Book•
Latent Markov Models for Longitudinal Data
29 Oct 2012-
TL;DR: This book discusses Latent Markov Modeling as a guide to Bayesian inference via reversible jump, and its applications include selection and hypothesis testing, and modeling and inference of latent variable models and their applications.
Abstract: 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
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TL;DR: In this article, the authors introduce latent class, latent profile, and latent transition models for individual differences in learning and development, which allow analyzing how the observed heterogeneity in a group can be traced back to underlying homogeneous subgroups (e.g., learners differing systematically in their developmental phases).
139Â citations
TL;DR: The seqHMM package in R is designed for the efficient modeling of sequences and other categorical time series data containing one or multiple subjects with one or several interdependent sequences using HMMs and MHMMs.
Abstract: Sequence analysis is being more and more widely used for the analysis of social sequences and other multivariate categorical time series data. However, it is often complex to describe, visualize, and compare large sequence data, especially when there are multiple parallel sequences per subject. Hidden (latent) Markov models (HMMs) are able to detect underlying latent structures and they can be used in various longitudinal settings: to account for measurement error, to detect unobservable states, or to compress information across several types of observations. Extending to mixture hidden Markov models (MHMMs) allows clustering data into homogeneous subsets, with or without external covariates.
The seqHMM package in R is designed for the efficient modeling of sequences and other categorical time series data containing one or multiple subjects with one or multiple interdependent sequences using HMMs and MHMMs. Also other restricted variants of the MHMM can be fitted, e.g., latent class models, Markov models, mixture Markov models, or even ordinary multinomial regression models with suitable parameterization of the HMM. Good graphical presentations of data and models are useful during the whole analysis process from the first glimpse at the data to model fitting and presentation of results. The package provides easy options for plotting parallel sequence data, and proposes visualizing HMMs as directed graphs.
65Â citations
TL;DR: Drawing parallels between several disciplines focusing on processes generating variation in individuals' life-course, and contrast methodologies to disentangle these processes is drawn.
Abstract: What causes interindividual variation in fitness? Evidence of heritability of latent individual fitness traits has resparked a debate about the causes of variation in life histories in populations: neutralism versus empirical adaptationism. This debate about the processes underlying observed variation pits neutral stochastic demographic processes against evolutionarily relevant differences among individual fitness traits. Advancing this debate requires careful consideration of differences among inference approaches used by proponents of each hypothesis. Here we draw parallels between several disciplines focusing on processes generating variation in individuals' life-course, and we contrast methodologies to disentangle these processes. We draw on other disciplines to clarify terminology, risks of flawed inference, and expand the panel of hypotheses and formalizations of processes generating variation in life histories.
64Â citations
TL;DR: A comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data is provided and methods for selecting the number of states and for path prediction are outlined.
Abstract: We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. We illustrate the general version of the LM model which includes individual covariates, and several constrained versions. Constraints make the model more parsimonious and allow us to consider and test hypotheses of interest. These constraints may be put on the conditional distribution of the response variables given the latent process (measurement model) or on the distribution of the latent process (latent model). We also illustrate in detail maximum likelihood estimation through the Expectation–Maximization algorithm, which may be efficiently implemented by recursions taken from the hidden Markov literature. We outline methods for obtaining standard errors for the parameter estimates. We also illustrate methods for selecting the number of states and for path prediction. Finally, we mention issues related to Bayesian inference of LM models. Possibilities for further developments are given among the concluding remarks.
61Â citations