Mixed Hidden Markov Models for Longitudinal Data: An Overview
Mixed Hidden Markov Models for Longitudinal Data: An Overview
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DOI：
10.1111/j.1751-5823.2011.00160.x
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发表时间：
2011-12-01
影响因子：
2
通讯作者：
Maruotti, Antonello
中科院分区：
文献类型：
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作者：
Maruotti, Antonello
在本文中，我们回顾了统计方法，结合联合收割机隐马尔可夫模型（HHHMS）和随机效应模型在纵向设置，导致所谓的混合HHHMS类。这类模型有几个有趣的特征。它处理的响应变量对协变量的依赖，序列依赖，和未观察到的异质性在HMM框架。它利用了时间相关性的性质，如相对简单的依赖结构和高效的计算过程，并允许处理各种真实世界的时间相关数据。我们给出了详细的期望最大化算法计算模型参数的最大似然估计，我们说明了该方法与两个真实的应用程序描述专利数和研发支出之间的关系，并通过资本资产定价模型之间的股票和市场回报。
In this paper we review statistical methods which combine hidden Markov models (HMMs) and random effects models in a longitudinal setting, leading to the class of so-called mixed HMMs. This class of models has several interesting features. It deals with the dependence of a response variable on covariates, serial dependence, and unobserved heterogeneity in an HMM framework. It exploits the properties ofHMMs, such as the relatively simple dependence structure and the efficient computational procedure, and allows one to handle a variety of real-world time-dependent data. We give details of the Expectation-Maximization algorithm for computing the maximum likelihood estimates of model parameters and we illustrate the method with two real applications describing the relationship between patent counts and research and development expenditures, and between stock and market returns via the Capital Asset Pricing Model.