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.

Probabilistic Principal Component Analysis

Abstract: Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation of parameters in a latent variable model closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss the advantages conveyed by the definition of a probability density function for PCA.

Bayesian analysis of binary and polychotomous response data

Abstract: A vast literature in statistics, biometrics, and econometrics is concerned with the analysis of binary and polychotomous response data. The classical approach fits a categorical response regression model using maximum likelihood, and inferences about the model are based on the associated asymptotic theory. The accuracy of classical confidence statements is questionable for small sample sizes. In this article, exact Bayesian methods for modeling categorical response data are developed using the idea of data augmentation. The general approach can be summarized as follows. The probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data. Values of the latent data can be simulated from suitable truncated normal distributions. If the latent data are known, then the posterior distribution of the parameters can be computed using standard results for normal linear models. Draws from this posterior are used to sample new latent data, and t...

Integrating Person-Centered and Variable-Centered Analyses: Growth Mixture Modeling With Latent Trajectory Classes

Abstract: Background: Many alcohol research questions require methods that take a person-centered approach because the interest is in finding heterogeneous groups of individuals, such as those who are susceptible to alcohol dependence and those who are not. A person-centered focus also is useful with longitudinal data to represent heterogeneity in developmental trajectories. In alcohol, drug, and mental health research the recognition of heterogeneity has led to theories of multiple developmental pathways. Methods: This paper gives a brief overview of new methods that integrate variable- and person-centered analyses. Methods discussed include latent class analysis, latent transition analysis, latent class growth analysis, growth mixture modeling, and general growth mixture modeling. These methods are presented in a general latent variable modeling framework that expands traditional latent variable modeling by including not only continuous latent variables but also categorical latent variables. Results: Four examples that use the National Longitudinal Survey of Youth (NLSY) data are presented to illustrate latent class analysis, latent class growth analysis, growth mixture modeling, and general growth mixture modeling. Latent class analysis of antisocial behavior found four classes. Four heavy drinking trajectory classes were found. The relationship between the latent classes and background variables and consequences was studied. Conclusions: Person-centered and variable-centered analyses typically have been seen as different activities that use different types of models and software. This paper gives a brief overview of new methods that integrate variable- and person-centered analyses. The general framework makes it possible to combine these models and to study new models serving as a stimulus for asking research questions that have both person- and variable-centered aspects.

An introduction to latent class growth analysis and growth mixture modeling.

Abstract: In recent years, there has been a growing interest among researchers in the use of latent class and growth mixture modeling techniques for applications in the social and psychological sciences, in part due to advances in and availability of computer software designed for this purpose (e.g., Mplus and SAS Proc Traj). Latent growth modeling approaches, such as latent class growth analysis (LCGA) and growth mixture modeling (GMM), have been increasingly recognized for their usefulness for identifying homogeneous subpopulations within the larger heterogeneous population and for the identification of meaningful groups or classes of individuals. The purpose of this paper is to provide an overview of LCGA and GMM, compare the different techniques of latent growth modeling, discuss current debates and issues, and provide readers with a practical guide for conducting LCGA and GMM using the Mplus software. Researchers in the fields of social and psychological sciences are often interested in modeling the longitudinal developmental trajectories of individuals, whether for the study of personality development or for better understanding how social behaviors unfold over time (whether it be days, months, or years). This usually requires an extensive dataset consisting of longitudinal, repeated measures of variables, sometimes including multiple cohorts, and analyzing this data using various longitudinal latent variable modeling techniques such as latent growth curve models (cf. MacCallum & Austin, 2000). The objective of these approaches is to capture information about interindividual differences in intraindividual change over time (Nesselroade, 1991). However, conventional growth modeling approaches assume that individuals come from a single population and that a single growth trajectory can adequately approximate an entire population. Also, it is assumed that covariates that affect the growth factors influence each individual in the same way. Yet, theoretical frameworks and existing studies often categorize individuals into distinct subpopulations (e.g., socioeconomic classes, age groups, at-risk populations). For example, in the field of alcohol research, theoretical literature suggests different classes

Latent Class and Latent Transition Analysis: With Applications in the Social, Behavioral, and Health Sciences

