Litière Saskia, Alonso Ariel, Molenberghs Geert
Center for Statistics, Hasselt University, Agoralaan, Building D, B3590 Diepenbeek, Belgium.
Biometrics. 2007 Dec;63(4):1038-44. doi: 10.1111/j.1541-0420.2007.00782.x. Epub 2007 Apr 9.
Generalized linear mixed models (GLMMs) have become a frequently used tool for the analysis of non-Gaussian longitudinal data. Estimation is based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. Recent research is showing that the results obtained from these models are not always robust against departures from the assumptions on which these models are based. In the present work we have used simulations with a logistic random-intercept model to study the impact of misspecifying the random-effects distribution on the type I and II errors of the tests for the mean structure in GLMMs. We found that the misspecification can either increase or decrease the power of the tests, depending on the shape of the underlying random-effects distribution, and it can considerably inflate the type I error rate. Additionally, we have found a theoretical result which states that whenever a subset of fixed-effects parameters, not included in the random-effects structure equals zero, the corresponding maximum likelihood estimator will consistently estimate zero. This implies that under certain conditions a significant effect could be considered as a reliable result, even if the random-effects distribution is misspecified.
广义线性混合模型（GLMMs）已成为分析非高斯纵向数据的常用工具。估计基于最大似然理论，该理论假设潜在概率模型已正确设定。最近的研究表明，从这些模型获得的结果并非总是能稳健地抵御偏离其基于的假设。在本研究中，我们使用逻辑随机截距模型进行模拟，以研究错误指定随机效应分布对GLMMs中均值结构检验的I型和II型错误的影响。我们发现，错误指定可能会增加或降低检验功效，这取决于潜在随机效应分布的形状，并且它可能会大幅夸大I型错误率。此外，我们发现了一个理论结果，该结果表明，只要随机效应结构中未包含的固定效应参数的一个子集等于零，相应的最大似然估计量将始终估计为零。这意味着在某些条件下，即使随机效应分布被错误指定，显著效应也可被视为可靠结果。
