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Generalized Linear Latent Variable Models with Flexible Distribution of Latent Variables

Genton, Marc G.
Published in Scandinavian Journal of Statistics. 2012, vol. 39, no. 4, p. 663-680
Abstract 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 analyzing 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.
Keywords Factor analysisLatent variableNon-gaussian distributionSemi-nonparametric distributionVisualization
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IRINCHEEVA, Irina, CANTONI, Eva, GENTON, Marc G. Generalized Linear Latent Variable Models with Flexible Distribution of Latent Variables. In: Scandinavian Journal of Statistics, 2012, vol. 39, n° 4, p. 663-680. https://archive-ouverte.unige.ch/unige:24297

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Deposited on : 2012-12-03

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