标题： 纵向分类数据的潜在马尔可夫模型概述 显示英文标题

标题： An overview of latent Markov models for longitudinal categorical data

摘要： 我们提供了对潜在马尔可夫(LM)模型的全面概述，用于分析纵向分类数据。这些模型的主要假设是，给定一个遵循一阶马尔可夫链的潜在过程，响应变量是条件独立的。我们首先说明基本的LM模型，在该模型中，每个响应变量给定相应潜在变量以及潜在过程的初始和转移概率的条件分布是不受约束的。对于这个模型，我们还详细说明了通过期望最大化算法进行最大似然估计，该算法可以通过隐藏马尔可夫文献中已知的递归方法高效实现。然后我们说明了基本LM模型的几个约束版本，这些版本使模型更加简洁，并允许我们包含和检验感兴趣的假设。这些约束可以施加在给定潜在过程的响应变量的条件分布（测量模型）或潜在过程的分布（潜在模型）上。我们还处理了LM模型的扩展，以包括个体协变量和多层数据。协变量可能影响测量模型或潜在模型；我们根据应用背景讨论这两种不同方法的含义。最后，我们概述了获取参数估计的标准误差、选择状态数量和路径预测的方法。通过描述文献中相关的社会经济应用来说明模型和相关推断。 显示英文摘要

摘要： We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. The main assumption behind these models is that the response variables are conditionally independent given a latent process which follows a first-order Markov chain. We first illustrate the basic LM model in which the conditional distribution of each response variable given the corresponding latent variable and the initial and transition probabilities of the latent process are unconstrained. For this model we also illustrate in detail maximum likelihood estimation through the Expectation-Maximization algorithm, which may be efficiently implemented by recursions known in the hidden Markov literature. We then illustrate several constrained versions of the basic LM model, which make the model more parsimonious and allow us to include and test hypotheses of interest. These constraints may be put on the conditional distribution of the response variables given the latent process (measurement model) or on the distribution of the latent process (latent model). We also deal with extensions of LM model for the inclusion of individual covariates and to multilevel data. Covariates may affect the measurement or the latent model; we discuss the implications of these two different approaches according to the context of application. Finally, we outline methods for obtaining standard errors for the parameter estimates, for selecting the number of states and for path prediction. Models and related inference are illustrated by the description of relevant socio-economic applications available in the literature.