Abstract: List of Figures. List of Tables. Acknowledgments. Acronyms. Part I Fundamentals. 1. General Introduction. 1.1 Overview. 1.2 Conceptual foundation and brief history of the latent class model. 1.3 Why select a categorical latent variable approach? 1.4 Scope of this book. 1.5 Empirical example of LCA: Adolescent delinquency. 1.6 Empirical example of LTA: Adolescent delinquency. 1.7 About this book. 1.8 The examples in this book. 1.9 Software. 1.10 Additional resources: The book's web site. 1.11 Suggested supplemental readings. 1.12 Points to remember. 1.13 What's next. 2. The latent class model. 2.1 Overview. 2.2 Empirical example: Pubertal development. 2.3 The role of item-response probabilities to label the latent classes in the pubertal development example. 2.4 Empirical example: Health risk behaviors. 2.5 LCA: Model and notation. 2.6 Suggested supplemental readings. 2.7 Points to remember. 2.8 What's next. 3. The relation between the latent variable and its indicators. 3.1 Overview. 3.2 The latent class measurement model. 3.3 Homogeneity and latent class separation. 3.4 The precision with which the observed variables measure the latent variable. 3.5 Expressing the degree of uncertainty: Mean posterior probabilities and entropy. 3.6 Points to remember. 3.7 What's next. 4. Parameter estimation and model selection. 4.1 Overview. 4.2 Maximum Likelihood estimation. 4.3 Model fit and model selection. 4.4 Finding the ML solution. 4.5 Empirical example of using many starting values. 4.6 Empirical examples of selecting the number of latent classes. 4.7 More about parameter restrictions. 4.8 Standard errors. 4.9 Suggested supplemental readings. 4.10 Points to remember. 4.11 What's next. Part II Advanced LCA. 5. Multiple-group LCA. 5.1 Overview. 5.2 Introduction. 5.3 Multiple-group LCA: Model and notation. 5.4 Computing the number of parameters estimated. 5.5 Expressing group differences in the LCA model. 5.6 Measurement invariance. 5.7 Establishing whether the number of latent classes is identical across groups. 5.8 Establishing invariance of item-response probabilities across groups. 5.9 Interpretation when measurement invariance does not hold. 5.10 Strategies when measurement invariance does not hold. 5.11 Significant differences and important differences. 5.12 Testing equivalence of latent class prevalences across groups. 5.13 Suggested supplemental readings. 5.14 Points to remember. 5.15 What's next. 6. LCA with Covariates. 6.1 Overview. 6.2 Empirical example: Positive health behaviors. 6.3 Preparing to conduct LCA with covariates. 6.4 LCA with covariates: Model and notation. 6.5 Hypothesis testing in LCA with covariates. 6.6 Interpretation of the intercepts and regression coefficients. 6.7 Empirical examples of LCA with a single covariate. 6.8 Empirical example of multiple covariates and interaction terms. 6.9 Multiple-group LCA with covariates: Model and notation. 6.10 Grouping variable or covariate? 6.11 Use of a Bayesian prior to stabilize estimation. 6.12 Binomial logistic regression. 6.13 Suggested supplemental readings. 6.14 Points to remember. 6.15 What's next. Part III Latent Class Models for Longitudinal Data. 7. RMLCA and LTA. 7.1 Overview. 7.2 RMLCA. 7.3 LTA. 7.4 LTA model parameters. 7.5 LTA: Model and notation. 7.6 Degrees of freedom associated with latent transition models. 7.7 Empirical example: Adolescent depression. 7.8 Empirical example: Dating and sexual risk behavior. 7.9 Interpreting what a latent transition model reveals about change. 7.10 Parameter restrictions in LTA. 7.11 Testing the hypotheses of measurement invariance across times. 7.12 Testing the hypotheses about change between times. 7.13 Relation between RMLCA and LTA. 7.14 Invariance of the transition probability matrix. 7.15 Suggested supplemental readings. 7.16 Points to remember. 7.17 What's next. 8. Multiple-Group LTA and LTA with Covariates. 8.1 Overview. 8.2 LTA with a grouping variable. 8.3 Multiple-group LTA: Model and notation. 8.4 Computing the number of parameters estimated in multiple-group latent transition models. 8.5 Hypothesis tests concerning group differences: General consideration. 8.6 Overall hypothesis tests about group differences in LTA. 8.7 Testing the hypothesis of equality of latent status prevalences. 8.8 Testing the hypothesis of equality of transition probabilities. 8.9 Incorporating covariates in LTA. 8.10 LTA with covariates: Model and notation. 8.11 Hypothesis testing in LTA with covariates. 8.12 Including both a grouping variable and a covariate in LTA. 8.13 Binomial logistic regression. 8.14 The relation between multiple-group LTA and LTA with a covariate. 8.15 Suggested supplemental readings. 8.16 Points to remember. Topic Index. Author Index.