Asymptotic Properties of Nonlinear Mixed-E¤ects Models in Large Samples
نویسنده
چکیده
The asymptotic properties of four estimators for nonlinear mixed-e¤ects models are investigated: maximum likelihood estimator (MLE), an estimator based on the ...rst-order approximation to the expectation function (Vonesh and Carter (1992)), the two-stage, and the Lindstrom-Bates (1990) estimators. Two asymptotic situations are considered: (i) when N ! 1 and ni is ...nite, (ii) N ! 1 and minni ! 1; where N is the number of individuals and ni is the number of observations on the ith individual. For a simple one-parameter balanced exponential model only the MLE is consistent when the numbers of observations per individuals, fnig are ...nite. The estimator based on the ...rst-order approximation is always inconsistent, i.e., has a systematic bias. The asymptotic bias for the other three estimators is evaluated when N ! 1 and ni = const. When N ! 1 and minni ! 1; the MLE, Lindstrom-Bates and two-stage estimators are equivalent. The bias for the two-stage estimator based on a second order approximation is evaluated in general nonlinear mixed-e¤ects model, and a bias-corrected version of this estimator is proposed.
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