Rent 9781439817087 | Latent Markov Models for Longitudinal Data

Summary Table of Contents

Exploring the theory and applications of latent Markov modeling in a common conceptual framework, this book presents a nontechnical overview of latent Markov models and their potential in socio-economic applications. The statistical approach of the text emphasizes inference and the use of models in applications. The book first describes the latent Markov model proposed by Wiggins, taking into account other models in the field, such as latent transition analysis and hidden Markov analysis. The authors then lead readers to the possibility of impl... MORE

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List of Figures	p. xi
List of Tables	p. xiii
Preface	p. xvii
Overview on latent Markov modeling	p. 1
Introduction	p. 1
Literature review on latent Markov models	p. 4
Alternative approaches	p. 7
Example datasets	p. 8
Marijuana consumption dataset	p. 8
Criminal conviction history dataset	p. 9
Labor market dataset	p. 11
Student math achievement dataset	p. 13
Background on latent variable and Markov chain models	p. 17
Introduction	p. 17
Latent variable models	p. 17
Expectation-Maximization algorithm	p. 21
Standard errors	p. 25
Latent class model	p. 26
Basic version	p. 27
Advanced versions	p. 28
Maximum likelihood estimation	p. 32
Selection of the number of latent classes	p. 33
Applications	p. 35
Marijuana consumption dataset	p. 35
Criminal conviction history dataset	p. 38
Markov chain model for longitudinal data	p. 41
Basic version	p. 41
Advanced versions	p. 43
Likelihood inference	p. 44
Maximum likelihood estimation	p. 45
Model selection	p. 46
Applications	p. 46
Marijuana consumption dataset	p. 46
Criminal conviction history dataset	p. 48
Basic latent Markov model	p. 51
Introduction	p. 51
Univariate formulation	p. 51
Multivariate formulation	p. 56
Model identifiability	p. 58
Maximum likelihood estimation	p. 59
Expectation-Maximization algorithm	p. 60
Univariate formulation	p. 60
Multivariate formulation	p. 63
Initialization of the algorithm and model identifiability	p. 64
Alternative algorithms for maximum likelihood estimation	p. 66
Standard errors	p. 67
Selection of the number of latent states	p. 67
Applications	p. 68
Marijuana consumption dataset	p. 69
Criminal conviction history dataset	p. 74
Efficient implementation of recursions	p. 77
Constrained latent Markov models	p. 79
Introduction	p. 79
Constraints on the measurement model	p. 80
Univariate formulation	p. 80
Binary response variables	p. 81
Categorical response variables	p. 83
Multivariate formulation	p. 85
Constraints on the latent model	p. 86
Linear model on the transition probabilities	p. 87
Generalized linear model on the transition probabilities	p. 88
Maximum likelihood estimation	p. 90
Expectation-Maximization algorithm	p. 91
Univariate formulation	p. 91
Multivariate formulation	p. 93
Initialization of the algorithm and model identifiability	p. 93
Model selection and hypothesis testing	p. 94
Model selection	p. 94
Hypothesis testing	p. 95
Applications	p. 96
Marijuana consumption dataset	p. 96
Criminal conviction history dataset	p. 100
Marginal parametrization	p. 102
Implementation of the M-step	p. 105
Including individual covariates and relaxing basic model assumptions	p. 109
Introduction	p. 109
Notation	p. 110
Covariates in the measurement model	p. 112
Univariate formulation	p. 112
Multivariate formulation	p. 114
Covariates in the latent model	p. 115
Interpretation of the resulting models	p. 116
Maximum likelihood estimation	p. 117
Expectation-Maximization algorithm	p. 118
Observed information matrix, identifiabhity, and standard errors	p. 120
Relaxing local independence	p. 121
Conditional serial dependence	p. 121
Conditional contemporary dependence	p. 123
Higher order extensions	p. 126
Applications	p. 130
Criminal conviction history dataset	p. 130
Labor market dataset	p. 134
Multivariate link function	p. 137
Including random effects and extension to multilevel data	p. 139
Introduction	p. 139
Random-effects formulation	p. 139
Model assumptions	p. 140
Random effects in the measurement model	p. 140
Random effects in the latent model	p. 142
Manifest distribution	p. 143
Maximum likelihood estimation	p. 145
Multilevel formulation	p. 148
Model assumptions	p. 148
Manifest distribution and maximum likelihood estimation	p. 151
Application to the student math achievement dataset	p. 152
Advanced topics about latent Markov modeling	p. 157
Introduction	p. 157
Dealing with continuous response variables	p. 157
Linear regression	p. 158
Quantile regression	p. 159
Estimation	p. 160
Dealing with missing responses	p. 162
Additional computational issues	p. 164
Maximization of the likelihood through the Newton-Raphson algorithm	p. 164
A general description of the algorithm	p. 164
Use for latent Markov models	p. 165
Parametric bootstrap	p. 166
Decoding and forecasting	p. 168
Local decoding	p. 169
Global decoding	p. 170
Forecasting	p. 171
Selection of the number of latent states	p. 172
Bayesian latent Markov models	p. 177
Introduction	p. 177
Prior distributions	p. 178
Basic latent Markov model	p. 178
Constrained and extended latent Markov models	p. 180
Bayesian inference via Reversible Jump	p. 181
Reversible Jump algorithm	p. 181
Post-processing the Reversible Jump output	p. 186
Inference based on the simulated posterior distribution	p. 187
Alternative sampling strategy	p. 188
Continuous birth and death process based on data augmentation	p. 188
Parallel sampling	p. 190
Application to the labor market dataset	p. 190
Software	p. 197
Introduction	p. 197
Package LMest	p. 197
List of Main Symbols	p. 209
Bibliography	p. 215
Index	p. 231
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