A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure

• Published in: Journal of the American Statistical Association Vol. 104; no. 486; pp. 816 - 831
• Main Authors: Bartolucci, Francesco, Farcomeni, Alessio
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.06.2009; American Statistical Association; Taylor & Francis Ltd
• Subjects: Algorithms; Applications; Children; Datasets; Dependence relationships; Distribution theory; Dynamic modeling; Dynamic models; EM algorithm; Employment; Exact sciences and technology; Female labour; General topics; Hidden Markov chains; Labour market; Longitudinal studies; Marginal link function; Markov analysis; Markov models; Markovian processes; Mathematical functions; Mathematics; Matrices; Maximum likelihood estimators; Modeling; Multivariate analysis; Panel data; Parametric models; Probability; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Standard error; State dependence; Statistical methods; Statistics; Theory and Methods; Parameter estimation; Conditional distribution; Vector distribution; Labour market; Multivariate analysis; Covariate; Stochastic method; Parameterization; Statistical simulation; Markov chain; Hypothesis test; Heterogeneity; Statistical test; Panel data; Marginal distribution; Distribution function; Logit model; Sampling; Dynamic model; Data analysis; Multivariate distribution; Hidden Markov chains; Statistical method; Marginal link function; Categorical data; Maximum likelihood; State dependence; EM algorithm; Application
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/jasa.2009.0107

For the analysis of multivariate categorical longitudinal data, we propose an extension of the dynamic logit model. The resulting model is based on a marginal parameterization of the conditional distribution of each vector of response variables given the covariates, the lagged response variables, and a set of subject-specific parameters for the unobserved heterogeneity. The latter ones are assumed to follow a first-order Markov chain. For the maximum likelihood estimation of the model parameters, we outline an EM algorithm. The data analysis approach based on the proposed model is illustrated by a simulation study and an application to a dataset, which derives from the Panel Study on Income Dynamics and concerns fertility and female participation to the labor market.