Latent Markov models for longitudinal data /

Latent Markov models for longitudinal data /

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Bibliographic Details
Author / Creator:Bartolucci, Francesco, author.
Imprint:Boca Raton, FL : CRC Press, [2013]
©2013
Description:xix, 234 pages : illustrations ; 24 cm.
Language:English
Series:Chapman & Hall/CRC statistics in the social and behavioral sciences series
Statistics in the social and behavioral sciences series.
Subject:
Markov processes.
Markov processes.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/8943160
Hidden Bibliographic Details
Other authors / contributors:Farcomeni, Alessio, author.
Pennoni, Fulvia, author.
ISBN:9781439817087 (hardback)
1439817081 (hardback)
Notes:Includes bibliographical references and index.
Summary:"Preface Latent Markov models represent an important class of latent variable models for the analysis of longitudinal data, when the response variables measure common characteristics of interest which are not directly observable. Typically, the response variables are categorical, even if nothing precludes that they have a di erent nature. These models nd application in many relevant elds, such as educational and health sciences, when the latent characteristics correspond, for instance, to a certain type of ability or to the quality-of-life. Important applications are also in the study of certain human behaviors which are relevant for the social and economic research. The main feature that distinguishes latent Markov models from other models for longitudinal data is that the individual characteristics of interest, and their evolution in time, are represented by a latent process which follows a Markov chain. This implies that we are in the eld of discrete latent variable models, where the latent variables may assume a nite number of values. Latent Markov models are then strongly related to the latent class model, which represents an important tool for classifying a sample of subjects on the basis of a series of categorical response variables. The latter model is based on a discrete latent variable, the di erent values of which correspond to di erent subpopulations (named latent classes) having a common distribution about the response variables. The latent Markov model may be seen as an extension of the latent class model in which subjects are allowed to move between the latent classes during the period of observation"--
Table of Contents:
  • List of Figures
  • List of Tables
  • Preface
  • 1. Overview on latent Markov modeling
  • 1.1. Introduction
  • 1.2. Literature review on latent Markov models
  • 1.3. Alternative approaches
  • 1.4. Example datasets
  • 1.4.1. Marijuana consumption dataset
  • 1.4.2. Criminal conviction history dataset
  • 1.4.3. Labor market dataset
  • 1.4.4. Student math achievement dataset
  • 2. Background on latent variable and Markov chain models
  • 2.1. Introduction
  • 2.2. Latent variable models
  • 2.3. Expectation-Maximization algorithm
  • 2.4. Standard errors
  • 2.5. Latent class model
  • 2.5.1. Basic version
  • 2.5.2. Advanced versions
  • 2.5.3. Maximum likelihood estimation
  • 2.5.4. Selection of the number of latent classes
  • 2.6. Applications
  • 2.6.1. Marijuana consumption dataset
  • 2.6.2. Criminal conviction history dataset
  • 2.7. Markov chain model for longitudinal data
  • 2.7.1. Basic version
  • 2.7.2. Advanced versions
  • 2.7.3. Likelihood inference
  • 2.7.4. Maximum likelihood estimation
  • 2.7.5. Model selection
  • 2.8. Applications
  • 2.8.1. Marijuana consumption dataset
  • 2.8.2. Criminal conviction history dataset
  • 3. Basic latent Markov model
  • 3.1. Introduction
  • 3.2. Univariate formulation
  • 3.3. Multivariate formulation
  • 3.4. Model identifiability
  • 3.5. Maximum likelihood estimation
  • 3.5.1. Expectation-Maximization algorithm
  • 3.5.1.1. Univariate formulation
  • 3.5.1.2. Multivariate formulation
  • 3.5.1.3. Initialization of the algorithm and model identifiability
