#> Converged after 2 iterations
coef(fit_em)
#> b0 b1 b2 b3 c
#> 0.5503440 0.9940975 -0.8387766 -0.1535927 0.0000000
logLik(fit_em)
#> 'log Lik.' -1192.331 (df=5)
vcov(fit_em)
#> b0 b1 b2 b3 c
#> b0 0.08658573 -0.036631987 0.04091179 -0.034224858 -0.04507052
#> b1 -0.03663199 0.024578025 -0.02262850 0.008356037 0.02094865
#> b2 0.04091179 -0.022628503 0.03622273 -0.018122854 -0.02559373
#> b3 -0.03422486 0.008356037 -0.01812285 0.026512557 0.01832306
#> c -0.04507052 0.020948650 -0.02559373 0.018323057 0.02497989
fitted(fit_em)
#> [1] 0.45487411 0.76352613 0.87628488 0.22037531 0.78877573 0.28435576
#> [7] 0.52239129 0.42976528 0.78877573 0.76352613 0.83721296 0.71125529
#> [13] 0.45487411 0.50931523 0.73056430 0.35368440 0.58839620 0.71125529
#> [19] 0.45487411 0.32690028 0.42976528 0.80887717 0.87628488 0.83721296
#> [25] 0.66316115 0.50931523 0.76352613 0.50931523 0.71125529 0.27034765
#> [31] 0.50931523 0.65268611 0.78877573 0.32690028 0.45487411 0.52239129
#> [37] 0.66316115 0.83721296 0.50931523 0.58910004 0.27034765 0.50931523
#> [43] 0.50931523 0.78877573 0.78877573 0.45487411 0.32690028 0.50931523
#> [49] 0.22037531 0.52239129 0.52239129 0.27034765 0.14127713 0.52239129
#> [55] 0.32690028 0.58839620 0.32690028 0.52239129 0.52239129 0.52239129
#> [61] 0.87910405 0.66316115 0.32690028 0.22037531 0.65268611 0.73056430
#> [67] 0.22037531 0.73056430 0.08738702 0.93072359 0.42976528 0.22037531
#> [73] 0.45487411 0.58839620 0.50931523 0.22037531 0.65268611 0.22390881
#> [79] 0.32690028 0.50931523 0.52239129 0.58839620 0.22037531 0.35368440
#> [85] 0.50931523 0.65268611 0.28435576 0.35368440 0.45487411 0.73056430
#> [91] 0.28435576 0.71125529 0.45487411 0.71125529 0.27034765 0.22037531
#> [97] 0.38897634 0.83721296 0.27034765 0.84727053 0.94872579 0.52239129
#> [103] 0.52239129 0.66316115 0.38897634 0.17320152 0.78877573 0.78877573
#> [109] 0.66316115 0.14127713 0.65268611 0.45487411 0.38897634 0.83721296
#> [115] 0.32690028 0.58839620 0.32690028 0.87628488 0.22037531 0.45487411
#> [121] 0.76352613 0.45487411 0.27034765 0.83721296 0.27034765 0.50931523
#> [127] 0.27034765 0.22390881 0.27034765 0.28435576 0.45487411 0.42976528
#> [133] 0.42976528 0.83721296 0.38897634 0.38897634 0.13202412 0.58910004
#> [139] 0.73056430 0.83721296 0.38897634 0.17739435 0.28435576 0.78877573
#> [145] 0.50931523 0.66316115 0.90702032 0.73056430 0.22037531 0.32690028
#> [151] 0.27034765 0.22037531 0.66316115 0.45487411 0.83721296 0.35368440
#> [157] 0.22037531 0.90702032 0.93072359 0.38897634 0.42976528 0.52239129
#> [163] 0.90702032 0.14127713 0.42976528 0.45487411 0.66316115 0.90702032
#> [169] 0.27034765 0.78877573 0.28435576 0.66316115 0.58910004 0.58839620
#> [175] 0.73056430 0.42976528 0.45487411 0.76352613 0.87628488 0.17739435
#> [181] 0.38897634 0.87628488 0.90702032 0.80887717 0.58910004 0.50931523
#> [187] 0.87628488 0.35368440 0.11151645 0.73056430 0.32690028 0.50931523
#> [193] 0.73056430 0.14127713 0.90702032 0.58839620 0.58839620 0.66316115
#> [199] 0.78877573 0.45487411 0.32690028 0.58839620 0.22390881 0.78877573
#> [205] 0.87628488 0.73056430 0.73056430 0.45487411 0.78877573 0.38897634
#> [211] 0.58910004 0.38897634 0.22390881 0.52239129 0.17739435 0.28435576
#> [217] 0.73056430 0.78877573 0.93072359 0.73056430 0.58910004 0.38897634
#> [223] 0.38897634 0.73056430 0.38897634 0.42976528 0.73056430 0.50931523
#> [229] 0.58839620 0.52239129 0.35368440 0.90702032 0.87628488 0.35368440
#> [235] 0.83721296 0.73056430 0.58839620 0.93072359 0.32690028 0.90702032
#> [241] 0.73056430 0.65268611 0.66316115 0.45487411 0.50931523 0.32690028
#> [247] 0.45487411 0.58839620 0.58910004 0.32690028 0.83721296 0.50931523
#> [253] 0.78877573 0.66316115 0.58910004 0.58910004 0.66316115 0.45487411
#> [259] 0.71125529 0.78877573 0.08738702 0.65268611 0.35368440 0.27034765
#> [265] 0.66316115 0.58839620 0.83721296 0.45487411 0.76352613 0.14127713
#> [271] 0.45487411 0.66316115 0.78877573 0.35368440 0.90702032 0.32690028
#> [277] 0.52239129 0.17739435 0.35368440 0.52239129 0.27034765 0.73056430
#> [283] 0.58839620 0.42976528 0.58910004 0.76352613 0.50931523 0.78877573
#> [289] 0.93072359 0.42976528 0.42976528 0.27034765 0.32690028 0.58839620
#> [295] 0.45487411 0.83721296 0.58910004 0.50931523 0.58910004 0.83721296
#> [301] 0.58910004 0.38897634 0.35368440 0.22390881 0.66316115 0.90702032
#> [307] 0.78877573 0.90702032 0.42976528 0.38897634 0.66316115 0.27034765
#> [313] 0.45487411 0.52239129 0.84727053 0.78877573 0.52239129 0.65268611
#> [319] 0.58839620 0.32690028 0.27034765 0.52239129 0.73056430 0.06807856
#> [325] 0.65268611 0.73056430 0.35368440 0.78877573 0.73056430 0.14127713
#> [331] 0.32690028 0.38897634 0.45487411 0.27034765 0.87628488 0.50931523
#> [337] 0.58839620 0.45487411 0.66316115 0.38897634 0.66316115 0.58910004
#> [343] 0.78877573 0.73056430 0.50931523 0.50931523 0.45487411 0.42976528
#> [349] 0.83721296 0.27034765 0.17739435 0.83721296 0.58839620 0.66316115
#> [355] 0.28435576 0.83721296 0.52239129 0.27034765 0.28435576 0.42976528
#> [361] 0.76352613 0.27034765 0.52239129 0.28435576 0.87628488 0.45487411
#> [367] 0.35368440 0.32690028 0.27034765 0.58910004 0.35368440 0.52239129
#> [373] 0.22037531 0.42976528 0.58839620 0.32690028 0.14127713 0.73056430
#> [379] 0.50931523 0.78877573 0.83721296 0.52239129 0.42976528 0.58839620
#> [385] 0.66316115 0.93072359 0.50931523 0.96223973 0.35368440 0.11151645
#> [391] 0.32690028 0.38897634 0.71125529 0.52239129 0.50931523 0.38897634
#> [397] 0.42976528 0.80887717 0.80887717 0.83721296 0.22390881 0.32690028
#> [403] 0.45487411 0.83721296 0.90702032 0.38897634 0.52239129 0.58910004
#> [409] 0.45487411 0.80887717 0.65268611 0.45487411 0.78877573 0.42976528
#> [415] 0.58839620 0.17739435 0.52239129 0.28435576 0.42976528 0.11151645
#> [421] 0.32690028 0.65268611 0.45487411 0.45487411 0.52239129 0.35368440
#> [427] 0.65268611 0.65268611 0.52239129 0.50931523 0.38897634 0.45487411
#> [433] 0.50931523 0.83721296 0.32690028 0.76352613 0.78877573 0.27034765
#> [439] 0.22390881 0.52239129 0.58910004 0.52239129 0.73056430 0.22037531
#> [445] 0.32690028 0.78877573 0.65268611 0.65268611 0.17739435 0.32690028
#> [451] 0.58910004 0.14127713 0.80887717 0.52239129 0.50931523 0.71125529
#> [457] 0.52239129 0.58910004 0.32690028 0.73056430 0.52239129 0.58910004
#> [463] 0.71125529 0.78877573 0.17320152 0.27034765 0.52239129 0.73056430
#> [469] 0.58910004 0.65268611 0.58839620 0.66316115 0.32690028 0.50931523
#> [475] 0.78877573 0.73056430 0.35368440 0.52239129 0.52239129 0.73056430
#> [481] 0.83721296 0.58910004 0.78877573 0.73056430 0.50931523 0.32690028
#> [487] 0.78877573 0.66316115 0.45487411 0.65268611 0.73056430 0.22037531
#> [493] 0.22037531 0.32690028 0.50931523 0.17739435 0.28435576 0.58910004
#> [499] 0.50931523 0.76352613 0.83721296 0.22390881 0.38897634 0.32690028
#> [505] 0.50931523 0.42976528 0.32690028 0.45487411 0.32690028 0.32690028
#> [511] 0.32690028 0.13202412 0.17320152 0.66316115 0.71125529 0.28435576
#> [517] 0.38897634 0.42976528 0.27034765 0.52239129 0.58839620 0.52239129
#> [523] 0.87910405 0.76352613 0.52239129 0.65268611 0.87628488 0.58910004
#> [529] 0.27034765 0.83721296 0.83721296 0.58910004 0.38897634 0.42976528
#> [535] 0.32690028 0.66316115 0.66316115 0.73056430 0.50931523 0.52239129
#> [541] 0.27034765 0.38897634 0.65268611 0.35368440 0.50931523 0.73056430
#> [547] 0.52239129 0.45487411 0.38897634 0.22037531 0.45487411 0.22037531
#> [553] 0.73056430 0.45487411 0.35368440 0.45487411 0.65268611 0.27034765
#> [559] 0.66316115 0.52239129 0.83721296 0.22390881 0.50931523 0.78877573
#> [565] 0.45487411 0.58910004 0.27034765 0.73056430 0.90702032 0.42976528
#> [571] 0.50931523 0.71125529 0.38897634 0.45487411 0.50931523 0.52239129
#> [577] 0.38897634 0.73056430 0.14127713 0.38897634 0.42976528 0.17739435
#> [583] 0.50931523 0.50931523 0.52239129 0.27034765 0.45487411 0.11151645
#> [589] 0.78877573 0.45487411 0.87628488 0.17320152 0.35368440 0.58839620
#> [595] 0.50931523 0.50931523 0.45487411 0.22037531 0.58910004 0.66316115
#> [601] 0.27034765 0.22390881 0.38897634 0.27034765 0.32690028 0.73056430
#> [607] 0.83721296 0.73056430 0.76352613 0.58910004 0.66316115 0.58910004
#> [613] 0.58839620 0.76352613 0.45487411 0.11151645 0.50931523 0.11151645
#> [619] 0.73056430 0.28435576 0.45487411 0.17739435 0.45487411 0.45487411
#> [625] 0.38897634 0.17739435 0.78877573 0.42976528 0.87628488 0.73056430
#> [631] 0.22037531 0.66316115 0.58839620 0.78877573 0.73056430 0.83721296
#> [637] 0.66316115 0.73056430 0.58839620 0.87628488 0.42976528 0.58839620
#> [643] 0.58839620 0.58910004 0.22037531 0.35368440 0.32690028 0.35368440
#> [649] 0.42976528 0.50931523 0.84727053 0.42976528 0.73056430 0.73056430
#> [655] 0.66316115 0.45487411 0.78877573 0.73056430 0.17739435 0.73056430
#> [661] 0.32690028 0.78877573 0.27034765 0.32690028 0.32690028 0.96223973
#> [667] 0.58839620 0.66316115 0.28435576 0.22037531 0.38897634 0.58910004
#> [673] 0.45487411 0.32690028 0.73056430 0.58910004 0.17739435 0.45487411
#> [679] 0.32690028 0.45487411 0.14127713 0.42976528 0.32690028 0.11151645
#> [685] 0.66316115 0.87628488 0.45487411 0.80887717 0.32690028 0.38897634
#> [691] 0.83721296 0.52239129 0.50931523 0.52239129 0.22390881 0.78877573
#> [697] 0.78877573 0.50931523 0.27034765 0.78877573 0.22390881 0.27034765
#> [703] 0.90702032 0.27034765 0.38897634 0.28435576 0.78877573 0.42976528
#> [709] 0.42976528 0.32690028 0.11151645 0.87628488 0.78877573 0.58839620
#> [715] 0.52239129 0.52239129 0.58839620 0.17739435 0.32690028 0.50931523
#> [721] 0.52239129 0.42976528 0.50931523 0.58839620 0.83721296 0.71125529
#> [727] 0.17739435 0.38897634 0.52239129 0.66316115 0.38897634 0.73056430
#> [733] 0.58839620 0.38897634 0.65268611 0.38897634 0.73056430 0.22037531
#> [739] 0.35368440 0.80887717 0.52239129 0.58910004 0.80887717 0.73056430
#> [745] 0.32690028 0.52239129 0.22390881 0.87628488 0.71125529 0.28435576
#> [751] 0.71125529 0.58910004 0.58910004 0.66316115 0.50931523 0.73056430
#> [757] 0.42976528 0.38897634 0.66316115 0.93072359 0.22037531 0.38897634
#> [763] 0.65268611 0.14127713 0.27034765 0.32690028 0.50931523 0.58839620
#> [769] 0.50931523 0.35368440 0.35368440 0.87628488 0.73056430 0.52239129
#> [775] 0.32690028 0.35368440 0.65268611 0.73056430 0.38897634 0.83721296
#> [781] 0.66316115 0.35368440 0.78877573 0.38897634 0.42976528 0.32690028
#> [787] 0.27034765 0.50931523 0.50931523 0.58910004 0.28435576 0.83721296
#> [793] 0.50931523 0.73056430 0.17739435 0.50931523 0.45487411 0.58839620
