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Generalized Linear Latent Variable Models with Flexible Distribution of Latent Variables
Author(s) -
IRINCHEEVA IRINA,
CANTONI EVA,
GENTON MARC G.
Publication year - 2012
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2011.00777.x
Subject(s) - latent variable , mathematics , local independence , latent variable model , latent class model , nonparametric statistics , probabilistic latent semantic analysis , flexibility (engineering) , statistics , econometrics , computer science , artificial intelligence
. 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.