  • 3.5.2. Alternative algorithms for maximum likelihood estimation
  • 3.5.3. Standard errors
  • 3.6. Selection of the number of latent states
  • 3.7. Applications
  • 3.7.1. Marijuana consumption dataset
  • 3.7.2. Criminal conviction history dataset
  • Appendix 1. Efficient implementation of recursions
  • 4. Constrained latent Markov models
  • 4.1. Introduction
  • 4.2. Constraints on the measurement model
  • 4.2.1. Univariate formulation
  • 4.2.1.1. Binary response variables
  • 4.2.1.2. Categorical response variables
  • 4.2.2. Multivariate formulation
  • 4.3. Constraints on the latent model
  • 4.3.1. Linear model on the transition probabilities
  • 4.3.2. Generalized linear model on the transition probabilities
  • 4.4. Maximum likelihood estimation
  • 4.4.1. Expectation-Maximization algorithm
  • 4.4.1.1. Univariate formulation
  • 4.4.1.2. Multivariate formulation
  • 4.4.1.3. Initialization of the algorithm and model identifiability
  • 4.5. Model selection and hypothesis testing
  • 4.5.1. Model selection
  • 4.5.2. Hypothesis testing
  • 4.6. Applications
  • 4.6.1. Marijuana consumption dataset
  • 4.6.2. Criminal conviction history dataset
  • Appendix 1. Marginal parametrization
  • Appendix 2. Implementation of the M-step
  • 5. Including individual covariates and relaxing basic model assumptions
  • 5.1. Introduction
  • 5.2. Notation
  • 5.3. Covariates in the measurement model
  • 5.3.1. Univariate formulation
  • 5.3.2. Multivariate formulation
  • 5.4. Covariates in the latent model
  • 5.5. Interpretation of the resulting models
  • 5.6. Maximum likelihood estimation
  • 5.6.1. Expectation-Maximization algorithm
  • 5.7. Observed information matrix, identifiabhity, and standard errors
  • 5.8. Relaxing local independence
  • 5.8.1. Conditional serial dependence
  • 5.8.2. Conditional contemporary dependence
  • 5.9. Higher order extensions
  • 5.10. Applications
  • 5.10.1. Criminal conviction history dataset
  • 5.10.2. Labor market dataset
  • Appendix 1. Multivariate link function
  • 6. Including random effects and extension to multilevel data
  • 6.1. Introduction
  • 6.2. Random-effects formulation
  • 6.2.1. Model assumptions
  • 6.2.1.1. Random effects in the measurement model
  • 6.2.1.2. Random effects in the latent model
  • 6.2.2. Manifest distribution
  • 6.3. Maximum likelihood estimation
  • 6.4. Multilevel formulation
  • 6.4.1. Model assumptions
  • 6.4.2. Manifest distribution and maximum likelihood estimation
  • 6.5. Application to the student math achievement dataset
  • 7. Advanced topics about latent Markov modeling
  • 7.1. Introduction
  • 7.2. Dealing with continuous response variables
  • 7.2.1. Linear regression
  • 7.2.2. Quantile regression
  • 7.2.3. Estimation
  • 7.3. Dealing with missing responses
  • 7.4. Additional computational issues
  • 7.4.1. Maximization of the likelihood through the Newton-Raphson algorithm
  • 7.4.1.1. A general description of the algorithm
  • 7.4.1.2. Use for latent Markov models
  • 7.4.2. Parametric bootstrap
  • 7.5. Decoding and forecasting
  • 7.5.1. Local decoding
  • 7.5.2. Global decoding
  • 7.5.3. Forecasting
  • 7.6. Selection of the number of latent states
  • 8. Bayesian latent Markov models
  • 8.1. Introduction
  • 8.2. Prior distributions
  • 8.2.1. Basic latent Markov model
  • 8.2.2. Constrained and extended latent Markov models
  • 8.3. Bayesian inference via Reversible Jump
  • 8.3.1. Reversible Jump algorithm
  • 8.3.2. Post-processing the Reversible Jump output
  • 8.3.3. Inference based on the simulated posterior distribution
  • 8.4. Alternative sampling strategy
  • 8.4.1. Continuous birth and death process based on data augmentation
  • 8.4.2. Parallel sampling
  • 8.5. Application to the labor market dataset
  • A. Software
  • A.1. Introduction
  • A.2. Package LMest
  • List of Main Symbols
  • Bibliography
  • Index
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