#> [799] 0.35368440 0.27034765 0.58839620 0.58839620 0.78877573 0.80887717
#> [805] 0.71125529 0.73056430 0.32690028 0.42976528 0.27034765 0.80887717
#> [811] 0.83721296 0.52239129 0.71125529 0.78877573 0.27034765 0.42976528
#> [817] 0.22037531 0.52239129 0.45487411 0.17739435 0.78877573 0.73056430
#> [823] 0.78877573 0.87628488 0.87628488 0.38897634 0.42976528 0.17739435
#> [829] 0.50931523 0.45487411 0.22037531 0.22390881 0.52239129 0.52239129
#> [835] 0.32690028 0.22037531 0.45487411 0.35368440 0.83721296 0.58910004
#> [841] 0.66316115 0.42976528 0.73056430 0.28435576 0.58910004 0.38897634
#> [847] 0.27034765 0.27034765 0.73056430 0.14127713 0.50931523 0.42976528
#> [853] 0.58839620 0.22390881 0.58839620 0.38897634 0.52239129 0.58839620
#> [859] 0.52239129 0.73056430 0.52239129 0.73056430 0.65268611 0.76352613
#> [865] 0.45487411 0.58910004 0.80887717 0.52239129 0.58839620 0.27034765
#> [871] 0.58839620 0.87628488 0.66316115 0.38897634 0.90702032 0.73056430
#> [877] 0.58839620 0.35368440 0.45487411 0.65268611 0.38897634 0.17739435
#> [883] 0.50931523 0.87628488 0.58839620 0.45487411 0.66316115 0.58839620
#> [889] 0.38897634 0.78877573 0.42976528 0.17739435 0.42976528 0.65268611
#> [895] 0.58910004 0.45487411 0.32690028 0.80887717 0.65268611 0.66316115
#> [901] 0.58839620 0.32690028 0.76352613 0.32690028 0.73056430 0.27034765
#> [907] 0.73056430 0.58910004 0.32690028 0.78877573 0.66316115 0.38897634
#> [913] 0.58910004 0.58839620 0.38897634 0.78877573 0.38897634 0.45487411
#> [919] 0.58910004 0.87628488 0.58910004 0.35368440 0.42976528 0.50931523
#> [925] 0.66316115 0.17739435 0.58839620 0.58910004 0.50931523 0.58910004
#> [931] 0.73056430 0.76352613 0.58839620 0.42976528 0.58839620 0.38897634
#> [937] 0.58910004 0.71125529 0.17739435 0.73056430 0.52239129 0.42976528
#> [943] 0.38897634 0.87628488 0.32690028 0.58910004 0.17739435 0.22390881
#> [949] 0.58839620 0.50931523 0.58910004 0.52239129 0.38897634 0.87628488
#> [955] 0.66316115 0.17739435 0.50931523 0.52239129 0.22037531 0.83721296
#> [961] 0.76352613 0.27034765 0.17739435 0.66316115 0.22037531 0.22037531
#> [967] 0.45487411 0.65268611 0.45487411 0.27034765 0.38897634 0.14127713
#> [973] 0.58839620 0.71125529 0.38897634 0.66316115 0.71125529 0.71125529
#> [979] 0.66316115 0.73056430 0.65268611 0.90702032 0.58839620 0.78877573
#> [985] 0.22037531 0.66316115 0.58839620 0.27034765 0.52239129 0.58910004
#> [991] 0.06807856 0.58910004 0.52239129 0.38897634 0.73056430 0.35368440
#> [997] 0.90702032 0.38897634 0.87628488 0.66316115
#> [ reached 'max' / getOption("max.print") -- omitted 1000 entries ]
#> attr(,"label")
#> [1] "Fitted values"
residuals(fit_em)
#> [1] -0.45487411 0.23647387 0.12371512 -0.22037531 0.21122427 -0.28435576
#> [7] 0.47760871 0.57023472 0.21122427 0.23647387 0.16278704 0.28874471
#> [13] -0.45487411 -0.50931523 -0.73056430 -0.35368440 0.41160380 0.28874471
#> [19] -0.45487411 -0.32690028 0.57023472 0.19112283 0.12371512 0.16278704
#> [25] 0.33683885 0.49068477 0.23647387 -0.50931523 0.28874471 -0.27034765
#> [31] -0.50931523 -0.65268611 -0.78877573 -0.32690028 0.54512589 -0.52239129
#> [37] -0.66316115 0.16278704 0.49068477 -0.58910004 -0.27034765 0.49068477
#> [43] -0.50931523 0.21122427 0.21122427 -0.45487411 -0.32690028 0.49068477
#> [49] 0.77962469 -0.52239129 0.47760871 -0.27034765 0.85872287 -0.52239129
#> [55] 0.67309972 0.41160380 -0.32690028 0.47760871 -0.52239129 0.47760871
#> [61] 0.12089595 -0.66316115 0.67309972 -0.22037531 0.34731389 -0.73056430
#> [67] -0.22037531 0.26943570 -0.08738702 0.06927641 -0.42976528 -0.22037531
#> [73] 0.54512589 0.41160380 -0.50931523 0.77962469 0.34731389 -0.22390881
#> [79] -0.32690028 0.49068477 0.47760871 -0.58839620 -0.22037531 -0.35368440
#> [85] -0.50931523 -0.65268611 0.71564424 -0.35368440 -0.45487411 -0.73056430
#> [91] -0.28435576 0.28874471 -0.45487411 0.28874471 0.72965235 -0.22037531
#> [97] 0.61102366 0.16278704 -0.27034765 0.15272947 0.05127421 0.47760871
#> [103] 0.47760871 0.33683885 -0.38897634 -0.17320152 0.21122427 -0.78877573
#> [109] 0.33683885 -0.14127713 0.34731389 -0.45487411 0.61102366 0.16278704
#> [115] -0.32690028 -0.58839620 0.67309972 0.12371512 -0.22037531 0.54512589
#> [121] 0.23647387 -0.45487411 -0.27034765 0.16278704 -0.27034765 0.49068477
#> [127] 0.72965235 -0.22390881 -0.27034765 -0.28435576 0.54512589 -0.42976528
#> [133] -0.42976528 0.16278704 -0.38897634 -0.38897634 -0.13202412 0.41089996
#> [139] 0.26943570 0.16278704 -0.38897634 0.82260565 -0.28435576 0.21122427
#> [145] 0.49068477 -0.66316115 0.09297968 0.26943570 -0.22037531 0.67309972
#> [151] -0.27034765 -0.22037531 0.33683885 -0.45487411 0.16278704 -0.35368440
#> [157] -0.22037531 0.09297968 0.06927641 0.61102366 0.57023472 0.47760871
#> [163] -0.90702032 -0.14127713 0.57023472 -0.45487411 0.33683885 -0.90702032
#> [169] -0.27034765 0.21122427 -0.28435576 0.33683885 -0.58910004 0.41160380
#> [175] -0.73056430 0.57023472 -0.45487411 0.23647387 0.12371512 -0.17739435
#> [181] 0.61102366 0.12371512 0.09297968 0.19112283 -0.58910004 -0.50931523
#> [187] 0.12371512 -0.35368440 -0.11151645 0.26943570 -0.32690028 0.49068477
#> [193] 0.26943570 -0.14127713 0.09297968 0.41160380 -0.58839620 -0.66316115
#> [199] 0.21122427 0.54512589 -0.32690028 0.41160380 -0.22390881 0.21122427
#> [205] 0.12371512 -0.73056430 0.26943570 -0.45487411 0.21122427 -0.38897634
#> [211] -0.58910004 0.61102366 0.77609119 -0.52239129 -0.17739435 -0.28435576
#> [217] 0.26943570 0.21122427 0.06927641 0.26943570 0.41089996 -0.38897634
#> [223] -0.38897634 -0.73056430 -0.38897634 0.57023472 0.26943570 0.49068477
#> [229] 0.41160380 -0.52239129 0.64631560 0.09297968 0.12371512 0.64631560
#> [235] 0.16278704 -0.73056430 0.41160380 -0.93072359 -0.32690028 0.09297968
#> [241] 0.26943570 -0.65268611 0.33683885 0.54512589 0.49068477 -0.32690028
#> [247] -0.45487411 -0.58839620 0.41089996 -0.32690028 0.16278704 0.49068477
#> [253] 0.21122427 -0.66316115 -0.58910004 -0.58910004 0.33683885 0.54512589
#> [259] 0.28874471 0.21122427 -0.08738702 0.34731389 -0.35368440 -0.27034765
#> [265] 0.33683885 -0.58839620 0.16278704 -0.45487411 0.23647387 -0.14127713
#> [271] -0.45487411 -0.66316115 0.21122427 -0.35368440 0.09297968 -0.32690028
#> [277] -0.52239129 -0.17739435 0.64631560 -0.52239129 -0.27034765 0.26943570
#> [283] 0.41160380 -0.42976528 -0.58910004 -0.76352613 0.49068477 -0.78877573
#> [289] 0.06927641 -0.42976528 -0.42976528 -0.27034765 0.67309972 -0.58839620
#> [295] 0.54512589 0.16278704 0.41089996 -0.50931523 0.41089996 0.16278704
#> [301] 0.41089996 -0.38897634 -0.35368440 -0.22390881 -0.66316115 0.09297968
#> [307] 0.21122427 0.09297968 0.57023472 -0.38897634 -0.66316115 -0.27034765
#> [313] -0.45487411 -0.52239129 0.15272947 0.21122427 -0.52239129 -0.65268611
#> [319] 0.41160380 -0.32690028 0.72965235 0.47760871 0.26943570 -0.06807856
#> [325] 0.34731389 0.26943570 -0.35368440 0.21122427 0.26943570 -0.14127713
#> [331] -0.32690028 -0.38897634 -0.45487411 0.72965235 0.12371512 0.49068477
#> [337] -0.58839620 0.54512589 0.33683885 -0.38897634 -0.66316115 0.41089996
#> [343] 0.21122427 -0.73056430 0.49068477 0.49068477 0.54512589 0.57023472
#> [349] 0.16278704 -0.27034765 -0.17739435 0.16278704 -0.58839620 0.33683885
#> [355] -0.28435576 0.16278704 -0.52239129 -0.27034765 -0.28435576 0.57023472
#> [361] 0.23647387 0.72965235 -0.52239129 -0.28435576 0.12371512 -0.45487411
#> [367] -0.35368440 -0.32690028 -0.27034765 -0.58910004 -0.35368440 -0.52239129
#> [373] 0.77962469 -0.42976528 0.41160380 0.67309972 -0.14127713 -0.73056430
#> [379] 0.49068477 0.21122427 0.16278704 -0.52239129 0.57023472 -0.58839620
#> [385] -0.66316115 0.06927641 -0.50931523 0.03776027 -0.35368440 -0.11151645
#> [391] -0.32690028 -0.38897634 0.28874471 -0.52239129 -0.50931523 0.61102366
#> [397] -0.42976528 0.19112283 -0.80887717 0.16278704 -0.22390881 -0.32690028
#> [403] -0.45487411 -0.83721296 0.09297968 -0.38897634 0.47760871 0.41089996
#> [409] 0.54512589 0.19112283 0.34731389 0.54512589 0.21122427 -0.42976528
#> [415] -0.58839620 -0.17739435 0.47760871 -0.28435576 0.57023472 0.88848355
#> [421] -0.32690028 0.34731389 -0.45487411 -0.45487411 0.47760871 -0.35368440
#> [427] -0.65268611 0.34731389 -0.52239129 0.49068477 -0.38897634 0.54512589
#> [433] 0.49068477 0.16278704 -0.32690028 0.23647387 0.21122427 0.72965235
#> [439] 0.77609119 -0.52239129 0.41089996 0.47760871 0.26943570 -0.22037531
#> [445] -0.32690028 0.21122427 -0.65268611 -0.65268611 -0.17739435 -0.32690028
#> [451] 0.41089996 -0.14127713 0.19112283 0.47760871 0.49068477 0.28874471
#> [457] 0.47760871 0.41089996 0.67309972 0.26943570 0.47760871 0.41089996
#> [463] -0.71125529 -0.78877573 0.82679848 0.72965235 -0.52239129 0.26943570
#> [469] -0.58910004 0.34731389 -0.58839620 0.33683885 -0.32690028 -0.50931523
#> [475] 0.21122427 0.26943570 -0.35368440 -0.52239129 -0.52239129 0.26943570
#> [481] 0.16278704 -0.58910004 0.21122427 0.26943570 0.49068477 -0.32690028
#> [487] 0.21122427 -0.66316115 -0.45487411 0.34731389 -0.73056430 -0.22037531
#> [493] 0.77962469 -0.32690028 -0.50931523 0.82260565 0.71564424 0.41089996
#> [499] -0.50931523 0.23647387 -0.83721296 -0.22390881 -0.38897634 0.67309972
#> [505] -0.50931523 0.57023472 0.67309972 -0.45487411 0.67309972 0.67309972
#> [511] -0.32690028 -0.13202412 -0.17320152 0.33683885 -0.71125529 -0.28435576
#> [517] -0.38897634 0.57023472 -0.27034765 0.47760871 0.41160380 0.47760871
#> [523] 0.12089595 -0.76352613 0.47760871 0.34731389 0.12371512 -0.58910004
#> [529] -0.27034765 -0.83721296 0.16278704 -0.58910004 -0.38897634 0.57023472
#> [535] 0.67309972 0.33683885 0.33683885 0.26943570 0.49068477 0.47760871
#> [541] -0.27034765 -0.38897634 0.34731389 -0.35368440 0.49068477 0.26943570
#> [547] -0.52239129 -0.45487411 -0.38897634 0.77962469 -0.45487411 -0.22037531
#> [553] 0.26943570 0.54512589 0.64631560 -0.45487411 0.34731389 -0.27034765
#> [559] 0.33683885 0.47760871 0.16278704 -0.22390881 0.49068477 0.21122427
#> [565] 0.54512589 0.41089996 -0.27034765 -0.73056430 0.09297968 0.57023472
#> [571] -0.50931523 -0.71125529 -0.38897634 0.54512589 0.49068477 -0.52239129
#> [577] -0.38897634 0.26943570 0.85872287 -0.38897634 0.57023472 -0.17739435
#> [583] 0.49068477 -0.50931523 0.47760871 -0.27034765 -0.45487411 -0.11151645
#> [589] -0.78877573 0.54512589 0.12371512 -0.17320152 0.64631560 0.41160380
#> [595] -0.50931523 0.49068477 0.54512589 -0.22037531 0.41089996 -0.66316115
#> [601] 0.72965235 -0.22390881 0.61102366 0.72965235 -0.32690028 0.26943570
