Facoltà di scienze economiche

Estimation of generalized linear latent variable models

Huber, Philippe ; Ronchetti, Elvezio ; Victoria-Feser, Maria-Pia

In: Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2004, vol. 66, no. 4, p. 893–908

Generalized Linear Latent Variable Models (GLLVM), as defined in Bartholomew and Knott (1999) enable modelling of relationships between manifest and latent variables. They extend structural equation modelling techniques, which are powerful tools in the social sciences. However, because of the complexity of the log-likelihood function of a GLLVM, an approximation such as numerical integration must... Plus

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    Summary
    Generalized Linear Latent Variable Models (GLLVM), as defined in Bartholomew and Knott (1999) enable modelling of relationships between manifest and latent variables. They extend structural equation modelling techniques, which are powerful tools in the social sciences. However, because of the complexity of the log-likelihood function of a GLLVM, an approximation such as numerical integration must be used for inference. This can limit drastically the number of variables in the model and lead to biased estimators. In this paper, we propose a new estimator for the parameters of a GLLVM, based on a Laplace approximation to the likelihood function and which can be computed even for models with a large number of variables. The new estimator can be viewed as a M-estimator, leading to readily available asymptotic properties and correct inference. A simulation study shows its excellent finite sample properties, in particular when compared with a well established approach such as LISREL. A real data example on the measurement of wealth for the computation of multidimentional inequality is analysed to highlight the importance of the methodology.