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Estimation in nonlinear mixed-effects models using heavy-tailed distributions

机译：使用重尾分布的非线性混合效应模型估计

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摘要

Nonlinear mixed-effects models are very useful to analyze repeated measures data and are used in a variety of applications. Normal distributions for random effects and residual errors are usually assumed, but such assumptions make inferences vulnerable to the presence of outliers. In this work, we introduce an extension of a normal nonlinear mixed-effects model considering a subclass of elliptical contoured distributions for both random effects and residual errors. This elliptical subclass, the scale mixtures of normal (SMN) distributions, includes heavy-tailed multivari-ate distributions, such as Student-?, the contaminated normal and slash, among others, and represents an interesting alternative to outliers accommodation maintaining the elegance and simplicity of the maximum likelihood theory. We propose an exact estimation procedure to obtain the maximum likelihood estimates of the fixed-effects and variance components, using a stochastic approximation of the EM algorithm. We compare the performance of the normal and the SMN models with two real data sets.
机译：非线性混合效应模型对于分析重复测量数据非常有用，可用于多种应用中。通常假设随机效应和残留误差为正态分布，但是这种假设使推断容易受到异常值的影响。在这项工作中，我们介绍了考虑随机影响和残留误差的椭圆轮廓分布子类的正态非线性混合效应模型的扩展。此椭圆子类是正态（SMN）分布的比例混合，包括重尾多元分布，例如Student- ?、被污染的正态和斜杠等，是替代异常值的一种有趣替代方法，可以保持优雅和最大似然理论的简单性。我们提出了一种精确的估计程序，使用EM算法的随机逼近来获得固定效应和方差分量的最大似然估计。我们将正常模型和SMN模型的性能与两个真实数据集进行比较。

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