#> [607] -0.83721296 -0.73056430 0.23647387 0.41089996 0.33683885 -0.58910004
#> [613] -0.58839620 0.23647387 0.54512589 -0.11151645 -0.50931523 -0.11151645
#> [619] -0.73056430 -0.28435576 -0.45487411 0.82260565 -0.45487411 -0.45487411
#> [625] -0.38897634 -0.17739435 -0.78877573 0.57023472 0.12371512 0.26943570
#> [631] -0.22037531 -0.66316115 0.41160380 0.21122427 0.26943570 0.16278704
#> [637] 0.33683885 0.26943570 0.41160380 0.12371512 -0.42976528 -0.58839620
#> [643] 0.41160380 -0.58910004 0.77962469 -0.35368440 0.67309972 0.64631560
#> [649] -0.42976528 0.49068477 -0.84727053 -0.42976528 0.26943570 0.26943570
#> [655] -0.66316115 -0.45487411 -0.78877573 0.26943570 -0.17739435 0.26943570
#> [661] -0.32690028 0.21122427 -0.27034765 -0.32690028 0.67309972 0.03776027
#> [667] -0.58839620 0.33683885 0.71564424 -0.22037531 -0.38897634 0.41089996
#> [673] -0.45487411 -0.32690028 0.26943570 -0.58910004 -0.17739435 -0.45487411
#> [679] -0.32690028 0.54512589 -0.14127713 -0.42976528 -0.32690028 -0.11151645
#> [685] 0.33683885 -0.87628488 -0.45487411 0.19112283 -0.32690028 0.61102366
#> [691] 0.16278704 -0.52239129 0.49068477 -0.52239129 -0.22390881 0.21122427
#> [697] 0.21122427 0.49068477 0.72965235 0.21122427 0.77609119 0.72965235
#> [703] 0.09297968 -0.27034765 0.61102366 0.71564424 -0.78877573 -0.42976528
#> [709] 0.57023472 0.67309972 0.88848355 0.12371512 0.21122427 0.41160380
#> [715] -0.52239129 -0.52239129 0.41160380 -0.17739435 -0.32690028 -0.50931523
#> [721] 0.47760871 0.57023472 -0.50931523 -0.58839620 -0.83721296 -0.71125529
#> [727] -0.17739435 -0.38897634 -0.52239129 0.33683885 -0.38897634 -0.73056430
#> [733] -0.58839620 0.61102366 -0.65268611 0.61102366 0.26943570 -0.22037531
#> [739] -0.35368440 0.19112283 -0.52239129 -0.58910004 0.19112283 0.26943570
#> [745] -0.32690028 0.47760871 -0.22390881 -0.87628488 0.28874471 -0.28435576
#> [751] 0.28874471 -0.58910004 -0.58910004 0.33683885 -0.50931523 0.26943570
#> [757] -0.42976528 0.61102366 -0.66316115 0.06927641 -0.22037531 0.61102366
#> [763] 0.34731389 -0.14127713 0.72965235 -0.32690028 -0.50931523 -0.58839620
#> [769] -0.50931523 -0.35368440 -0.35368440 0.12371512 0.26943570 -0.52239129
#> [775] -0.32690028 -0.35368440 0.34731389 0.26943570 -0.38897634 0.16278704
#> [781] 0.33683885 0.64631560 0.21122427 -0.38897634 -0.42976528 0.67309972
#> [787] -0.27034765 0.49068477 0.49068477 0.41089996 0.71564424 0.16278704
#> [793] -0.50931523 0.26943570 -0.17739435 0.49068477 0.54512589 -0.58839620
#> [799] -0.35368440 -0.27034765 0.41160380 -0.58839620 0.21122427 0.19112283
#> [805] 0.28874471 -0.73056430 -0.32690028 -0.42976528 -0.27034765 0.19112283
#> [811] 0.16278704 -0.52239129 -0.71125529 0.21122427 -0.27034765 -0.42976528
#> [817] -0.22037531 -0.52239129 -0.45487411 -0.17739435 -0.78877573 0.26943570
#> [823] 0.21122427 0.12371512 0.12371512 0.61102366 0.57023472 -0.17739435
#> [829] -0.50931523 -0.45487411 -0.22037531 -0.22390881 -0.52239129 0.47760871
#> [835] -0.32690028 -0.22037531 0.54512589 -0.35368440 -0.83721296 0.41089996
#> [841] 0.33683885 0.57023472 -0.73056430 -0.28435576 -0.58910004 -0.38897634
#> [847] -0.27034765 -0.27034765 0.26943570 -0.14127713 -0.50931523 0.57023472
#> [853] -0.58839620 -0.22390881 0.41160380 -0.38897634 -0.52239129 0.41160380
#> [859] 0.47760871 -0.73056430 0.47760871 0.26943570 -0.65268611 0.23647387
#> [865] 0.54512589 -0.58910004 0.19112283 0.47760871 0.41160380 -0.27034765
#> [871] 0.41160380 0.12371512 0.33683885 0.61102366 0.09297968 0.26943570
#> [877] 0.41160380 0.64631560 0.54512589 0.34731389 -0.38897634 -0.17739435
#> [883] 0.49068477 0.12371512 0.41160380 0.54512589 0.33683885 0.41160380
#> [889] -0.38897634 0.21122427 0.57023472 -0.17739435 0.57023472 0.34731389
#> [895] 0.41089996 0.54512589 -0.32690028 0.19112283 -0.65268611 0.33683885
#> [901] -0.58839620 -0.32690028 0.23647387 0.67309972 0.26943570 -0.27034765
#> [907] 0.26943570 0.41089996 0.67309972 0.21122427 0.33683885 -0.38897634
#> [913] -0.58910004 0.41160380 -0.38897634 0.21122427 0.61102366 0.54512589
#> [919] 0.41089996 0.12371512 -0.58910004 0.64631560 -0.42976528 -0.50931523
#> [925] 0.33683885 -0.17739435 0.41160380 0.41089996 0.49068477 -0.58910004
#> [931] 0.26943570 0.23647387 0.41160380 -0.42976528 -0.58839620 -0.38897634
#> [937] -0.58910004 -0.71125529 -0.17739435 -0.73056430 -0.52239129 -0.42976528
#> [943] -0.38897634 0.12371512 -0.32690028 -0.58910004 -0.17739435 -0.22390881
#> [949] 0.41160380 0.49068477 0.41089996 0.47760871 -0.38897634 0.12371512
#> [955] 0.33683885 0.82260565 -0.50931523 -0.52239129 0.77962469 0.16278704
#> [961] 0.23647387 -0.27034765 0.82260565 -0.66316115 -0.22037531 -0.22037531
#> [967] -0.45487411 0.34731389 0.54512589 0.72965235 0.61102366 -0.14127713
#> [973] -0.58839620 -0.71125529 -0.38897634 0.33683885 -0.71125529 0.28874471
#> [979] 0.33683885 -0.73056430 0.34731389 0.09297968 -0.58839620 -0.78877573
#> [985] 0.77962469 -0.66316115 -0.58839620 -0.27034765 0.47760871 0.41089996
#> [991] -0.06807856 0.41089996 0.47760871 -0.38897634 0.26943570 -0.35368440
#> [997] -0.90702032 -0.38897634 0.12371512 0.33683885
#> [ reached 'max' / getOption("max.print") -- omitted 1000 entries ]
#> attr(,"label")
#> [1] "Residuals"
# PLF algorithm
(fit_plf <- estimNLR(
y = y, match = match, group = group,
formula = M$M1$formula, method = "plf",
lower = M$M1$lower, upper = M$M1$upper, start = start
))
#> Nonlinear regression model
#>
#> Model: y ~ c + (1 - c)/(1 + exp(-(b0 + b1 * x + b2 * g + b3 * x * g)))
#>
#> Coefficients:
#> b0 b1 b2 b3 c
#> 0.5503 0.9941 -0.8388 -0.1536 0.0028
#>
#> Maximum likelihood estimation using the PLF-based algorithm
#> Converged after 3 iterations
coef(fit_plf)
#> b0 b1 b2 b3 c
#> 0.550343985 0.994097463 -0.838776617 -0.153592745 0.002780102
logLik(fit_plf)
#> 'log Lik.' -1192.321 (df=5)
vcov(fit_plf)
#> b0 b1 b2 b3 c
#> b0 0.05495893 -0.021684101 0.02259576 -0.020979118 -0.02753933
#> b1 -0.02168410 0.017562348 -0.01398739 0.002060718 0.01266679
#> b2 0.02259576 -0.013987390 0.02572108 -0.010506627 -0.01546232
#> b3 -0.02097912 0.002060718 -0.01050663 0.021088110 0.01098863
#> c -0.02753933 0.012666789 -0.01546232 0.010988632 0.01526970
fitted(fit_plf)
#> [1] 0.45638962 0.76418355 0.87662882 0.22254275 0.78936295 0.28634532
#> [7] 0.52371909 0.43135059 0.78936295 0.76418355 0.83766553 0.71205803
#> [13] 0.45638962 0.51067938 0.73131336 0.35548122 0.58954050 0.71205803
#> [19] 0.45638962 0.32877157 0.43135059 0.80940851 0.87662882 0.83766553
#> [25] 0.66409760 0.51067938 0.76418355 0.51067938 0.71205803 0.27237616
#> [31] 0.51067938 0.65365167 0.78936295 0.32877157 0.45638962 0.52371909
#> [37] 0.66409760 0.83766553 0.51067938 0.59024238 0.27237616 0.51067938
#> [43] 0.51067938 0.78936295 0.78936295 0.45638962 0.32877157 0.51067938
#> [49] 0.22254275 0.52371909 0.52371909 0.27237616 0.14366447 0.52371909
#> [55] 0.32877157 0.58954050 0.32877157 0.52371909 0.52371909 0.52371909
#> [61] 0.87944015 0.66409760 0.32877157 0.22254275 0.65365167 0.73131336
#> [67] 0.22254275 0.73131336 0.08992418 0.93091619 0.43135059 0.22254275
#> [73] 0.45638962 0.58954050 0.51067938 0.22254275 0.65365167 0.22606643
#> [79] 0.32877157 0.51067938 0.52371909 0.58954050 0.22254275 0.35548122
#> [85] 0.51067938 0.65365167 0.28634532 0.35548122 0.45638962 0.73131336
#> [91] 0.28634532 0.71205803 0.45638962 0.71205803 0.27237616 0.22254275
#> [97] 0.39067504 0.83766553 0.27237616 0.84769514 0.94886834 0.52371909
#> [103] 0.52371909 0.66409760 0.39067504 0.17550010 0.78936295 0.78936295
#> [109] 0.66409760 0.14366447 0.65365167 0.45638962 0.39067504 0.83766553
#> [115] 0.32877157 0.58954050 0.32877157 0.87662882 0.22254275 0.45638962
#> [121] 0.76418355 0.45638962 0.27237616 0.83766553 0.27237616 0.51067938
#> [127] 0.27237616 0.22606643 0.27237616 0.28634532 0.45638962 0.43135059
#> [133] 0.43135059 0.83766553 0.39067504 0.39067504 0.13443718 0.59024238
#> [139] 0.73131336 0.83766553 0.39067504 0.17968128 0.28634532 0.78936295
#> [145] 0.51067938 0.66409760 0.90727881 0.73131336 0.22254275 0.32877157
#> [151] 0.27237616 0.22254275 0.66409760 0.45638962 0.83766553 0.35548122
#> [157] 0.22254275 0.90727881 0.93091619 0.39067504 0.43135059 0.52371909
#> [163] 0.90727881 0.14366447 0.43135059 0.45638962 0.66409760 0.90727881
#> [169] 0.27237616 0.78936295 0.28634532 0.66409760 0.59024238 0.58954050
#> [175] 0.73131336 0.43135059 0.45638962 0.76418355 0.87662882 0.17968128
#> [181] 0.39067504 0.87662882 0.90727881 0.80940851 0.59024238 0.51067938
#> [187] 0.87662882 0.35548122 0.11398653 0.73131336 0.32877157 0.51067938
#> [193] 0.73131336 0.14366447 0.90727881 0.58954050 0.58954050 0.66409760
#> [199] 0.78936295 0.45638962 0.32877157 0.58954050 0.22606643 0.78936295
#> [205] 0.87662882 0.73131336 0.73131336 0.45638962 0.78936295 0.39067504
#> [211] 0.59024238 0.39067504 0.22606643 0.52371909 0.17968128 0.28634532
#> [217] 0.73131336 0.78936295 0.93091619 0.73131336 0.59024238 0.39067504
#> [223] 0.39067504 0.73131336 0.39067504 0.43135059 0.73131336 0.51067938
#> [229] 0.58954050 0.52371909 0.35548122 0.90727881 0.87662882 0.35548122
#> [235] 0.83766553 0.73131336 0.58954050 0.93091619 0.32877157 0.90727881
#> [241] 0.73131336 0.65365167 0.66409760 0.45638962 0.51067938 0.32877157
#> [247] 0.45638962 0.58954050 0.59024238 0.32877157 0.83766553 0.51067938
#> [253] 0.78936295 0.66409760 0.59024238 0.59024238 0.66409760 0.45638962
#> [259] 0.71205803 0.78936295 0.08992418 0.65365167 0.35548122 0.27237616
#> [265] 0.66409760 0.58954050 0.83766553 0.45638962 0.76418355 0.14366447
#> [271] 0.45638962 0.66409760 0.78936295 0.35548122 0.90727881 0.32877157
#> [277] 0.52371909 0.17968128 0.35548122 0.52371909 0.27237616 0.73131336
#> [283] 0.58954050 0.43135059 0.59024238 0.76418355 0.51067938 0.78936295
#> [289] 0.93091619 0.43135059 0.43135059 0.27237616 0.32877157 0.58954050
#> [295] 0.45638962 0.83766553 0.59024238 0.51067938 0.59024238 0.83766553
#> [301] 0.59024238 0.39067504 0.35548122 0.22606643 0.66409760 0.90727881
#> [307] 0.78936295 0.90727881 0.43135059 0.39067504 0.66409760 0.27237616
#> [313] 0.45638962 0.52371909 0.84769514 0.78936295 0.52371909 0.65365167
#> [319] 0.58954050 0.32877157 0.27237616 0.52371909 0.73131336 0.07066939
#> [325] 0.65365167 0.73131336 0.35548122 0.78936295 0.73131336 0.14366447
#> [331] 0.32877157 0.39067504 0.45638962 0.27237616 0.87662882 0.51067938
#> [337] 0.58954050 0.45638962 0.66409760 0.39067504 0.66409760 0.59024238
#> [343] 0.78936295 0.73131336 0.51067938 0.51067938 0.45638962 0.43135059
