Three Multivariate Models: Factor Analysis, Latent Structure Analysis, and Latent Profile Analysis

1959/09/01 by W. A. Gibson, Walker Gibson · 330 citations
Agricultural and Biological Sciences · Mathematics · Psychology · #Color perception and design #Confirmatory factor analysis #Curse of dimensionality #Econometrics #Factor analysis #Latent class model #Latent variable #Latent variable model #Local independence #Mathematics #Metric (unit) #Multivariate statistics #Sensory Analysis and Statistical Methods #Statistics #Structural equation modeling

paper · doi:10.1007/bf02289845

published in Psychometrika 24(3), 229-252 (Springer Science+Business Media)

openalex publication_date 1959/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

The factor analysis model and Lazarsfeld's latent structure scheme for analyzing dichotomous attributes are derived to show how the latter model avoids three knotty problems in factor analysis: communality estimation, rotation, and curvilinearity. Then the latent structure model is generalized into latent profile analysis for the study of interrelations among quantitative measures. Four latent profile examples are presented and discussed in terms of their limitations and the problems of latent metric and dimensionality thereby raised. The possibility of treating higher order empirical relations in a manner paralleling their various uses in the latent structure model is indicated.

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