Abstract

Nonlinear mixed-effects models allow modeling repeated measures over time. The fixed effects of these models allow incorporating covariates, whereas the random effects reflect the multiple sources of heterogeneity and correlation between and within the units. To estimate the parameters of these models, it is necessary to use iterative processes, which can be done through different approaches, some of which are applied by the statistical software SAS.

In this work, through simulation, we studied the performance of the estimators of a Wood’s incomplete gamma function, obtained through three different methods: linearization method through a Taylor series expansion on the empirical best linear unbiased predictor of random effects, applied by the NLINMIX macro, and expansion around the expected value of random effects, applied by both the NLINMIX macro and the NLMIXED procedure. We also investigated the impact of an incorrect specification of the covariance matrix for random errors.

The linearization method through a Taylor series expansion on the empirical best linear unbiased predictor of random effects, applied by the NLINMIX macro, provided estimators with good performance, approximately normally distributed and with biases lower than those obtained with the other methods, even when the covariance matrix for random errors was incorrectly specified.

摘要

非线性混合效应模型允许对随时间的重复测量进行建模。这些模型的固定效应允许合并协变量，而随机效应反映了单元之间和单元内异质性和相关性的多个来源。为了估计这些模型的参数，有必要使用迭代过程，这可以通过不同的方法来完成，其中一些是由统计软件 SAS 应用的。

在这项工作中，通过模拟，我们研究了 Wood 不完全 gamma 函数的估计器的性能，该函数通过三种不同的方法获得： 通过对随机效应的经验最佳线性无偏预测器进行泰勒级数展开的线性化方法，由 NLINMIX 宏应用，并围绕随机效应的预期值展开，由 NLINMIX 宏和 NLMIXED 过程应用。我们还调查了不正确指定协方差矩阵对随机误差的影响。

通过对随机效应的经验最佳线性无偏预测器进行泰勒级数展开的线性化方法，由 NLINMIX 宏应用，提供了具有良好性能的估计器，近似正态分布且偏差低于使用其他方法获得的那些，即使当协方差随机错误的矩阵被错误地指定。