#> [349] 0.83766553 0.27237616 0.17968128 0.83766553 0.58954050 0.66409760
#> [355] 0.28634532 0.83766553 0.52371909 0.27237616 0.28634532 0.43135059
#> [361] 0.76418355 0.27237616 0.52371909 0.28634532 0.87662882 0.45638962
#> [367] 0.35548122 0.32877157 0.27237616 0.59024238 0.35548122 0.52371909
#> [373] 0.22254275 0.43135059 0.58954050 0.32877157 0.14366447 0.73131336
#> [379] 0.51067938 0.78936295 0.83766553 0.52371909 0.43135059 0.58954050
#> [385] 0.66409760 0.93091619 0.51067938 0.96234471 0.35548122 0.11398653
#> [391] 0.32877157 0.39067504 0.71205803 0.52371909 0.51067938 0.39067504
#> [397] 0.43135059 0.80940851 0.80940851 0.83766553 0.22606643 0.32877157
#> [403] 0.45638962 0.83766553 0.90727881 0.39067504 0.52371909 0.59024238
#> [409] 0.45638962 0.80940851 0.65365167 0.45638962 0.78936295 0.43135059
#> [415] 0.58954050 0.17968128 0.52371909 0.28634532 0.43135059 0.11398653
#> [421] 0.32877157 0.65365167 0.45638962 0.45638962 0.52371909 0.35548122
#> [427] 0.65365167 0.65365167 0.52371909 0.51067938 0.39067504 0.45638962
#> [433] 0.51067938 0.83766553 0.32877157 0.76418355 0.78936295 0.27237616
#> [439] 0.22606643 0.52371909 0.59024238 0.52371909 0.73131336 0.22254275
#> [445] 0.32877157 0.78936295 0.65365167 0.65365167 0.17968128 0.32877157
#> [451] 0.59024238 0.14366447 0.80940851 0.52371909 0.51067938 0.71205803
#> [457] 0.52371909 0.59024238 0.32877157 0.73131336 0.52371909 0.59024238
#> [463] 0.71205803 0.78936295 0.17550010 0.27237616 0.52371909 0.73131336
#> [469] 0.59024238 0.65365167 0.58954050 0.66409760 0.32877157 0.51067938
#> [475] 0.78936295 0.73131336 0.35548122 0.52371909 0.52371909 0.73131336
#> [481] 0.83766553 0.59024238 0.78936295 0.73131336 0.51067938 0.32877157
#> [487] 0.78936295 0.66409760 0.45638962 0.65365167 0.73131336 0.22254275
#> [493] 0.22254275 0.32877157 0.51067938 0.17968128 0.28634532 0.59024238
#> [499] 0.51067938 0.76418355 0.83766553 0.22606643 0.39067504 0.32877157
#> [505] 0.51067938 0.43135059 0.32877157 0.45638962 0.32877157 0.32877157
#> [511] 0.32877157 0.13443718 0.17550010 0.66409760 0.71205803 0.28634532
#> [517] 0.39067504 0.43135059 0.27237616 0.52371909 0.58954050 0.52371909
#> [523] 0.87944015 0.76418355 0.52371909 0.65365167 0.87662882 0.59024238
#> [529] 0.27237616 0.83766553 0.83766553 0.59024238 0.39067504 0.43135059
#> [535] 0.32877157 0.66409760 0.66409760 0.73131336 0.51067938 0.52371909
#> [541] 0.27237616 0.39067504 0.65365167 0.35548122 0.51067938 0.73131336
#> [547] 0.52371909 0.45638962 0.39067504 0.22254275 0.45638962 0.22254275
#> [553] 0.73131336 0.45638962 0.35548122 0.45638962 0.65365167 0.27237616
#> [559] 0.66409760 0.52371909 0.83766553 0.22606643 0.51067938 0.78936295
#> [565] 0.45638962 0.59024238 0.27237616 0.73131336 0.90727881 0.43135059
#> [571] 0.51067938 0.71205803 0.39067504 0.45638962 0.51067938 0.52371909
#> [577] 0.39067504 0.73131336 0.14366447 0.39067504 0.43135059 0.17968128
#> [583] 0.51067938 0.51067938 0.52371909 0.27237616 0.45638962 0.11398653
#> [589] 0.78936295 0.45638962 0.87662882 0.17550010 0.35548122 0.58954050
#> [595] 0.51067938 0.51067938 0.45638962 0.22254275 0.59024238 0.66409760
#> [601] 0.27237616 0.22606643 0.39067504 0.27237616 0.32877157 0.73131336
#> [607] 0.83766553 0.73131336 0.76418355 0.59024238 0.66409760 0.59024238
#> [613] 0.58954050 0.76418355 0.45638962 0.11398653 0.51067938 0.11398653
#> [619] 0.73131336 0.28634532 0.45638962 0.17968128 0.45638962 0.45638962
#> [625] 0.39067504 0.17968128 0.78936295 0.43135059 0.87662882 0.73131336
#> [631] 0.22254275 0.66409760 0.58954050 0.78936295 0.73131336 0.83766553
#> [637] 0.66409760 0.73131336 0.58954050 0.87662882 0.43135059 0.58954050
#> [643] 0.58954050 0.59024238 0.22254275 0.35548122 0.32877157 0.35548122
#> [649] 0.43135059 0.51067938 0.84769514 0.43135059 0.73131336 0.73131336
#> [655] 0.66409760 0.45638962 0.78936295 0.73131336 0.17968128 0.73131336
#> [661] 0.32877157 0.78936295 0.27237616 0.32877157 0.32877157 0.96234471
#> [667] 0.58954050 0.66409760 0.28634532 0.22254275 0.39067504 0.59024238
#> [673] 0.45638962 0.32877157 0.73131336 0.59024238 0.17968128 0.45638962
#> [679] 0.32877157 0.45638962 0.14366447 0.43135059 0.32877157 0.11398653
#> [685] 0.66409760 0.87662882 0.45638962 0.80940851 0.32877157 0.39067504
#> [691] 0.83766553 0.52371909 0.51067938 0.52371909 0.22606643 0.78936295
#> [697] 0.78936295 0.51067938 0.27237616 0.78936295 0.22606643 0.27237616
#> [703] 0.90727881 0.27237616 0.39067504 0.28634532 0.78936295 0.43135059
#> [709] 0.43135059 0.32877157 0.11398653 0.87662882 0.78936295 0.58954050
#> [715] 0.52371909 0.52371909 0.58954050 0.17968128 0.32877157 0.51067938
#> [721] 0.52371909 0.43135059 0.51067938 0.58954050 0.83766553 0.71205803
#> [727] 0.17968128 0.39067504 0.52371909 0.66409760 0.39067504 0.73131336
#> [733] 0.58954050 0.39067504 0.65365167 0.39067504 0.73131336 0.22254275
#> [739] 0.35548122 0.80940851 0.52371909 0.59024238 0.80940851 0.73131336
#> [745] 0.32877157 0.52371909 0.22606643 0.87662882 0.71205803 0.28634532
#> [751] 0.71205803 0.59024238 0.59024238 0.66409760 0.51067938 0.73131336
#> [757] 0.43135059 0.39067504 0.66409760 0.93091619 0.22254275 0.39067504
#> [763] 0.65365167 0.14366447 0.27237616 0.32877157 0.51067938 0.58954050
#> [769] 0.51067938 0.35548122 0.35548122 0.87662882 0.73131336 0.52371909
#> [775] 0.32877157 0.35548122 0.65365167 0.73131336 0.39067504 0.83766553
#> [781] 0.66409760 0.35548122 0.78936295 0.39067504 0.43135059 0.32877157
#> [787] 0.27237616 0.51067938 0.51067938 0.59024238 0.28634532 0.83766553
#> [793] 0.51067938 0.73131336 0.17968128 0.51067938 0.45638962 0.58954050
#> [799] 0.35548122 0.27237616 0.58954050 0.58954050 0.78936295 0.80940851
#> [805] 0.71205803 0.73131336 0.32877157 0.43135059 0.27237616 0.80940851
#> [811] 0.83766553 0.52371909 0.71205803 0.78936295 0.27237616 0.43135059
#> [817] 0.22254275 0.52371909 0.45638962 0.17968128 0.78936295 0.73131336
#> [823] 0.78936295 0.87662882 0.87662882 0.39067504 0.43135059 0.17968128
#> [829] 0.51067938 0.45638962 0.22254275 0.22606643 0.52371909 0.52371909
#> [835] 0.32877157 0.22254275 0.45638962 0.35548122 0.83766553 0.59024238
#> [841] 0.66409760 0.43135059 0.73131336 0.28634532 0.59024238 0.39067504
#> [847] 0.27237616 0.27237616 0.73131336 0.14366447 0.51067938 0.43135059
#> [853] 0.58954050 0.22606643 0.58954050 0.39067504 0.52371909 0.58954050
#> [859] 0.52371909 0.73131336 0.52371909 0.73131336 0.65365167 0.76418355
#> [865] 0.45638962 0.59024238 0.80940851 0.52371909 0.58954050 0.27237616
#> [871] 0.58954050 0.87662882 0.66409760 0.39067504 0.90727881 0.73131336
#> [877] 0.58954050 0.35548122 0.45638962 0.65365167 0.39067504 0.17968128
#> [883] 0.51067938 0.87662882 0.58954050 0.45638962 0.66409760 0.58954050
#> [889] 0.39067504 0.78936295 0.43135059 0.17968128 0.43135059 0.65365167
#> [895] 0.59024238 0.45638962 0.32877157 0.80940851 0.65365167 0.66409760
#> [901] 0.58954050 0.32877157 0.76418355 0.32877157 0.73131336 0.27237616
#> [907] 0.73131336 0.59024238 0.32877157 0.78936295 0.66409760 0.39067504
#> [913] 0.59024238 0.58954050 0.39067504 0.78936295 0.39067504 0.45638962
#> [919] 0.59024238 0.87662882 0.59024238 0.35548122 0.43135059 0.51067938
#> [925] 0.66409760 0.17968128 0.58954050 0.59024238 0.51067938 0.59024238
#> [931] 0.73131336 0.76418355 0.58954050 0.43135059 0.58954050 0.39067504
#> [937] 0.59024238 0.71205803 0.17968128 0.73131336 0.52371909 0.43135059
#> [943] 0.39067504 0.87662882 0.32877157 0.59024238 0.17968128 0.22606643
#> [949] 0.58954050 0.51067938 0.59024238 0.52371909 0.39067504 0.87662882
#> [955] 0.66409760 0.17968128 0.51067938 0.52371909 0.22254275 0.83766553
#> [961] 0.76418355 0.27237616 0.17968128 0.66409760 0.22254275 0.22254275
#> [967] 0.45638962 0.65365167 0.45638962 0.27237616 0.39067504 0.14366447
#> [973] 0.58954050 0.71205803 0.39067504 0.66409760 0.71205803 0.71205803
#> [979] 0.66409760 0.73131336 0.65365167 0.90727881 0.58954050 0.78936295
#> [985] 0.22254275 0.66409760 0.58954050 0.27237616 0.52371909 0.59024238
#> [991] 0.07066939 0.59024238 0.52371909 0.39067504 0.73131336 0.35548122
#> [997] 0.90727881 0.39067504 0.87662882 0.66409760
#> [ reached 'max' / getOption("max.print") -- omitted 1000 entries ]
#> attr(,"label")
#> [1] "Fitted values"
residuals(fit_plf)
#> [1] -0.45638962 0.23581645 0.12337118 -0.22254275 0.21063705 -0.28634532
#> [7] 0.47628091 0.56864941 0.21063705 0.23581645 0.16233447 0.28794197
#> [13] -0.45638962 -0.51067938 -0.73131336 -0.35548122 0.41045950 0.28794197
#> [19] -0.45638962 -0.32877157 0.56864941 0.19059149 0.12337118 0.16233447
#> [25] 0.33590240 0.48932062 0.23581645 -0.51067938 0.28794197 -0.27237616
#> [31] -0.51067938 -0.65365167 -0.78936295 -0.32877157 0.54361038 -0.52371909
#> [37] -0.66409760 0.16233447 0.48932062 -0.59024238 -0.27237616 0.48932062
#> [43] -0.51067938 0.21063705 0.21063705 -0.45638962 -0.32877157 0.48932062
#> [49] 0.77745725 -0.52371909 0.47628091 -0.27237616 0.85633553 -0.52371909
#> [55] 0.67122843 0.41045950 -0.32877157 0.47628091 -0.52371909 0.47628091
#> [61] 0.12055985 -0.66409760 0.67122843 -0.22254275 0.34634833 -0.73131336
#> [67] -0.22254275 0.26868664 -0.08992418 0.06908381 -0.43135059 -0.22254275
#> [73] 0.54361038 0.41045950 -0.51067938 0.77745725 0.34634833 -0.22606643
#> [79] -0.32877157 0.48932062 0.47628091 -0.58954050 -0.22254275 -0.35548122
#> [85] -0.51067938 -0.65365167 0.71365468 -0.35548122 -0.45638962 -0.73131336
#> [91] -0.28634532 0.28794197 -0.45638962 0.28794197 0.72762384 -0.22254275
#> [97] 0.60932496 0.16233447 -0.27237616 0.15230486 0.05113166 0.47628091
#> [103] 0.47628091 0.33590240 -0.39067504 -0.17550010 0.21063705 -0.78936295
#> [109] 0.33590240 -0.14366447 0.34634833 -0.45638962 0.60932496 0.16233447
#> [115] -0.32877157 -0.58954050 0.67122843 0.12337118 -0.22254275 0.54361038
#> [121] 0.23581645 -0.45638962 -0.27237616 0.16233447 -0.27237616 0.48932062
#> [127] 0.72762384 -0.22606643 -0.27237616 -0.28634532 0.54361038 -0.43135059
#> [133] -0.43135059 0.16233447 -0.39067504 -0.39067504 -0.13443718 0.40975762
#> [139] 0.26868664 0.16233447 -0.39067504 0.82031872 -0.28634532 0.21063705
#> [145] 0.48932062 -0.66409760 0.09272119 0.26868664 -0.22254275 0.67122843
#> [151] -0.27237616 -0.22254275 0.33590240 -0.45638962 0.16233447 -0.35548122
#> [157] -0.22254275 0.09272119 0.06908381 0.60932496 0.56864941 0.47628091
#> [163] -0.90727881 -0.14366447 0.56864941 -0.45638962 0.33590240 -0.90727881
#> [169] -0.27237616 0.21063705 -0.28634532 0.33590240 -0.59024238 0.41045950
