Bartolucci / Farcomeni / Pennoni Latent Markov Models for Longitudinal Data

Erscheinungsjahr 2012
ISBN: 978-1-4665-8371-9
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 252 Seiten

Reihe: Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences

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.

Zielgruppe

Applied statisticians in the social and behavioral sciences.

Autoren/Hrsg.

Bartolucci, Francesco

Farcomeni, Alessio

Pennoni, Fulvia

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

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

Über Autor(innen)

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.