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On the Relation Between the Linear Factor Model and the Latent Profile Model

Published online by Cambridge University Press:  01 January 2025

Peter F. Halpin ,
Conor V. Dolan ,
Raoul P. P. P. Grasman  and
Paul De Boeck
Peter F. Halpin*
Affiliation:
University of Amsterdam
Conor V. Dolan
Affiliation:
University of Amsterdam
Raoul P. P. P. Grasman
Affiliation:
University of Amsterdam
Paul De Boeck
Affiliation:
University of Amsterdam
*
Requests for reprints should be sent to Peter F. Halpin, Psychological Methods, University of Amsterdam, Roetersstraat 15, 5th floor, 1018 WB Amsterdam, The Netherlands. E-mail: p.f.halpin@uva.nl
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Abstract

The relationship between linear factor models and latent profile models is addressed within the context of maximum likelihood estimation based on the joint distribution of the manifest variables. Although the two models are well known to imply equivalent covariance decompositions, in general they do not yield equivalent estimates of the unconditional covariances. In particular, a 2-class latent profile model with Gaussian components underestimates the observed covariances but not the variances, when the data are consistent with a unidimensional Gaussian factor model. In explanation of this phenomenon we provide some results relating the unconditional covariances to the goodness of fit of the latent profile model, and to its excess multivariate kurtosis. The analysis also leads to some useful parameter restrictions related to symmetry.

Keywords

linear factor modellatent profile modelmaximum likelihoodKullback–Leibler divergencemultivariate kurtosis
Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 4 , October 2011 , pp. 564 - 583
Copyright
Copyright © 2011 The Psychometric Society

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