#> [175] -0.73131336 0.56864941 -0.45638962 0.23581645 0.12337118 -0.17968128
#> [181] 0.60932496 0.12337118 0.09272119 0.19059149 -0.59024238 -0.51067938
#> [187] 0.12337118 -0.35548122 -0.11398653 0.26868664 -0.32877157 0.48932062
#> [193] 0.26868664 -0.14366447 0.09272119 0.41045950 -0.58954050 -0.66409760
#> [199] 0.21063705 0.54361038 -0.32877157 0.41045950 -0.22606643 0.21063705
#> [205] 0.12337118 -0.73131336 0.26868664 -0.45638962 0.21063705 -0.39067504
#> [211] -0.59024238 0.60932496 0.77393357 -0.52371909 -0.17968128 -0.28634532
#> [217] 0.26868664 0.21063705 0.06908381 0.26868664 0.40975762 -0.39067504
#> [223] -0.39067504 -0.73131336 -0.39067504 0.56864941 0.26868664 0.48932062
#> [229] 0.41045950 -0.52371909 0.64451878 0.09272119 0.12337118 0.64451878
#> [235] 0.16233447 -0.73131336 0.41045950 -0.93091619 -0.32877157 0.09272119
#> [241] 0.26868664 -0.65365167 0.33590240 0.54361038 0.48932062 -0.32877157
#> [247] -0.45638962 -0.58954050 0.40975762 -0.32877157 0.16233447 0.48932062
#> [253] 0.21063705 -0.66409760 -0.59024238 -0.59024238 0.33590240 0.54361038
#> [259] 0.28794197 0.21063705 -0.08992418 0.34634833 -0.35548122 -0.27237616
#> [265] 0.33590240 -0.58954050 0.16233447 -0.45638962 0.23581645 -0.14366447
#> [271] -0.45638962 -0.66409760 0.21063705 -0.35548122 0.09272119 -0.32877157
#> [277] -0.52371909 -0.17968128 0.64451878 -0.52371909 -0.27237616 0.26868664
#> [283] 0.41045950 -0.43135059 -0.59024238 -0.76418355 0.48932062 -0.78936295
#> [289] 0.06908381 -0.43135059 -0.43135059 -0.27237616 0.67122843 -0.58954050
#> [295] 0.54361038 0.16233447 0.40975762 -0.51067938 0.40975762 0.16233447
#> [301] 0.40975762 -0.39067504 -0.35548122 -0.22606643 -0.66409760 0.09272119
#> [307] 0.21063705 0.09272119 0.56864941 -0.39067504 -0.66409760 -0.27237616
#> [313] -0.45638962 -0.52371909 0.15230486 0.21063705 -0.52371909 -0.65365167
#> [319] 0.41045950 -0.32877157 0.72762384 0.47628091 0.26868664 -0.07066939
#> [325] 0.34634833 0.26868664 -0.35548122 0.21063705 0.26868664 -0.14366447
#> [331] -0.32877157 -0.39067504 -0.45638962 0.72762384 0.12337118 0.48932062
#> [337] -0.58954050 0.54361038 0.33590240 -0.39067504 -0.66409760 0.40975762
#> [343] 0.21063705 -0.73131336 0.48932062 0.48932062 0.54361038 0.56864941
#> [349] 0.16233447 -0.27237616 -0.17968128 0.16233447 -0.58954050 0.33590240
#> [355] -0.28634532 0.16233447 -0.52371909 -0.27237616 -0.28634532 0.56864941
#> [361] 0.23581645 0.72762384 -0.52371909 -0.28634532 0.12337118 -0.45638962
#> [367] -0.35548122 -0.32877157 -0.27237616 -0.59024238 -0.35548122 -0.52371909
#> [373] 0.77745725 -0.43135059 0.41045950 0.67122843 -0.14366447 -0.73131336
#> [379] 0.48932062 0.21063705 0.16233447 -0.52371909 0.56864941 -0.58954050
#> [385] -0.66409760 0.06908381 -0.51067938 0.03765529 -0.35548122 -0.11398653
#> [391] -0.32877157 -0.39067504 0.28794197 -0.52371909 -0.51067938 0.60932496
#> [397] -0.43135059 0.19059149 -0.80940851 0.16233447 -0.22606643 -0.32877157
#> [403] -0.45638962 -0.83766553 0.09272119 -0.39067504 0.47628091 0.40975762
#> [409] 0.54361038 0.19059149 0.34634833 0.54361038 0.21063705 -0.43135059
#> [415] -0.58954050 -0.17968128 0.47628091 -0.28634532 0.56864941 0.88601347
#> [421] -0.32877157 0.34634833 -0.45638962 -0.45638962 0.47628091 -0.35548122
#> [427] -0.65365167 0.34634833 -0.52371909 0.48932062 -0.39067504 0.54361038
#> [433] 0.48932062 0.16233447 -0.32877157 0.23581645 0.21063705 0.72762384
#> [439] 0.77393357 -0.52371909 0.40975762 0.47628091 0.26868664 -0.22254275
#> [445] -0.32877157 0.21063705 -0.65365167 -0.65365167 -0.17968128 -0.32877157
#> [451] 0.40975762 -0.14366447 0.19059149 0.47628091 0.48932062 0.28794197
#> [457] 0.47628091 0.40975762 0.67122843 0.26868664 0.47628091 0.40975762
#> [463] -0.71205803 -0.78936295 0.82449990 0.72762384 -0.52371909 0.26868664
#> [469] -0.59024238 0.34634833 -0.58954050 0.33590240 -0.32877157 -0.51067938
#> [475] 0.21063705 0.26868664 -0.35548122 -0.52371909 -0.52371909 0.26868664
#> [481] 0.16233447 -0.59024238 0.21063705 0.26868664 0.48932062 -0.32877157
#> [487] 0.21063705 -0.66409760 -0.45638962 0.34634833 -0.73131336 -0.22254275
#> [493] 0.77745725 -0.32877157 -0.51067938 0.82031872 0.71365468 0.40975762
#> [499] -0.51067938 0.23581645 -0.83766553 -0.22606643 -0.39067504 0.67122843
#> [505] -0.51067938 0.56864941 0.67122843 -0.45638962 0.67122843 0.67122843
#> [511] -0.32877157 -0.13443718 -0.17550010 0.33590240 -0.71205803 -0.28634532
#> [517] -0.39067504 0.56864941 -0.27237616 0.47628091 0.41045950 0.47628091
#> [523] 0.12055985 -0.76418355 0.47628091 0.34634833 0.12337118 -0.59024238
#> [529] -0.27237616 -0.83766553 0.16233447 -0.59024238 -0.39067504 0.56864941
#> [535] 0.67122843 0.33590240 0.33590240 0.26868664 0.48932062 0.47628091
#> [541] -0.27237616 -0.39067504 0.34634833 -0.35548122 0.48932062 0.26868664
#> [547] -0.52371909 -0.45638962 -0.39067504 0.77745725 -0.45638962 -0.22254275
#> [553] 0.26868664 0.54361038 0.64451878 -0.45638962 0.34634833 -0.27237616
#> [559] 0.33590240 0.47628091 0.16233447 -0.22606643 0.48932062 0.21063705
#> [565] 0.54361038 0.40975762 -0.27237616 -0.73131336 0.09272119 0.56864941
#> [571] -0.51067938 -0.71205803 -0.39067504 0.54361038 0.48932062 -0.52371909
#> [577] -0.39067504 0.26868664 0.85633553 -0.39067504 0.56864941 -0.17968128
#> [583] 0.48932062 -0.51067938 0.47628091 -0.27237616 -0.45638962 -0.11398653
#> [589] -0.78936295 0.54361038 0.12337118 -0.17550010 0.64451878 0.41045950
#> [595] -0.51067938 0.48932062 0.54361038 -0.22254275 0.40975762 -0.66409760
#> [601] 0.72762384 -0.22606643 0.60932496 0.72762384 -0.32877157 0.26868664
#> [607] -0.83766553 -0.73131336 0.23581645 0.40975762 0.33590240 -0.59024238
#> [613] -0.58954050 0.23581645 0.54361038 -0.11398653 -0.51067938 -0.11398653
#> [619] -0.73131336 -0.28634532 -0.45638962 0.82031872 -0.45638962 -0.45638962
#> [625] -0.39067504 -0.17968128 -0.78936295 0.56864941 0.12337118 0.26868664
#> [631] -0.22254275 -0.66409760 0.41045950 0.21063705 0.26868664 0.16233447
#> [637] 0.33590240 0.26868664 0.41045950 0.12337118 -0.43135059 -0.58954050
#> [643] 0.41045950 -0.59024238 0.77745725 -0.35548122 0.67122843 0.64451878
#> [649] -0.43135059 0.48932062 -0.84769514 -0.43135059 0.26868664 0.26868664
#> [655] -0.66409760 -0.45638962 -0.78936295 0.26868664 -0.17968128 0.26868664
#> [661] -0.32877157 0.21063705 -0.27237616 -0.32877157 0.67122843 0.03765529
#> [667] -0.58954050 0.33590240 0.71365468 -0.22254275 -0.39067504 0.40975762
#> [673] -0.45638962 -0.32877157 0.26868664 -0.59024238 -0.17968128 -0.45638962
#> [679] -0.32877157 0.54361038 -0.14366447 -0.43135059 -0.32877157 -0.11398653
#> [685] 0.33590240 -0.87662882 -0.45638962 0.19059149 -0.32877157 0.60932496
#> [691] 0.16233447 -0.52371909 0.48932062 -0.52371909 -0.22606643 0.21063705
#> [697] 0.21063705 0.48932062 0.72762384 0.21063705 0.77393357 0.72762384
#> [703] 0.09272119 -0.27237616 0.60932496 0.71365468 -0.78936295 -0.43135059
#> [709] 0.56864941 0.67122843 0.88601347 0.12337118 0.21063705 0.41045950
#> [715] -0.52371909 -0.52371909 0.41045950 -0.17968128 -0.32877157 -0.51067938
#> [721] 0.47628091 0.56864941 -0.51067938 -0.58954050 -0.83766553 -0.71205803
#> [727] -0.17968128 -0.39067504 -0.52371909 0.33590240 -0.39067504 -0.73131336
#> [733] -0.58954050 0.60932496 -0.65365167 0.60932496 0.26868664 -0.22254275
#> [739] -0.35548122 0.19059149 -0.52371909 -0.59024238 0.19059149 0.26868664
#> [745] -0.32877157 0.47628091 -0.22606643 -0.87662882 0.28794197 -0.28634532
#> [751] 0.28794197 -0.59024238 -0.59024238 0.33590240 -0.51067938 0.26868664
#> [757] -0.43135059 0.60932496 -0.66409760 0.06908381 -0.22254275 0.60932496
#> [763] 0.34634833 -0.14366447 0.72762384 -0.32877157 -0.51067938 -0.58954050
#> [769] -0.51067938 -0.35548122 -0.35548122 0.12337118 0.26868664 -0.52371909
#> [775] -0.32877157 -0.35548122 0.34634833 0.26868664 -0.39067504 0.16233447
#> [781] 0.33590240 0.64451878 0.21063705 -0.39067504 -0.43135059 0.67122843
#> [787] -0.27237616 0.48932062 0.48932062 0.40975762 0.71365468 0.16233447
#> [793] -0.51067938 0.26868664 -0.17968128 0.48932062 0.54361038 -0.58954050
#> [799] -0.35548122 -0.27237616 0.41045950 -0.58954050 0.21063705 0.19059149
#> [805] 0.28794197 -0.73131336 -0.32877157 -0.43135059 -0.27237616 0.19059149
#> [811] 0.16233447 -0.52371909 -0.71205803 0.21063705 -0.27237616 -0.43135059
#> [817] -0.22254275 -0.52371909 -0.45638962 -0.17968128 -0.78936295 0.26868664
#> [823] 0.21063705 0.12337118 0.12337118 0.60932496 0.56864941 -0.17968128
#> [829] -0.51067938 -0.45638962 -0.22254275 -0.22606643 -0.52371909 0.47628091
#> [835] -0.32877157 -0.22254275 0.54361038 -0.35548122 -0.83766553 0.40975762
#> [841] 0.33590240 0.56864941 -0.73131336 -0.28634532 -0.59024238 -0.39067504
#> [847] -0.27237616 -0.27237616 0.26868664 -0.14366447 -0.51067938 0.56864941
#> [853] -0.58954050 -0.22606643 0.41045950 -0.39067504 -0.52371909 0.41045950
#> [859] 0.47628091 -0.73131336 0.47628091 0.26868664 -0.65365167 0.23581645
#> [865] 0.54361038 -0.59024238 0.19059149 0.47628091 0.41045950 -0.27237616
#> [871] 0.41045950 0.12337118 0.33590240 0.60932496 0.09272119 0.26868664
#> [877] 0.41045950 0.64451878 0.54361038 0.34634833 -0.39067504 -0.17968128
#> [883] 0.48932062 0.12337118 0.41045950 0.54361038 0.33590240 0.41045950
#> [889] -0.39067504 0.21063705 0.56864941 -0.17968128 0.56864941 0.34634833
#> [895] 0.40975762 0.54361038 -0.32877157 0.19059149 -0.65365167 0.33590240
#> [901] -0.58954050 -0.32877157 0.23581645 0.67122843 0.26868664 -0.27237616
#> [907] 0.26868664 0.40975762 0.67122843 0.21063705 0.33590240 -0.39067504
#> [913] -0.59024238 0.41045950 -0.39067504 0.21063705 0.60932496 0.54361038
#> [919] 0.40975762 0.12337118 -0.59024238 0.64451878 -0.43135059 -0.51067938
#> [925] 0.33590240 -0.17968128 0.41045950 0.40975762 0.48932062 -0.59024238
#> [931] 0.26868664 0.23581645 0.41045950 -0.43135059 -0.58954050 -0.39067504
#> [937] -0.59024238 -0.71205803 -0.17968128 -0.73131336 -0.52371909 -0.43135059
#> [943] -0.39067504 0.12337118 -0.32877157 -0.59024238 -0.17968128 -0.22606643
#> [949] 0.41045950 0.48932062 0.40975762 0.47628091 -0.39067504 0.12337118
#> [955] 0.33590240 0.82031872 -0.51067938 -0.52371909 0.77745725 0.16233447
#> [961] 0.23581645 -0.27237616 0.82031872 -0.66409760 -0.22254275 -0.22254275
#> [967] -0.45638962 0.34634833 0.54361038 0.72762384 0.60932496 -0.14366447
#> [973] -0.58954050 -0.71205803 -0.39067504 0.33590240 -0.71205803 0.28794197
#> [979] 0.33590240 -0.73131336 0.34634833 0.09272119 -0.58954050 -0.78936295
