Topic
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.
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TL;DR: This review considers a common question in data analysis: What is the most useful way to analyze longitudinal repeated measures data and presents several classic SEMs based on the inclusion of invariant common factors and why these are so important.
Abstract: This review considers a common question in data analysis: What is the most useful way to analyze longitudinal repeated measures data? We discuss some contemporary forms of structural equation models (SEMs) based on the inclusion of latent variables. The specific goals of this review are to clarify basic SEM definitions, consider relations to classical models, focus on testable features of the new models, and provide recent references to more complete presentations. A broader goal is to illustrate why so many researchers are enthusiastic about the SEM approach to data analysis. We first outline some classic problems in longitudinal data analysis, consider definitions of differences and changes, and raise issues about measurement errors. We then present several classic SEMs based on the inclusion of invariant common factors and explain why these are so important. This leads to newer SEMs based on latent change scores, and we explain why these are useful.
1,509 citations
TL;DR: This paper proposed a framework for representing personality constructs at four levels of abstraction, i.e., partial disaggregation, total aggregation, partial aggregation and total disaggregation models, where each dimension is either freely correlated with the other dimensions or loading on one or more order factors.
Abstract: This article proposes a framework for representing personality constructs at four levels of abstraction. The total aggregation model is the composite formed by the sum of scores on all items in a scale. The partial aggregation model treats separate dimensions of a personality construct as indicators of a single latent variable, with each dimension being an aggregation of items. The partial disaggregation model represents each dimension as a separate latent variable, either freely correlated with the other dimensions or loading on one or more than one higher order factor; the measures of the dimensions are multiple indicators formed as aggregates of subsets of items. The total disaggregation model also represents each dimension as a separate latent variable but, unlike the partial disaggregation model, uses each item in the scale as an indicator of its respective factor. Illustrations of the models are provided on the State Self‐Esteem Scale—including tests of psychometric properties, invariance, and gener...
1,507 citations
TL;DR: A form of nonlinear latent variable model called the generative topographic mapping, for which the parameters of the model can be determined using the expectation-maximization algorithm, is introduced.
Abstract: Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis which is based on a linear transformations between the latent space and the data space. In this paper we introduce a form of non-linear latent variable model called the Generative Topographic Mapping, for which the parameters of the model can be determined using the EM algorithm. GTM provides a principled alternative to the widely used Self-Organizing Map (SOM) of Kohonen (1982), and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from flow diagnostics for a multi-phase oil pipeline.
1,469 citations
TL;DR: In this article, the authors provide a step-by-step guide to analysing measurement invariance of latent constructs, which is important in research across groups, or across time.
Abstract: The analysis of measurement invariance of latent constructs is important in research across groups, or across time. By establishing whether factor loadings, intercepts and residual variances are equivalent in a factor model that measures a latent concept, we can assure that comparisons that are made on the latent variable are valid across groups or time. Establishing measurement invariance involves running a set of increasingly constrained structural equation models, and testing whether differences between these models are significant. This paper provides a step-by-step guide to analysing measurement invariance.
1,457 citations
TL;DR: In this paper, the authors consider a model in which one observes multiple indicators and multiple causes of a single latent variable and derive the maximum-likelihood estimators and their asymptotic variance-covariance matrix.
Abstract: We consider a model in which one observes multiple indicators and multiple causes of a single latent variable. In terms of the multivariate regression of the indicators on the causes, the model implies restrictions of two types: (i) the regression coefficient matrix has rank one, (ii) the residual variance-covariance matrix satisfies a factor analysis model with one common factor. The first type of restriction is familiar to econometricians and the second to psychometricians. We derive the maximum-likelihood estimators and their asymptotic variance-covariance matrix. Two alternative “limited information” estimators are also considered and compared with the maximum-likelihood estimators in terms of efficiency.
1,453 citations