Department of Biostatistics, School of Public Health, Hamadan University of Medical Sciences, Hamadan, Iran.
Department of Mathematics, University of Bergen, Bergen, Norway.
Stat Med. 2021 May 10;40(10):2373-2388. doi: 10.1002/sim.8908. Epub 2021 Feb 15.
Hidden Markov and semi-Markov models (H(S)MMs) constitute useful tools for modeling observations subject to certain dependency structures. The hidden states render these models very flexible and allow them to capture many different types of latent patterns and dynamics present in the data. This has led to the increased popularity of these models, which have been applied to a variety of problems in various domains and settings, including longitudinal data. In many longitudinal studies, the response variable is categorical or count-type. Generalized linear mixed models (GLMMs) can be used to analyze a wide range of variables, including categorical and count. The present study proposes a model that combines HSMMs with GLMMs, leading to generalized linear mixed hidden semi-Markov models (GLM-HSMMs). These models can account for time-varying unobserved heterogeneity and handle different response types. Parameter estimation is achieved using a Monte Carlo Newton-Raphson (MCNR)-like algorithm. In our proposed model, the distribution of the random effects depends on hidden states. We illustrate the applicability of GLM-HSMMs with an example in the field of occupational health, where the response variable consists of count values. Furthermore, we assess the performance of our MCNR-like algorithm through a simulation study.
隐马尔可夫和半马尔可夫模型（H(S)MMs）是用于对受某些依赖结构影响的观测建模的有用工具。隐藏状态使这些模型非常灵活，并允许它们捕获数据中存在的许多不同类型的潜在模式和动态。这导致了这些模型的普及，它们已被应用于各个领域和场景中的各种问题，包括纵向数据。在许多纵向研究中，因变量是分类或计数类型。广义线性混合模型（GLMMs）可用于分析包括分类和计数在内的广泛变量。本研究提出了一种将 H(S)MMs 与 GLMMs 相结合的模型，从而产生了广义线性混合隐半马尔可夫模型（GLM-HSMMs）。这些模型可以解释随时间变化的未观测异质性并处理不同的响应类型。通过类似于蒙特卡罗牛顿 - 拉普森（MCNR）的算法来实现参数估计。在我们提出的模型中，随机效应的分布取决于隐藏状态。我们通过职业健康领域的一个示例说明了 GLM-HSMMs 的适用性，其中因变量由计数值组成。此外，我们通过模拟研究评估了我们的类似于 MCNR 的算法的性能。