#> [985] 0.77745725 -0.66409760 -0.58954050 -0.27237616 0.47628091 0.40975762
#> [991] -0.07066939 0.40975762 0.47628091 -0.39067504 0.26868664 -0.35548122
#> [997] -0.90727881 -0.39067504 0.12337118 0.33590240
#> [ reached 'max' / getOption("max.print") -- omitted 1000 entries ]
#> attr(,"label")
#> [1] "Residuals"
# iteratively reweighted least squares for 2PL model
M <- formulaNLR(model = "2PL", parameterization = "logistic")
(fit_irls <- estimNLR(
y = y, match = match, group = group,
formula = M$M1$formula, method = "irls"
))
#> Nonlinear regression model
#>
#> Model: y ~ exp(x + g + x:g) / (1 + exp(x + g + x:g))
#>
#> Coefficients:
#> (Intercept) x g x:g
#> 0.5503 0.9941 -0.8388 -0.1536
#>
#> Maximum likelihood estimation using the iteratively reweighted least squares algorithm
#> Converged after 4 iterations
coef(fit_irls)
#> (Intercept) x g x:g
#> 0.5503440 0.9940975 -0.8387766 -0.1535927
logLik(fit_irls)
#> 'log Lik.' -1192.331 (df=4)
vcov(fit_irls)
#> (Intercept) x g x:g
#> (Intercept) 0.005266250 0.001165077 -0.0052662505 -0.0011650775
#> x 0.001165077 0.007010056 -0.0011650775 -0.0070100558
#> g -0.005266250 -0.001165077 0.0100000836 0.0006504587
#> x:g -0.001165077 -0.007010056 0.0006504587 0.0130723680
fitted(fit_irls)
#> 1 2 3 4 5 6 7
#> 0.45487411 0.76352613 0.87628488 0.22037531 0.78877573 0.28435576 0.52239129
#> 8 9 10 11 12 13 14
#> 0.42976528 0.78877573 0.76352613 0.83721296 0.71125529 0.45487411 0.50931523
#> 15 16 17 18 19 20 21
#> 0.73056430 0.35368440 0.58839620 0.71125529 0.45487411 0.32690028 0.42976528
#> 22 23 24 25 26 27 28
#> 0.80887717 0.87628488 0.83721296 0.66316115 0.50931523 0.76352613 0.50931523
#> 29 30 31 32 33 34 35
#> 0.71125529 0.27034765 0.50931523 0.65268611 0.78877573 0.32690028 0.45487411
#> 36 37 38 39 40 41 42
#> 0.52239129 0.66316115 0.83721296 0.50931523 0.58910004 0.27034765 0.50931523
#> 43 44 45 46 47 48 49
#> 0.50931523 0.78877573 0.78877573 0.45487411 0.32690028 0.50931523 0.22037531
#> 50 51 52 53 54 55 56
#> 0.52239129 0.52239129 0.27034765 0.14127713 0.52239129 0.32690028 0.58839620
#> 57 58 59 60 61 62 63
#> 0.32690028 0.52239129 0.52239129 0.52239129 0.87910405 0.66316115 0.32690028
#> 64 65 66 67 68 69 70
#> 0.22037531 0.65268611 0.73056430 0.22037531 0.73056430 0.08738702 0.93072359
#> 71 72 73 74 75 76 77
#> 0.42976528 0.22037531 0.45487411 0.58839620 0.50931523 0.22037531 0.65268611
#> 78 79 80 81 82 83 84
#> 0.22390881 0.32690028 0.50931523 0.52239129 0.58839620 0.22037531 0.35368440
#> 85 86 87 88 89 90 91
#> 0.50931523 0.65268611 0.28435576 0.35368440 0.45487411 0.73056430 0.28435576
#> 92 93 94 95 96 97 98
#> 0.71125529 0.45487411 0.71125529 0.27034765 0.22037531 0.38897634 0.83721296
#> 99 100 101 102 103 104 105
#> 0.27034765 0.84727053 0.94872579 0.52239129 0.52239129 0.66316115 0.38897634
#> 106 107 108 109 110 111 112
#> 0.17320152 0.78877573 0.78877573 0.66316115 0.14127713 0.65268611 0.45487411
#> 113 114 115 116 117 118 119
#> 0.38897634 0.83721296 0.32690028 0.58839620 0.32690028 0.87628488 0.22037531
#> 120 121 122 123 124 125 126
#> 0.45487411 0.76352613 0.45487411 0.27034765 0.83721296 0.27034765 0.50931523
#> 127 128 129 130 131 132 133
#> 0.27034765 0.22390881 0.27034765 0.28435576 0.45487411 0.42976528 0.42976528
#> 134 135 136 137 138 139 140
#> 0.83721296 0.38897634 0.38897634 0.13202412 0.58910004 0.73056430 0.83721296
#> 141 142 143 144 145 146 147
#> 0.38897634 0.17739435 0.28435576 0.78877573 0.50931523 0.66316115 0.90702032
#> 148 149 150 151 152 153 154
#> 0.73056430 0.22037531 0.32690028 0.27034765 0.22037531 0.66316115 0.45487411
#> 155 156 157 158 159 160 161
#> 0.83721296 0.35368440 0.22037531 0.90702032 0.93072359 0.38897634 0.42976528
#> 162 163 164 165 166 167 168
#> 0.52239129 0.90702032 0.14127713 0.42976528 0.45487411 0.66316115 0.90702032
#> 169 170 171 172 173 174 175
#> 0.27034765 0.78877573 0.28435576 0.66316115 0.58910004 0.58839620 0.73056430
#> 176 177 178 179 180 181 182
#> 0.42976528 0.45487411 0.76352613 0.87628488 0.17739435 0.38897634 0.87628488
#> 183 184 185 186 187 188 189
#> 0.90702032 0.80887717 0.58910004 0.50931523 0.87628488 0.35368440 0.11151645
#> 190 191 192 193 194 195 196
#> 0.73056430 0.32690028 0.50931523 0.73056430 0.14127713 0.90702032 0.58839620
#> 197 198 199 200 201 202 203
#> 0.58839620 0.66316115 0.78877573 0.45487411 0.32690028 0.58839620 0.22390881
#> 204 205 206 207 208 209 210
#> 0.78877573 0.87628488 0.73056430 0.73056430 0.45487411 0.78877573 0.38897634
#> 211 212 213 214 215 216 217
#> 0.58910004 0.38897634 0.22390881 0.52239129 0.17739435 0.28435576 0.73056430
#> 218 219 220 221 222 223 224
#> 0.78877573 0.93072359 0.73056430 0.58910004 0.38897634 0.38897634 0.73056430
#> 225 226 227 228 229 230 231
#> 0.38897634 0.42976528 0.73056430 0.50931523 0.58839620 0.52239129 0.35368440
#> 232 233 234 235 236 237 238
#> 0.90702032 0.87628488 0.35368440 0.83721296 0.73056430 0.58839620 0.93072359
#> 239 240 241 242 243 244 245
#> 0.32690028 0.90702032 0.73056430 0.65268611 0.66316115 0.45487411 0.50931523
#> 246 247 248 249 250 251 252
#> 0.32690028 0.45487411 0.58839620 0.58910004 0.32690028 0.83721296 0.50931523
#> 253 254 255 256 257 258 259
#> 0.78877573 0.66316115 0.58910004 0.58910004 0.66316115 0.45487411 0.71125529
#> 260 261 262 263 264 265 266
#> 0.78877573 0.08738702 0.65268611 0.35368440 0.27034765 0.66316115 0.58839620
#> 267 268 269 270 271 272 273
#> 0.83721296 0.45487411 0.76352613 0.14127713 0.45487411 0.66316115 0.78877573
#> 274 275 276 277 278 279 280
#> 0.35368440 0.90702032 0.32690028 0.52239129 0.17739435 0.35368440 0.52239129
#> 281 282 283 284 285 286 287
#> 0.27034765 0.73056430 0.58839620 0.42976528 0.58910004 0.76352613 0.50931523
#> 288 289 290 291 292 293 294
#> 0.78877573 0.93072359 0.42976528 0.42976528 0.27034765 0.32690028 0.58839620
#> 295 296 297 298 299 300 301
#> 0.45487411 0.83721296 0.58910004 0.50931523 0.58910004 0.83721296 0.58910004
#> 302 303 304 305 306 307 308
#> 0.38897634 0.35368440 0.22390881 0.66316115 0.90702032 0.78877573 0.90702032
#> 309 310 311 312 313 314 315
#> 0.42976528 0.38897634 0.66316115 0.27034765 0.45487411 0.52239129 0.84727053
#> 316 317 318 319 320 321 322
#> 0.78877573 0.52239129 0.65268611 0.58839620 0.32690028 0.27034765 0.52239129
#> 323 324 325 326 327 328 329
#> 0.73056430 0.06807856 0.65268611 0.73056430 0.35368440 0.78877573 0.73056430
#> 330 331 332 333 334 335 336
#> 0.14127713 0.32690028 0.38897634 0.45487411 0.27034765 0.87628488 0.50931523
#> 337 338 339 340 341 342 343
#> 0.58839620 0.45487411 0.66316115 0.38897634 0.66316115 0.58910004 0.78877573
#> 344 345 346 347 348 349 350
#> 0.73056430 0.50931523 0.50931523 0.45487411 0.42976528 0.83721296 0.27034765
#> 351 352 353 354 355 356 357
#> 0.17739435 0.83721296 0.58839620 0.66316115 0.28435576 0.83721296 0.52239129
#> 358 359 360 361 362 363 364
#> 0.27034765 0.28435576 0.42976528 0.76352613 0.27034765 0.52239129 0.28435576
#> 365 366 367 368 369 370 371
#> 0.87628488 0.45487411 0.35368440 0.32690028 0.27034765 0.58910004 0.35368440
#> 372 373 374 375 376 377 378
#> 0.52239129 0.22037531 0.42976528 0.58839620 0.32690028 0.14127713 0.73056430
#> 379 380 381 382 383 384 385
#> 0.50931523 0.78877573 0.83721296 0.52239129 0.42976528 0.58839620 0.66316115
#> 386 387 388 389 390 391 392
#> 0.93072359 0.50931523 0.96223973 0.35368440 0.11151645 0.32690028 0.38897634
#> 393 394 395 396 397 398 399
#> 0.71125529 0.52239129 0.50931523 0.38897634 0.42976528 0.80887717 0.80887717
#> 400 401 402 403 404 405 406
#> 0.83721296 0.22390881 0.32690028 0.45487411 0.83721296 0.90702032 0.38897634
#> 407 408 409 410 411 412 413
#> 0.52239129 0.58910004 0.45487411 0.80887717 0.65268611 0.45487411 0.78877573
#> 414 415 416 417 418 419 420
#> 0.42976528 0.58839620 0.17739435 0.52239129 0.28435576 0.42976528 0.11151645
#> 421 422 423 424 425 426 427
#> 0.32690028 0.65268611 0.45487411 0.45487411 0.52239129 0.35368440 0.65268611
#> 428 429 430 431 432 433 434
#> 0.65268611 0.52239129 0.50931523 0.38897634 0.45487411 0.50931523 0.83721296
#> 435 436 437 438 439 440 441
#> 0.32690028 0.76352613 0.78877573 0.27034765 0.22390881 0.52239129 0.58910004
#> 442 443 444 445 446 447 448
#> 0.52239129 0.73056430 0.22037531 0.32690028 0.78877573 0.65268611 0.65268611
#> 449 450 451 452 453 454 455
#> 0.17739435 0.32690028 0.58910004 0.14127713 0.80887717 0.52239129 0.50931523
#> 456 457 458 459 460 461 462
#> 0.71125529 0.52239129 0.58910004 0.32690028 0.73056430 0.52239129 0.58910004
#> 463 464 465 466 467 468 469
#> 0.71125529 0.78877573 0.17320152 0.27034765 0.52239129 0.73056430 0.58910004
#> 470 471 472 473 474 475 476
#> 0.65268611 0.58839620 0.66316115 0.32690028 0.50931523 0.78877573 0.73056430
#> 477 478 479 480 481 482 483
#> 0.35368440 0.52239129 0.52239129 0.73056430 0.83721296 0.58910004 0.78877573
#> 484 485 486 487 488 489 490
#> 0.73056430 0.50931523 0.32690028 0.78877573 0.66316115 0.45487411 0.65268611
#> 491 492 493 494 495 496 497
#> 0.73056430 0.22037531 0.22037531 0.32690028 0.50931523 0.17739435 0.28435576
#> 498 499 500 501 502 503 504
#> 0.58910004 0.50931523 0.76352613 0.83721296 0.22390881 0.38897634 0.32690028
#> 505 506 507 508 509 510 511
#> 0.50931523 0.42976528 0.32690028 0.45487411 0.32690028 0.32690028 0.32690028
#> 512 513 514 515 516 517 518
#> 0.13202412 0.17320152 0.66316115 0.71125529 0.28435576 0.38897634 0.42976528
#> 519 520 521 522 523 524 525
#> 0.27034765 0.52239129 0.58839620 0.52239129 0.87910405 0.76352613 0.52239129
#> 526 527 528 529 530 531 532
#> 0.65268611 0.87628488 0.58910004 0.27034765 0.83721296 0.83721296 0.58910004
#> 533 534 535 536 537 538 539
#> 0.38897634 0.42976528 0.32690028 0.66316115 0.66316115 0.73056430 0.50931523
#> 540 541 542 543 544 545 546
#> 0.52239129 0.27034765 0.38897634 0.65268611 0.35368440 0.50931523 0.73056430
#> 547 548 549 550 551 552 553
#> 0.52239129 0.45487411 0.38897634 0.22037531 0.45487411 0.22037531 0.73056430
#> 554 555 556 557 558 559 560
#> 0.45487411 0.35368440 0.45487411 0.65268611 0.27034765 0.66316115 0.52239129
#> 561 562 563 564 565 566 567
#> 0.83721296 0.22390881 0.50931523 0.78877573 0.45487411 0.58910004 0.27034765
#> 568 569 570 571 572 573 574
#> 0.73056430 0.90702032 0.42976528 0.50931523 0.71125529 0.38897634 0.45487411
#> 575 576 577 578 579 580 581
#> 0.50931523 0.52239129 0.38897634 0.73056430 0.14127713 0.38897634 0.42976528
#> 582 583 584 585 586 587 588
#> 0.17739435 0.50931523 0.50931523 0.52239129 0.27034765 0.45487411 0.11151645
