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.

Power and Sample Size Computation for Wald Tests in Latent Class Models

Abstract: Latent class (LC) analysis is used by social, behavioral, and medical science researchers among others as a tool for clustering (or unsupervised classification) with categorical response variables, for analyzing the agreement between multiple raters, for evaluating the sensitivity and specificity of diagnostic tests in the absence of a gold standard, and for modeling heterogeneity in developmental trajectories. Despite the increased popularity of LC analysis, little is known about statistical power and required sample size in LC modeling. This paper shows how to perform power and sample size computations in LC models using Wald tests for the parameters describing association between the categorical latent variable and the response variables. Moreover, the design factors affecting the statistical power of these Wald tests are studied. More specifically, we show how design factors which are specific for LC analysis, such as the number of classes, the class proportions, and the number of response variables, affect the information matrix. The proposed power computation approach is illustrated using realistic scenarios for the design factors. A simulation study conducted to assess the performance of the proposed power analysis procedure shows that it performs well in all situations one may encounter in practice.

Semiparametric Bayesian analysis of structural equation models with fixed covariates

Abstract: Latent variables play the most important role in structural equation modeling. In almost all existing structural equation models (SEMs), it is assumed that the distribution of the latent variables is normal. As this assumption is likely to be violated in many biomedical researches, a semiparametric Bayesian approach for relaxing it is developed in this paper. In the context of SEMs with covariates, we provide a general Bayesian framework in which a semiparametric hierarchical modeling with an approximate truncation Dirichlet process prior distribution is specified for the latent variables. The stick-breaking prior and the blocked Gibbs sampler are used for efficient simulation in the posterior analysis. The developed methodology is applied to a study of kidney disease in diabetes patients. A simulation study is conducted to reveal the empirical performance of the proposed approach. Supplementary electronic material for this paper is available in Wiley InterScience at http://www.mrw.interscience.wiley.com/suppmat/1097-0258/suppmat/.

Modeling Interaction Effects in Latent Growth Curve Models

Abstract: This article presents an extension of Joreskog and Yang's (1996) method of estimating interaction effects among latent variables to latent growth curve models. Models involving a product of 2 latent factors of either static or dynamic variables (parental monitoring and rule-setting) predicting an outcome growth variable (adolescents' initial status and rate of change in antisocial behavior) are used as substantive illustrations. The results are discussed in terms of practical and statistical problems associated with interaction analyses in latent curve models, and in structural equation models with latent variables in general.

Normative beliefs and modality styles: a latent class and latent variable model of travel behaviour

Abstract: We study the interrelation of normative beliefs, which are an individual’s perception of the beliefs of others regarding a specific behaviour, and modality styles, which represent the part of an individual’s lifestyle that is characterised by the use of a certain set of modes. In recent years, travel behaviour research has increasingly sought to understand the effect of social influence on mobility-related behaviour. One stream of literature has adopted representations rooted in social psychology to explain behaviour as a function of latent psycho-social constructs including normative beliefs. Another stream of literature has employed a lifestyle-oriented approach to identify segments or modality styles within a population that differ in terms of their orientation towards different modes of transport. Our study proposes an integrated conceptual framework that combines elements of these two streams of literature. Modality styles are hypothesised to be a function of normative beliefs towards the use of different modes of transport; mobility-related attitudes and behaviours are in turn hypothesised to be functions of modality styles. The conceptual model is operationalised using a latent class and latent variable model and empirically validated using data collected through an Australian consumer panel. We demonstrate how this integrated model framework may be used to understand the relationship between normative beliefs, modality styles and travel behaviour. In addition, we show how the model can be applied to predict how extant modality styles and patterns of travel behaviour may change over time in response to concurrent shifts in normative beliefs.

Bayesian Latent Factor Regression for Functional and Longitudinal Data

Abstract: In studies involving functional data, it is commonly of interest to model the impact of predictors on the distribution of the curves, allowing flexible effects on not only the mean curve but also the distribution about the mean. Characterizing the curve for each subject as a linear combination of a high-dimensional set of potential basis functions, we place a sparse latent factor regression model on the basis coefficients. We induce basis selection by choosing a shrinkage prior that allows many of the loadings to be close to zero. The number of latent factors is treated as unknown through a highly-efficient, adaptive-blocked Gibbs sampler. Predictors are included on the latent variables level, while allowing different predictors to impact different latent factors. This model induces a framework for functional response regression in which the distribution of the curves is allowed to change flexibly with predictors. The performance is assessed through simulation studies and the methods are applied to data on blood pressure trajectories during pregnancy.