This work deals with the analysis of longitudinal ordinal responses. The novelty of the proposed approach is in modeling simultaneously the temporal dynamics of a latent trait of interest, measured via the observed ordinal responses, and the answering behaviors influenced by response styles, through hidden Markov models (HMMs) with two latent components. This approach enables the modeling of (i) the substantive latent trait, controlling for response styles; (ii) the change over time of latent trait and answering behavior, allowing also dependence on individual characteristics. For the proposed HMMs, estimation procedures, methods for standard errors calculation, measures of goodness of fit and classification, and full-conditional residuals are discussed. The proposed model is fitted to ordinal longitudinal data from the Survey on Household Income and Wealth (Bank of Italy) to give insights on the evolution of households financial capability.

这项工作涉及纵向顺序响应的分析。所提出方法的新颖之处在于，通过具有两个潜在组件的隐马尔可夫模型（HMM），同时对潜在感兴趣特征的时间动态进行建模，通过观察到的顺序响应以及受响应风格影响的回答行为进行测量。这种方法可以对（i）实质性潜在特征进行建模，控制反应风格；(ii) 潜在特征和回答行为随时间的变化，也允许依赖于个体特征。对于所提出的 HMM，讨论了估计程序、标准误差计算方法、拟合优度和分类的度量以及全条件残差。