#> 589 590 591 592 593 594 595
#> 0.78877573 0.45487411 0.87628488 0.17320152 0.35368440 0.58839620 0.50931523
#> 596 597 598 599 600 601 602
#> 0.50931523 0.45487411 0.22037531 0.58910004 0.66316115 0.27034765 0.22390881
#> 603 604 605 606 607 608 609
#> 0.38897634 0.27034765 0.32690028 0.73056430 0.83721296 0.73056430 0.76352613
#> 610 611 612 613 614 615 616
#> 0.58910004 0.66316115 0.58910004 0.58839620 0.76352613 0.45487411 0.11151645
#> 617 618 619 620 621 622 623
#> 0.50931523 0.11151645 0.73056430 0.28435576 0.45487411 0.17739435 0.45487411
#> 624 625 626 627 628 629 630
#> 0.45487411 0.38897634 0.17739435 0.78877573 0.42976528 0.87628488 0.73056430
#> 631 632 633 634 635 636 637
#> 0.22037531 0.66316115 0.58839620 0.78877573 0.73056430 0.83721296 0.66316115
#> 638 639 640 641 642 643 644
#> 0.73056430 0.58839620 0.87628488 0.42976528 0.58839620 0.58839620 0.58910004
#> 645 646 647 648 649 650 651
#> 0.22037531 0.35368440 0.32690028 0.35368440 0.42976528 0.50931523 0.84727053
#> 652 653 654 655 656 657 658
#> 0.42976528 0.73056430 0.73056430 0.66316115 0.45487411 0.78877573 0.73056430
#> 659 660 661 662 663 664 665
#> 0.17739435 0.73056430 0.32690028 0.78877573 0.27034765 0.32690028 0.32690028
#> 666 667 668 669 670 671 672
#> 0.96223973 0.58839620 0.66316115 0.28435576 0.22037531 0.38897634 0.58910004
#> 673 674 675 676 677 678 679
#> 0.45487411 0.32690028 0.73056430 0.58910004 0.17739435 0.45487411 0.32690028
#> 680 681 682 683 684 685 686
#> 0.45487411 0.14127713 0.42976528 0.32690028 0.11151645 0.66316115 0.87628488
#> 687 688 689 690 691 692 693
#> 0.45487411 0.80887717 0.32690028 0.38897634 0.83721296 0.52239129 0.50931523
#> 694 695 696 697 698 699 700
#> 0.52239129 0.22390881 0.78877573 0.78877573 0.50931523 0.27034765 0.78877573
#> 701 702 703 704 705 706 707
#> 0.22390881 0.27034765 0.90702032 0.27034765 0.38897634 0.28435576 0.78877573
#> 708 709 710 711 712 713 714
#> 0.42976528 0.42976528 0.32690028 0.11151645 0.87628488 0.78877573 0.58839620
#> 715 716 717 718 719 720 721
#> 0.52239129 0.52239129 0.58839620 0.17739435 0.32690028 0.50931523 0.52239129
#> 722 723 724 725 726 727 728
#> 0.42976528 0.50931523 0.58839620 0.83721296 0.71125529 0.17739435 0.38897634
#> 729 730 731 732 733 734 735
#> 0.52239129 0.66316115 0.38897634 0.73056430 0.58839620 0.38897634 0.65268611
#> 736 737 738 739 740 741 742
#> 0.38897634 0.73056430 0.22037531 0.35368440 0.80887717 0.52239129 0.58910004
#> 743 744 745 746 747 748 749
#> 0.80887717 0.73056430 0.32690028 0.52239129 0.22390881 0.87628488 0.71125529
#> 750 751 752 753 754 755 756
#> 0.28435576 0.71125529 0.58910004 0.58910004 0.66316115 0.50931523 0.73056430
#> 757 758 759 760 761 762 763
#> 0.42976528 0.38897634 0.66316115 0.93072359 0.22037531 0.38897634 0.65268611
#> 764 765 766 767 768 769 770
#> 0.14127713 0.27034765 0.32690028 0.50931523 0.58839620 0.50931523 0.35368440
#> 771 772 773 774 775 776 777
#> 0.35368440 0.87628488 0.73056430 0.52239129 0.32690028 0.35368440 0.65268611
#> 778 779 780 781 782 783 784
#> 0.73056430 0.38897634 0.83721296 0.66316115 0.35368440 0.78877573 0.38897634
#> 785 786 787 788 789 790 791
#> 0.42976528 0.32690028 0.27034765 0.50931523 0.50931523 0.58910004 0.28435576
#> 792 793 794 795 796 797 798
#> 0.83721296 0.50931523 0.73056430 0.17739435 0.50931523 0.45487411 0.58839620
#> 799 800 801 802 803 804 805
#> 0.35368440 0.27034765 0.58839620 0.58839620 0.78877573 0.80887717 0.71125529
#> 806 807 808 809 810 811 812
#> 0.73056430 0.32690028 0.42976528 0.27034765 0.80887717 0.83721296 0.52239129
#> 813 814 815 816 817 818 819
#> 0.71125529 0.78877573 0.27034765 0.42976528 0.22037531 0.52239129 0.45487411
#> 820 821 822 823 824 825 826
#> 0.17739435 0.78877573 0.73056430 0.78877573 0.87628488 0.87628488 0.38897634
#> 827 828 829 830 831 832 833
#> 0.42976528 0.17739435 0.50931523 0.45487411 0.22037531 0.22390881 0.52239129
#> 834 835 836 837 838 839 840
#> 0.52239129 0.32690028 0.22037531 0.45487411 0.35368440 0.83721296 0.58910004
#> 841 842 843 844 845 846 847
#> 0.66316115 0.42976528 0.73056430 0.28435576 0.58910004 0.38897634 0.27034765
#> 848 849 850 851 852 853 854
#> 0.27034765 0.73056430 0.14127713 0.50931523 0.42976528 0.58839620 0.22390881
#> 855 856 857 858 859 860 861
#> 0.58839620 0.38897634 0.52239129 0.58839620 0.52239129 0.73056430 0.52239129
#> 862 863 864 865 866 867 868
#> 0.73056430 0.65268611 0.76352613 0.45487411 0.58910004 0.80887717 0.52239129
#> 869 870 871 872 873 874 875
#> 0.58839620 0.27034765 0.58839620 0.87628488 0.66316115 0.38897634 0.90702032
#> 876 877 878 879 880 881 882
#> 0.73056430 0.58839620 0.35368440 0.45487411 0.65268611 0.38897634 0.17739435
#> 883 884 885 886 887 888 889
#> 0.50931523 0.87628488 0.58839620 0.45487411 0.66316115 0.58839620 0.38897634
#> 890 891 892 893 894 895 896
#> 0.78877573 0.42976528 0.17739435 0.42976528 0.65268611 0.58910004 0.45487411
#> 897 898 899 900 901 902 903
#> 0.32690028 0.80887717 0.65268611 0.66316115 0.58839620 0.32690028 0.76352613
#> 904 905 906 907 908 909 910
#> 0.32690028 0.73056430 0.27034765 0.73056430 0.58910004 0.32690028 0.78877573
#> 911 912 913 914 915 916 917
#> 0.66316115 0.38897634 0.58910004 0.58839620 0.38897634 0.78877573 0.38897634
#> 918 919 920 921 922 923 924
#> 0.45487411 0.58910004 0.87628488 0.58910004 0.35368440 0.42976528 0.50931523
#> 925 926 927 928 929 930 931
#> 0.66316115 0.17739435 0.58839620 0.58910004 0.50931523 0.58910004 0.73056430
#> 932 933 934 935 936 937 938
#> 0.76352613 0.58839620 0.42976528 0.58839620 0.38897634 0.58910004 0.71125529
#> 939 940 941 942 943 944 945
#> 0.17739435 0.73056430 0.52239129 0.42976528 0.38897634 0.87628488 0.32690028
#> 946 947 948 949 950 951 952
#> 0.58910004 0.17739435 0.22390881 0.58839620 0.50931523 0.58910004 0.52239129
#> 953 954 955 956 957 958 959
#> 0.38897634 0.87628488 0.66316115 0.17739435 0.50931523 0.52239129 0.22037531
#> 960 961 962 963 964 965 966
#> 0.83721296 0.76352613 0.27034765 0.17739435 0.66316115 0.22037531 0.22037531
#> 967 968 969 970 971 972 973
#> 0.45487411 0.65268611 0.45487411 0.27034765 0.38897634 0.14127713 0.58839620
#> 974 975 976 977 978 979 980
#> 0.71125529 0.38897634 0.66316115 0.71125529 0.71125529 0.66316115 0.73056430
#> 981 982 983 984 985 986 987
#> 0.65268611 0.90702032 0.58839620 0.78877573 0.22037531 0.66316115 0.58839620
#> 988 989 990 991 992 993 994
#> 0.27034765 0.52239129 0.58910004 0.06807856 0.58910004 0.52239129 0.38897634
#> 995 996 997 998 999 1000
#> 0.73056430 0.35368440 0.90702032 0.38897634 0.87628488 0.66316115
#> [ reached 'max' / getOption("max.print") -- omitted 1000 entries ]
#> attr(,"label")
#> [1] "Fitted values"
residuals(fit_irls)
#> 1 2 3 4 5 6 7
#> -1.834439 1.309713 1.141181 -1.282668 1.267787 -1.397342 1.914274
#> 8 9 10 11 12 13 14
#> 2.326852 1.267787 1.309713 1.194439 1.405965 -1.834439 -2.037968
#> 15 16 17 18 19 20 21
#> -3.711461 -1.547232 1.699535 1.405965 -1.834439 -1.485664 2.326852
#> 22 23 24 25 26 27 28
#> 1.236282 1.141181 1.194439 1.507929 1.963421 1.309713 -2.037968
#> 29 30 31 32 33 34 35
#> 1.405965 -1.370516 -2.037968 -2.879240 -4.734304 -1.485664 2.198410
#> 36 37 38 39 40 41 42
#> -2.093764 -2.968779 1.194439 1.963421 -2.433682 -1.370516 1.963421
#> 43 44 45 46 47 48 49
#> -2.037968 1.267787 1.267787 -1.834439 -1.485664 1.963421 4.537713
#> 50 51 52 53 54 55 56
#> -2.093764 1.914274 -1.370516 7.078287 -2.093764 3.059037 1.699535
#> 57 58 59 60 61 62 63
#> -1.485664 1.914274 -2.093764 1.914274 1.137522 -2.968779 3.059037
#> 64 65 66 67 68 69 70
#> -1.282668 1.532130 -3.711461 -1.282668 1.368805 -1.095755 1.074433
#> 71 72 73 74 75 76 77
#> -1.753664 -1.282668 2.198410 1.699535 -2.037968 4.537713 1.532130
#> 78 79 80 81 82 83 84
#> -1.288508 -1.485664 1.963421 1.914274 -2.429521 -1.282668 -1.547232
#> 85 86 87 88 89 90 91
#> -2.037968 -2.879240 3.516721 -1.547232 -1.834439 -3.711461 -1.397342
#> 92 93 94 95 96 97 98
#> 1.405965 -1.834439 1.405965 3.698941 -1.282668 2.570850 1.194439
#> 99 100 101 102 103 104 105
#> -1.370516 1.180261 1.054045 1.914274 1.914274 1.507929 -1.636598
#> 106 107 108 109 110 111 112
#> -1.209485 1.267787 -4.734304 1.507929 -1.164520 1.532130 -1.834439
#> 113 114 115 116 117 118 119
#> 2.570850 1.194439 -1.485664 -2.429521 3.059037 1.141181 -1.282668
#> 120 121 122 123 124 125 126
#> 2.198410 1.309713 -1.834439 -1.370516 1.194439 -1.370516 1.963421
#> 127 128 129 130 131 132 133
#> 3.698941 -1.288508 -1.370516 -1.397342 2.198410 -1.753664 -1.753664
#> 134 135 136 137 138 139 140
#> 1.194439 -1.636598 -1.636598 -1.152106 1.697505 1.368805 1.194439
#> 141 142 143 144 145 146 147
#> -1.636598 5.637158 -1.397342 1.267787 1.963421 -2.968779 1.102511
#> 148 149 150 151 152 153 154
#> 1.368805 -1.282668 3.059037 -1.370516 -1.282668 1.507929 -1.834439
#> 155 156 157 158 159 160 161
#> 1.194439 -1.547232 -1.282668 1.102511 1.074433 2.570850 2.326852
#> 162 163 164 165 166 167 168
#> 1.914274 -10.755038 -1.164520 2.326852 -1.834439 1.507929 -10.755038
#> 169 170 171 172 173 174 175
#> -1.370516 1.267787 -1.397342 1.507929 -2.433682 1.699535 -3.711461
#> 176 177 178 179 180 181 182
#> 2.326852 -1.834439 1.309713 1.141181 -1.215649 2.570850 1.141181
#> 183 184 185 186 187 188 189
#> 1.102511 1.236282 -2.433682 -2.037968 1.141181 -1.547232 -1.125513
#> 190 191 192 193 194 195 196
#> 1.368805 -1.485664 1.963421 1.368805 -1.164520 1.102511 1.699535
#> 197 198 199 200 201 202 203
#> -2.429521 -2.968779 1.267787 2.198410 -1.485664 1.699535 -1.288508
#> 204 205 206 207 208 209 210
#> 1.267787 1.141181 -3.711461 1.368805 -1.834439 1.267787 -1.636598
#> 211 212 213 214 215 216 217
#> -2.433682 2.570850 4.466104 -2.093764 -1.215649 -1.397342 1.368805
#> 218 219 220 221 222 223 224
#> 1.267787 1.074433 1.368805 1.697505 -1.636598 -1.636598 -3.711461
#> 225 226 227 228 229 230 231
#> -1.636598 2.326852 1.368805 1.963421 1.699535 -2.093764 2.827379
#> 232 233 234 235 236 237 238
#> 1.102511 1.141181 2.827379 1.194439 -3.711461 1.699535 -14.434929
#> 239 240 241 242 243 244 245
#> -1.485664 1.102511 1.368805 -2.879240 1.507929 2.198410 1.963421
#> 246 247 248 249 250 251 252
#> -1.485664 -1.834439 -2.429521 1.697505 -1.485664 1.194439 1.963421
#> 253 254 255 256 257 258 259
#> 1.267787 -2.968779 -2.433682 -2.433682 1.507929 2.198410 1.405965
#> 260 261 262 263 264 265 266
#> 1.267787 -1.095755 1.532130 -1.547232 -1.370516 1.507929 -2.429521
#> 267 268 269 270 271 272 273
#> 1.194439 -1.834439 1.309713 -1.164520 -1.834439 -2.968779 1.267787
#> 274 275 276 277 278 279 280
