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 the Italian households financial capability.
翻译:这项工作涉及纵向或横向反应分析。拟议方法的新颖之处在于通过观察到的正反反应和受响应风格影响的反应行为,通过隐蔽的Markov模型(HMMs),通过两个潜在组成部分,同时模拟潜在兴趣特征的时间动态,通过隐蔽的Markov模型(HMMs),通过隐蔽的Markov模型(HMMs),通过两种潜在组成部分,进行以下模式的建模:(一) 实质性潜在特征,控制反应风格;(二) 潜在特质和应答行为随时间的变化,也允许依赖个人特征。对于拟议的HMMs,则讨论了估算程序、标准误差计算方法、适当性和分类的优劣度计量以及完全有条件的剩余物。拟议模型与《家庭收入和财富调查》(意大利银行)的垂直纵向数据相匹配,以洞察意大利家庭财政能力的演变。