Generalized Linear Latent Variable Models with Flexible Distribution of Latent Variables

Irina Irincheeva*, Eva Cantoni, Marc G. Genton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We consider a semi-nonparametric specification for the density of latent variables in Generalized Linear Latent Variable Models (GLLVM). This specification is flexible enough to allow for an asymmetric, multi-modal, heavy or light tailed smooth density. The degree of flexibility required by many applications of GLLVM can be achieved through this semi-nonparametric specification with a finite number of parameters estimated by maximum likelihood. Even with this additional flexibility, we obtain an explicit expression of the likelihood for conditionally normal manifest variables. We show by simulations that the estimated density of latent variables capture the true one with good degree of accuracy and is easy to visualize. By analysing two real data sets we show that a flexible distribution of latent variables is a useful tool for exploring the adequacy of the GLLVM in practice.

Original languageEnglish (US)
Pages (from-to)663-680
Number of pages18
JournalScandinavian Journal of Statistics
Issue number4
StatePublished - Dec 2012


  • Factor analysis
  • Latent variable
  • Non-Gaussian distribution
  • Semi-nonparametric distribution
  • Visualization

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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