Type I and type II error under random-effects misspecification in generalized linear mixed models
Type I and type II error under random-effects misspecification in generalized linear mixed models
复制标题
DOI：
10.1111/j.1541-0420.2007.00782.x
复制
发表时间：
2007-12-01
期刊：
影响因子：
1.9
通讯作者：
Molenberghs, Geert
中科院分区：
文献类型：
--
作者：
Litiere, Saskia;Alonso, Ariel;Molenberghs, Geert
广义线性混合模型（glmm）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，该理论假设正确指定了潜在的概率模型。最近的研究表明，从这些模型中获得的结果对于偏离这些模型所基于的假设并不总是可靠的。在本工作中，我们使用逻辑随机截距模型进行模拟，研究了错误指定随机效应分布对glmm中平均结构测试的I型和II型误差的影响。我们发现，根据潜在随机效应分布的形状，错误的规范可以增加或减少测试的能力，并且它可以大大增加I型错误率。此外，我们还发现了一个理论结果，该结果表明，每当固定效应参数的子集（不包括在随机效应结构中）等于零时，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，即使随机效应分布不准确，显著效应也可以被认为是可靠的结果。
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.