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

Peter F. Halpin, Conor V. Dolan, Raoul P P P Grasman, Paul De Boeck

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)564-583
Number of pages20
Issue number4
StatePublished - Oct 2011


  • Kullback-Leibler divergence
  • latent profile model
  • linear factor model
  • maximum likelihood
  • multivariate kurtosis

ASJC Scopus subject areas

  • General Psychology
  • Applied Mathematics


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