Latent Markov Models for Longitudinal Data
By Francesco Bartolucci, Alessio Farcomeni, Fulvia Pennoni
Published October 29th 2012 by Chapman and Hall/CRC – 252 pages
Series: Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences
Description
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.
Contents
Overview on Latent Markov Modeling
Introduction
Literature review on latent Markov models
Alternative approaches
Example datasets
Background on Latent Variable and Markov Chain Models
Introduction
Latent variable models
Expectation-Maximization algorithm
Standard errors
Latent class model
Selection of the number of latent classes
Applications
Markov chain model for longitudinal data
Applications
Basic Latent Markov Model
Introduction
Univariate formulation
Multivariate formulation
Model identifiability
Maximum likelihood estimation
Selection 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 testing
Applications
Including Individual Covariates and Relaxing Basic Model Assumptions
Introduction
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 formulation
Maximum likelihood estimation
Multilevel formulation
Application 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
Author Bio
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.
Name: Latent Markov Models for Longitudinal Data (Hardback) – Chapman and Hall/CRC
Description: By Francesco Bartolucci, Alessio Farcomeni, Fulvia Pennoni. 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...
Categories: Quantitative Methods, Statistics & Computing, Statistical Theory & Methods, Regression Analysis and Multivariate Statistics
