Vermunt Jeroen K
Department of Methodology and Statistics, Tilburg University, Tilburg, The Netherlands.
Stat Methods Med Res. 2008 Feb;17(1):33-51. doi: 10.1177/0962280207081238. Epub 2007 Sep 13.
An extension of latent class (LC) and finite mixture models is described for the analysis of hierarchical data sets. As is typical in multilevel analysis, the dependence between lower-level units within higher-level units is dealt with by assuming that certain model parameters differ randomly across higher-level observations. One of the special cases is an LC model in which group-level differences in the logit of belonging to a particular LC are captured with continuous random effects. Other variants are obtained by including random effects in the model for the response variables rather than for the LCs. The variant that receives most attention in this article is an LC model with discrete random effects: higher-level units are clustered based on the likelihood of their members belonging to the various LCs. This yields a model with mixture distributions at two levels, namely at the group and the subject level. This model is illustrated with three rather different empirical examples. The appendix describes an adapted version of the expectation-maximization algorithm that can be used for maximum likelihood estimation, as well as providing setups for estimating the multilevel LC model with generally available software.
本文描述了一种潜在类别（LC）和有限混合模型的扩展方法，用于分析分层数据集。在多水平分析中，通常的做法是通过假设某些模型参数在更高层次的观测中随机变化，来处理更高层次单元内较低层次单元之间的依赖性。其中一种特殊情况是LC模型，在该模型中，属于特定LC的logit的组水平差异通过连续随机效应来捕捉。其他变体是通过在响应变量的模型而非LC的模型中纳入随机效应而获得的。本文中最受关注的变体是具有离散随机效应的LC模型：更高层次的单元根据其成员属于各种LC的可能性进行聚类。这产生了一个在两个层次上具有混合分布的模型，即组水平和个体水平。本文用三个截然不同的实证例子对该模型进行了说明。附录描述了一种可用于最大似然估计的期望最大化算法的改编版本，并提供了使用通用软件估计多水平LC模型的设置。
