Pairwise Likelihood Inference for Nested Hidden Markov Chain Models for Multilevel Longitudinal Data

• 成果类型: Article
• 署名作者: Bartolucci, Francesco; Lupparelli, Monia
• 署名单位: University of Perugia; University of Bologna
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.998935
• 发表日期: 2016
• 页码: 216-228
• 关键词: binary data; probabilistic functions; statistical-analysis; speech recognition; algorithm; identification; Heterogeneity; performance; extension; selection

摘要

In the context of multilevel longitudinal data, where sample units are collected in clusters, an important aspect that should be accounted for is the unobserved heterogeneity between sample units and between clusters. For this aim, we propose an approach based on nested hidden (latent) Markov chains, which are associated with every sample unit and with every cluster. The approach allows us to account for the previously mentioned forms of unobserved heterogeneity in a dynamic fashion; it also allows us to account for the correlation that may arise between the responses provided by the units belonging to the same cluster. Under the assumed model, computing the manifest distribution of these response variables is infeasible even with a few units per cluster. Therefore, we make inference on this model through a composite likelihood function based on all the possible pairs of subjects within each cluster. Properties of the composite likelihood estimator are assessed by simulation. The proposed approach is illustrated through an application to a dataset concerning a sample of Italian workers in which a binary response variable for the worker receiving an illness benefit was repeatedly observed. Supplementary materials for this article are available online.