In this paper, an ordinal multilevel latent Markov model based on separate random effects is proposed. In detail, two distinct second-level discrete effects are considered in the model, one affecting the initial probability vector and the other affecting the transition probability matrix of the first-level ordinal latent Markov process. To model these separate effects, we consider a bi-dimensional mixture specification that allows to avoid unverifiable assumptions on the random effect distribution and to derive a two-way clustering of second-level units. Starting from a general model where the two random effects are dependent, we also obtain the independence model as a special case. The proposal is applied to data on the physical health status of a sample of elderly residents grouped into nursing homes. A simulation study assessing the performance of the proposal is also included.

本文提出了一种基于分离随机效应的序数多级隐马尔可夫模型。具体来说，模型中考虑了两种不同的二级离散效应，一种影响初始概率向量，另一种影响一级序数隐马尔可夫过程的转移概率矩阵。为了对这些单独的效应进行建模，我们考虑了一个二维混合规范，它允许避免对随机效应分布的无法验证的假设，并导出二级单元的双向聚类。从两个随机效应相互依赖的一般模型开始，我们还获得了作为特例的独立模型。该建议适用于分组到疗养院的老年居民样本的身体健康状况数据。