Assessing the goodness-of-fit of latent variable models for categorical data becomes a problem in presence of sparse data since the classical goodness-of-fit statistics are badly approximated by the chi square distribution. A good solution to this problem is represented by statistical tests based on the residuals associated to marginal distributions of the manifest variables (Cagnone and Mignani, 2007; Maydeu-Olivares and Joe, 2005; Reiser, 1996). The quadratic form associated to the test involves the use of a generalized inverse of the covariance matrix of the sample proportions. In this article we prove that the rank of the Moore-Penrose generalized inverse is univocally determined and hence it can be used appropriately.

A note on goodness of fit test in latent variable models with categorical variables / Cagnone S.. - In: COMMUNICATIONS IN STATISTICS. THEORY AND METHODS. - ISSN 0361-0926. - STAMPA. - 41:(2012), pp. 2983-2990. [10.1080/03610926.2011.622424]

A note on goodness of fit test in latent variable models with categorical variables

CAGNONE, SILVIA
2012

Abstract

Assessing the goodness-of-fit of latent variable models for categorical data becomes a problem in presence of sparse data since the classical goodness-of-fit statistics are badly approximated by the chi square distribution. A good solution to this problem is represented by statistical tests based on the residuals associated to marginal distributions of the manifest variables (Cagnone and Mignani, 2007; Maydeu-Olivares and Joe, 2005; Reiser, 1996). The quadratic form associated to the test involves the use of a generalized inverse of the covariance matrix of the sample proportions. In this article we prove that the rank of the Moore-Penrose generalized inverse is univocally determined and hence it can be used appropriately.
2012
A note on goodness of fit test in latent variable models with categorical variables / Cagnone S.. - In: COMMUNICATIONS IN STATISTICS. THEORY AND METHODS. - ISSN 0361-0926. - STAMPA. - 41:(2012), pp. 2983-2990. [10.1080/03610926.2011.622424]
Cagnone S.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/106048
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