Latent variable model

About: Latent variable model is a research topic. Over the lifetime, 3589 publications have been published within this topic receiving 235061 citations.

Book Review: Latent Variable Models: An Introduction to Factor, Path, and Structural Equation Analysis (4th ed.)

Abstract: The first edition of the book, published in 1987, was one of the early and popular texts on factor, path, and structural models. In its fourth edition, it remains an excellent text on basic principles and analyses of covariance structures for researchers in the fields of education, psychology, and social sciences. In recent decades, confirmatory factor analysis, path analysis, and structural equation modeling (SEM) have become basic research tools. Loehlin argues that these methods are ‘‘at heart’’ one, and the path diagram approach makes these methods accessible to students who are not very mathematical. This book explains a number of statistical methods, such as factor analysis, path analysis, and structural equation models, and does so in a clear, easy-to-grasp manner and with fully worked-out examples. The book represents an approach that is neither too mathematical nor merely simplistic, focused on the mechanics of running analyses. Loehlin uses path diagrams with a minimum of equations to present structural equation and factor analysis models. The book departs from other introductory texts because it is not based on any particular software (e.g., AMOS, EQS, or LISREL) and provides examples from several widely used software programs. The style of the book is easy to understand, and notes at the end of each chapter provide additional technical references for the interested readers. For those familiar with previous editions of the book, the overall contents of the book would look familiar. New material in the fourth edition includes missing data, nonnormality, mediation, and factorial invariance. Following are this reviewer’s comments on the contents of the book. Chapter 1 focuses on underlying relationships in models via path diagrams and introduces the reader to path models with observed and latent variables equations of path analysis, underand overdetermination of path models, and factor models. It provides a lucid coverage on basic ideas about path models via diagrams and sets the stage for further elucidation of statistical methods to study relationships among variables using factor, path, and structural models. Chapter 2 describes how models are fit to data, giving the reader a feel for an iterative minimization process. Topics addressed in the chapter are matrix formulation of path models, modelfitting programs (with examples from LISREL-SIMPLIS, EQS, and Mx), fit functions, chi-square tests, root mean square error of approximation (RMSEA), power to reject an incorrect model, and treatment of missing data. These topics apply to all models and provide the reader a firm grasp on what the author refers to as latent variable analysis.

A negative binomial model for time series of counts

Abstract: We study generalized linear models for time series of counts, where serial dependence is introduced through a dependent latent process in the link function. Conditional on the covariates and the latent process, the observation is modelled by a negative binomial distribution. To estimate the regression coefficients, we maximize the pseudolikelihood that is based on a generalized linear model with the latent process suppressed. We show the consistency and asymptotic normality of the generalized linear model estimator when the latent process is a stationary strongly mixing process. We extend the asymptotic results to generalized linear models for time series, where the observation variable, conditional on covariates and a latent process, is assumed to have a distribution from a one-parameter exponential family. Thus, we unify in a common framework the results for Poisson log-linear regression models of Davis et al. (2000), negative binomial logit regression models and other similarly specified generalized linear models. Language: en

Discrete-Time Discrete-State Latent Markov Models with Time-Constant and Time-Varying Covariates

Abstract: Discrete-time discrete-state Markov chain models can be used to describe individual change in categorical variables. But when the observed states are subject to measurement error, the observed transitions between two points in time will be partially spurious. Latent Markov models make it possible to separate true change from measurement error. The standard latent Markov model is, however, rather limited when the aim is to explain individual differences in the probability of occupying a particular state at a particular point in time. This paper presents a flexible logit regression approach which allows to regress the latent states occupied at the various points in time on both timeconstant and time-varying covariates. The regression approach combines features of causal log-linear models and latent class models with explanatory variables. In an application pupils' interest in physics at different points in time is explained by the time-constant covariate sex and the time-varying covariate physics grade. Results of both the complete and partially observed data are presented.