Generalized linear latent variable models (GLLVMs), as defined by Bartholomew and Knott, 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 can lead to biased estimators. 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 an 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 multidimensional inequality is analysed to highlight the importance of the methodology.

Estimation of generalized linear latent variable models / Philippe Huber; Elvezio Ronchetti; Maria-Pia Victoria-Feser. - In: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B STATISTICAL METHODOLOGY. - ISSN 1369-7412. - STAMPA. - 66:4(2004), pp. 893-908. [10.1111/j.1467-9868.2004.05627.x]

Estimation of generalized linear latent variable models

Maria-Pia Victoria-Feser
2004

Abstract

Generalized linear latent variable models (GLLVMs), as defined by Bartholomew and Knott, 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 can lead to biased estimators. 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 an 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 multidimensional inequality is analysed to highlight the importance of the methodology.
2004
Estimation of generalized linear latent variable models / Philippe Huber; Elvezio Ronchetti; Maria-Pia Victoria-Feser. - In: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B STATISTICAL METHODOLOGY. - ISSN 1369-7412. - STAMPA. - 66:4(2004), pp. 893-908. [10.1111/j.1467-9868.2004.05627.x]
Philippe Huber; Elvezio Ronchetti; Maria-Pia Victoria-Feser
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/952912
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