Latent Markov Models for Longitudinal Data

Drawing on the authors’ extensive research in the analysis of categorical longitudinal data, Latent Markov Models for Longitudinal Data focuses on the formulation of latent Markov models and the practical use of these models. Numerous examples illustrate how latent Markov models are used in economics, education, sociology, and other fields. The R and MATLAB® routines used for the examples are available on the authors’ website. The book provides you with the essential background on latent variable models, particularly the latent class model. It discusses how the Markov chain model and the latent class model represent a useful paradigm for latent Markov models. The authors illustrate the assumptions of the basic version of the latent Markov model and introduce maximum likelihood estimation through the Expectation-Maximization algorithm. They also cover constrained versions of the basic latent Markov model, describe the inclusion of the individual covariates, and address the random effects and multilevel extensions of the model. After covering advanced topics, the book concludes with a discussion on Bayesian inference as an alternative to maximum likelihood inference. As longitudinal data become increasingly relevant in many fields, researchers must rely on specific statistical and econometric models tailored to their application. A complete overview of latent Markov models, this book demonstrates how to use the models in three types of analysis: transition analysis with measurement errors, analyses that consider unobserved heterogeneity, and finding clusters of units and studying the transition between the clusters.

Overview on Latent Markov Modeling Introduction Literature review on latent Markov models Alternative approaches Example datasets Background on Latent Variable and Markov Chain ModelsIntroduction Latent variable models Expectation-Maximization algorithm Standard errors Latent class modelSelection of the number of latent classes ApplicationsMarkov chain model for longitudinal dataApplications Basic Latent Markov Model Introduction Univariate formulation Multivariate formulation Model identifiability Maximum likelihood estimationSelection of the number of latent states Applications Constrained Latent Markov Models Introduction Constraints on the measurement model Constraints on the latent model Maximum likelihood estimation Model selection and hypothesis testingApplications Including Individual Covariates and Relaxing Basic Model AssumptionsIntroduction Notation Covariates in the measurement model Covariates in the latent model Interpretation of the resulting models Maximum likelihood estimation Observed information matrix, identifiability, and standard errors Relaxing local independence Higher order extensions Applications Including Random Effects and Extension to Multilevel Data Introduction Random-effects formulationMaximum likelihood estimation Multilevel formulationApplication to the student math achievement dataset Advanced Topics about Latent Markov Modeling Introduction Dealing with continuous response variables Dealing with missing responses Additional computational issues Decoding and forecasting Selection of the number of latent states Bayesian Latent Markov Models Introduction Prior distributions Bayesian inference via reversible jump Alternative sampling Application to the labor market dataset Appendix: Software List of Main Symbols Bibliography Index

Francesco Bartolucci is a professor of statistics in the Department of Economics, Finance and Statistics at the University of Perugia, where he also coordinates the Ph.D. program in mathematical and statistical methods for the economic and social sciences. His main research interests include latent variable models for cross-sectional and longitudinal categorical data, with applications ranging from educational and psychometric contexts to the analysis of labor market data. Alessio Farcomeni is a researcher at the University of Rome "La Sapienza". His interests range from analysis of panel data and categorical time series to multiple testing, multivariate analysis and clustering, and model selection. Fulvia Pennoni is an assistant professor of statistics in the Department of Statistics at the University of Milano-Bicocca. Her main expertise encompasses latent variable modeling. She is currently carrying out research in methods and statistics with intensive statistical programming applications.