Likelihood Inference for a Class of Latent Markov Models under Linear Hypotheses on the Transition Probabilities
潜在马尔可夫模型转移概率线性假设的似然推断AI 解读 ↓
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潜在马尔可夫模型转移概率线性假设的似然推断
- 研究问题
- 对于纵向离散数据的潜在马尔可夫模型，如何估计受线性约束的转移概率，并检验潜在状态之间是否存在转移？
- 方法与思路
- 作者用隐马尔可夫递推构造受约束最大似然估计的EM算法，并在一定假设下推导嵌套线性假设的似然比检验分布。
- 材料陈述的贡献
- 摘要称检验的渐近零分布属于混合卡方类型，并给出潜在类别模型与潜在马尔可夫模型比较这一特例及模拟和应用。
- 阅读关注点
- 应核对线性约束的具体形式、渐近分布成立的条件、混合权重的计算方式，以及无状态转移检验的模型设定。
- 阅读边界
- 仅据所给Crossref摘要，不能确定正则条件、算法收敛性或模拟表现；教育测试和大麻使用应用的具体结果未提供。
原文摘要
Summary For a class of latent Markov models for discrete variables having a longitudinal structure, we introduce an approach for formulating and testing linear hypotheses on the transition probabilities of the latent process. For the maximum likelihood estimation of a latent Markov model under hypotheses of this type, we outline an EM algorithm that is based on well-known recursions in the hidden Markov literature. We also show that, under certain assumptions, the asymptotic null distribution of the likelihood ratio statistic for testing a linear hypothesis on the transition probabilities of a latent Markov model, against a less stringent linear hypothesis on the transition probabilities of the same model, is of χ¯2 type. As a particular case, we derive the asymptotic distribution of the likelihood ratio statistic between a latent class model and its latent Markov version, which may be used to test the hypothesis of absence of transition between latent states. The approach is illustrated through a series of simulations and two applications, the first of which is based on educational testing data that have been collected within the National Assessment of Educational Progress 1996, and the second on data, concerning the use of marijuana, which have been collected within the National Youth Survey 1976–1980.