#> -1.547232 1.102511 -1.485664 -2.093764 -1.215649 2.827379 -2.093764
#> 281 282 283 284 285 286 287
#> -1.370516 1.368805 1.699535 -1.753664 -2.433682 -4.228797 1.963421
#> 288 289 290 291 292 293 294
#> -4.734304 1.074433 -1.753664 -1.753664 -1.370516 3.059037 -2.429521
#> 295 296 297 298 299 300 301
#> 2.198410 1.194439 1.697505 -2.037968 1.697505 1.194439 1.697505
#> 302 303 304 305 306 307 308
#> -1.636598 -1.547232 -1.288508 -2.968779 1.102511 1.267787 1.102511
#> 309 310 311 312 313 314 315
#> 2.326852 -1.636598 -2.968779 -1.370516 -1.834439 -2.093764 1.180261
#> 316 317 318 319 320 321 322
#> 1.267787 -2.093764 -2.879240 1.699535 -1.485664 3.698941 1.914274
#> 323 324 325 326 327 328 329
#> 1.368805 -1.073052 1.532130 1.368805 -1.547232 1.267787 1.368805
#> 330 331 332 333 334 335 336
#> -1.164520 -1.485664 -1.636598 -1.834439 3.698941 1.141181 1.963421
#> 337 338 339 340 341 342 343
#> -2.429521 2.198410 1.507929 -1.636598 -2.968779 1.697505 1.267787
#> 344 345 346 347 348 349 350
#> -3.711461 1.963421 1.963421 2.198410 2.326852 1.194439 -1.370516
#> 351 352 353 354 355 356 357
#> -1.215649 1.194439 -2.429521 1.507929 -1.397342 1.194439 -2.093764
#> 358 359 360 361 362 363 364
#> -1.370516 -1.397342 2.326852 1.309713 3.698941 -2.093764 -1.397342
#> 365 366 367 368 369 370 371
#> 1.141181 -1.834439 -1.547232 -1.485664 -1.370516 -2.433682 -1.547232
#> 372 373 374 375 376 377 378
#> -2.093764 4.537713 -1.753664 1.699535 3.059037 -1.164520 -3.711461
#> 379 380 381 382 383 384 385
#> 1.963421 1.267787 1.194439 -2.093764 2.326852 -2.429521 -2.968779
#> 386 387 388 389 390 391 392
#> 1.074433 -2.037968 1.039242 -1.547232 -1.125513 -1.485664 -1.636598
#> 393 394 395 396 397 398 399
#> 1.405965 -2.093764 -2.037968 2.570850 -1.753664 1.236282 -5.232237
#> 400 401 402 403 404 405 406
#> 1.194439 -1.288508 -1.485664 -1.834439 -6.142995 1.102511 -1.636598
#> 407 408 409 410 411 412 413
#> 1.914274 1.697505 2.198410 1.236282 1.532130 2.198410 1.267787
#> 414 415 416 417 418 419 420
#> -1.753664 -2.429521 -1.215649 1.914274 -1.397342 2.326852 8.967286
#> 421 422 423 424 425 426 427
#> -1.485664 1.532130 -1.834439 -1.834439 1.914274 -1.547232 -2.879240
#> 428 429 430 431 432 433 434
#> 1.532130 -2.093764 1.963421 -1.636598 2.198410 1.963421 1.194439
#> 435 436 437 438 439 440 441
#> -1.485664 1.309713 1.267787 3.698941 4.466104 -2.093764 1.697505
#> 442 443 444 445 446 447 448
#> 1.914274 1.368805 -1.282668 -1.485664 1.267787 -2.879240 -2.879240
#> 449 450 451 452 453 454 455
#> -1.215649 -1.485664 1.697505 -1.164520 1.236282 1.914274 1.963421
#> 456 457 458 459 460 461 462
#> 1.405965 1.914274 1.697505 3.059037 1.368805 1.914274 1.697505
#> 463 464 465 466 467 468 469
#> -3.463267 -4.734304 5.773621 3.698941 -2.093764 1.368805 -2.433682
#> 470 471 472 473 474 475 476
#> 1.532130 -2.429521 1.507929 -1.485664 -2.037968 1.267787 1.368805
#> 477 478 479 480 481 482 483
#> -1.547232 -2.093764 -2.093764 1.368805 1.194439 -2.433682 1.267787
#> 484 485 486 487 488 489 490
#> 1.368805 1.963421 -1.485664 1.267787 -2.968779 -1.834439 1.532130
#> 491 492 493 494 495 496 497
#> -3.711461 -1.282668 4.537713 -1.485664 -2.037968 5.637158 3.516721
#> 498 499 500 501 502 503 504
#> 1.697505 -2.037968 1.309713 -6.142995 -1.288508 -1.636598 3.059037
#> 505 506 507 508 509 510 511
#> -2.037968 2.326852 3.059037 -1.834439 3.059037 3.059037 -1.485664
#> 512 513 514 515 516 517 518
#> -1.152106 -1.209485 1.507929 -3.463267 -1.397342 -1.636598 2.326852
#> 519 520 521 522 523 524 525
#> -1.370516 1.914274 1.699535 1.914274 1.137522 -4.228797 1.914274
#> 526 527 528 529 530 531 532
#> 1.532130 1.141181 -2.433682 -1.370516 -6.142995 1.194439 -2.433682
#> 533 534 535 536 537 538 539
#> -1.636598 2.326852 3.059037 1.507929 1.507929 1.368805 1.963421
#> 540 541 542 543 544 545 546
#> 1.914274 -1.370516 -1.636598 1.532130 -1.547232 1.963421 1.368805
#> 547 548 549 550 551 552 553
#> -2.093764 -1.834439 -1.636598 4.537713 -1.834439 -1.282668 1.368805
#> 554 555 556 557 558 559 560
#> 2.198410 2.827379 -1.834439 1.532130 -1.370516 1.507929 1.914274
#> 561 562 563 564 565 566 567
#> 1.194439 -1.288508 1.963421 1.267787 2.198410 1.697505 -1.370516
#> 568 569 570 571 572 573 574
#> -3.711461 1.102511 2.326852 -2.037968 -3.463267 -1.636598 2.198410
#> 575 576 577 578 579 580 581
#> 1.963421 -2.093764 -1.636598 1.368805 7.078287 -1.636598 2.326852
#> 582 583 584 585 586 587 588
#> -1.215649 1.963421 -2.037968 1.914274 -1.370516 -1.834439 -1.125513
#> 589 590 591 592 593 594 595
#> -4.734304 2.198410 1.141181 -1.209485 2.827379 1.699535 -2.037968
#> 596 597 598 599 600 601 602
#> 1.963421 2.198410 -1.282668 1.697505 -2.968779 3.698941 -1.288508
#> 603 604 605 606 607 608 609
#> 2.570850 3.698941 -1.485664 1.368805 -6.142995 -3.711461 1.309713
#> 610 611 612 613 614 615 616
#> 1.697505 1.507929 -2.433682 -2.429521 1.309713 2.198410 -1.125513
#> 617 618 619 620 621 622 623
#> -2.037968 -1.125513 -3.711461 -1.397342 -1.834439 5.637158 -1.834439
#> 624 625 626 627 628 629 630
#> -1.834439 -1.636598 -1.215649 -4.734304 2.326852 1.141181 1.368805
#> 631 632 633 634 635 636 637
#> -1.282668 -2.968779 1.699535 1.267787 1.368805 1.194439 1.507929
#> 638 639 640 641 642 643 644
#> 1.368805 1.699535 1.141181 -1.753664 -2.429521 1.699535 -2.433682
#> 645 646 647 648 649 650 651
#> 4.537713 -1.547232 3.059037 2.827379 -1.753664 1.963421 -6.547525
#> 652 653 654 655 656 657 658
#> -1.753664 1.368805 1.368805 -2.968779 -1.834439 -4.734304 1.368805
#> 659 660 661 662 663 664 665
#> -1.215649 1.368805 -1.485664 1.267787 -1.370516 -1.485664 3.059037
#> 666 667 668 669 670 671 672
#> 1.039242 -2.429521 1.507929 3.516721 -1.282668 -1.636598 1.697505
#> 673 674 675 676 677 678 679
#> -1.834439 -1.485664 1.368805 -2.433682 -1.215649 -1.834439 -1.485664
#> 680 681 682 683 684 685 686
#> 2.198410 -1.164520 -1.753664 -1.485664 -1.125513 1.507929 -8.083086
#> 687 688 689 690 691 692 693
#> -1.834439 1.236282 -1.485664 2.570850 1.194439 -2.093764 1.963421
#> 694 695 696 697 698 699 700
#> -2.093764 -1.288508 1.267787 1.267787 1.963421 3.698941 1.267787
#> 701 702 703 704 705 706 707
#> 4.466104 3.698941 1.102511 -1.370516 2.570850 3.516721 -4.734304
#> 708 709 710 711 712 713 714
#> -1.753664 2.326852 3.059037 8.967286 1.141181 1.267787 1.699535
#> 715 716 717 718 719 720 721
#> -2.093764 -2.093764 1.699535 -1.215649 -1.485664 -2.037968 1.914274
#> 722 723 724 725 726 727 728
#> 2.326852 -2.037968 -2.429521 -6.142995 -3.463267 -1.215649 -1.636598
#> 729 730 731 732 733 734 735
#> -2.093764 1.507929 -1.636598 -3.711461 -2.429521 2.570850 -2.879240
#> 736 737 738 739 740 741 742
#> 2.570850 1.368805 -1.282668 -1.547232 1.236282 -2.093764 -2.433682
#> 743 744 745 746 747 748 749
#> 1.236282 1.368805 -1.485664 1.914274 -1.288508 -8.083086 1.405965
#> 750 751 752 753 754 755 756
#> -1.397342 1.405965 -2.433682 -2.433682 1.507929 -2.037968 1.368805
#> 757 758 759 760 761 762 763
#> -1.753664 2.570850 -2.968779 1.074433 -1.282668 2.570850 1.532130
#> 764 765 766 767 768 769 770
#> -1.164520 3.698941 -1.485664 -2.037968 -2.429521 -2.037968 -1.547232
#> 771 772 773 774 775 776 777
#> -1.547232 1.141181 1.368805 -2.093764 -1.485664 -1.547232 1.532130
#> 778 779 780 781 782 783 784
#> 1.368805 -1.636598 1.194439 1.507929 2.827379 1.267787 -1.636598
#> 785 786 787 788 789 790 791
#> -1.753664 3.059037 -1.370516 1.963421 1.963421 1.697505 3.516721
#> 792 793 794 795 796 797 798
#> 1.194439 -2.037968 1.368805 -1.215649 1.963421 2.198410 -2.429521
#> 799 800 801 802 803 804 805
#> -1.547232 -1.370516 1.699535 -2.429521 1.267787 1.236282 1.405965
#> 806 807 808 809 810 811 812
#> -3.711461 -1.485664 -1.753664 -1.370516 1.236282 1.194439 -2.093764
#> 813 814 815 816 817 818 819
#> -3.463267 1.267787 -1.370516 -1.753664 -1.282668 -2.093764 -1.834439
#> 820 821 822 823 824 825 826
#> -1.215649 -4.734304 1.368805 1.267787 1.141181 1.141181 2.570850
#> 827 828 829 830 831 832 833
#> 2.326852 -1.215649 -2.037968 -1.834439 -1.282668 -1.288508 -2.093764
#> 834 835 836 837 838 839 840
#> 1.914274 -1.485664 -1.282668 2.198410 -1.547232 -6.142995 1.697505
#> 841 842 843 844 845 846 847
#> 1.507929 2.326852 -3.711461 -1.397342 -2.433682 -1.636598 -1.370516
#> 848 849 850 851 852 853 854
#> -1.370516 1.368805 -1.164520 -2.037968 2.326852 -2.429521 -1.288508
#> 855 856 857 858 859 860 861
#> 1.699535 -1.636598 -2.093764 1.699535 1.914274 -3.711461 1.914274
#> 862 863 864 865 866 867 868
#> 1.368805 -2.879240 1.309713 2.198410 -2.433682 1.236282 1.914274
#> 869 870 871 872 873 874 875
#> 1.699535 -1.370516 1.699535 1.141181 1.507929 2.570850 1.102511
#> 876 877 878 879 880 881 882
#> 1.368805 1.699535 2.827379 2.198410 1.532130 -1.636598 -1.215649
#> 883 884 885 886 887 888 889
#> 1.963421 1.141181 1.699535 2.198410 1.507929 1.699535 -1.636598
#> 890 891 892 893 894 895 896
#> 1.267787 2.326852 -1.215649 2.326852 1.532130 1.697505 2.198410
#> 897 898 899 900 901 902 903
#> -1.485664 1.236282 -2.879240 1.507929 -2.429521 -1.485664 1.309713
#> 904 905 906 907 908 909 910
#> 3.059037 1.368805 -1.370516 1.368805 1.697505 3.059037 1.267787
#> 911 912 913 914 915 916 917
#> 1.507929 -1.636598 -2.433682 1.699535 -1.636598 1.267787 2.570850
#> 918 919 920 921 922 923 924
#> 2.198410 1.697505 1.141181 -2.433682 2.827379 -1.753664 -2.037968
#> 925 926 927 928 929 930 931
#> 1.507929 -1.215649 1.699535 1.697505 1.963421 -2.433682 1.368805
#> 932 933 934 935 936 937 938
#> 1.309713 1.699535 -1.753664 -2.429521 -1.636598 -2.433682 -3.463267
#> 939 940 941 942 943 944 945
#> -1.215649 -3.711461 -2.093764 -1.753664 -1.636598 1.141181 -1.485664
#> 946 947 948 949 950 951 952
#> -2.433682 -1.215649 -1.288508 1.699535 1.963421 1.697505 1.914274
#> 953 954 955 956 957 958 959
#> -1.636598 1.141181 1.507929 5.637158 -2.037968 -2.093764 4.537713
#> 960 961 962 963 964 965 966
#> 1.194439 1.309713 -1.370516 5.637158 -2.968779 -1.282668 -1.282668
#> 967 968 969 970 971 972 973
#> -1.834439 1.532130 2.198410 3.698941 2.570850 -1.164520 -2.429521
#> 974 975 976 977 978 979 980
#> -3.463267 -1.636598 1.507929 -3.463267 1.405965 1.507929 -3.711461
#> 981 982 983 984 985 986 987
#> 1.532130 1.102511 -2.429521 -4.734304 4.537713 -2.968779 -2.429521
#> 988 989 990 991 992 993 994
#> -1.370516 1.914274 1.697505 -1.073052 1.697505 1.914274 -1.636598
#> 995 996 997 998 999 1000
#> 1.368805 -1.547232 -10.755038 -1.636598 1.141181 1.507929
#> [ reached 'max' / getOption("max.print") -- omitted 1000 entries ]
#> attr(,"label")
#> [1] "Residuals"