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Bayesian Inference for Graphical Factor Analysis Models

Published online by Cambridge University Press:  01 January 2025

Paolo Giudici  and
Elena Stanghellini
Paolo Giudici
Affiliation:
Dipartimento di Economia Politica e Metodi Quantitativi, Università di Pavia
Elena Stanghellini*
Affiliation:
Dipartimento di Scienze Statistiche, Università di Perugia
*
Requests for reprints should be sent to Elena Stanghellini, Dipartimento di Scienze Statistiche, Università di Perugia, Via A. Pascoli, 1 - C.P. 1315 Succ. 1, 06100 Perugia, ITALY. E-Mail: [email protected]
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Abstract

We generalize factor analysis models by allowing the concentration matrix of the residuals to have nonzero off-diagonal elements. The resulting model is named graphical factor analysis model. Allowing a structure of associations gives information about the correlation left unexplained by the unobserved variables, which can be used both in the confirmatory and exploratory context. We first present a sufficient condition for global identifiability of this class of models with a generic number of factors, thereby extending the results in Stanghellini (1997) and Vicard (2000). We then consider the issue of model comparison and show that fast local computations are possible for this purpose, if the conditional independence graphs on the residuals are restricted to be decomposable and a Bayesian approach is adopted. To achieve this aim, we propose a new reversible jump MCMC method to approximate the posterior probabilities of the considered models. We then study the evolution of political democracy in 75 developing countries based on eight measures of democracy in two different years.

Keywords

factor analysisgraphical Gaussian modelsidentificationmodel comparisonreversible jump MCMC
Type
Articles
Information
Psychometrika , Volume 66 , Issue 4 , December 2001 , pp. 577 - 591
Copyright
Copyright © 2001 The Psychometric Society

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Footnotes

We acknowledge support from M.U.R.S.T. of Italy and from the European Science Foundation H.S.S.S. Network. We are grateful to the referees and the Editor for many useful suggestions and comments which led to a substantial improvement of the paper. We also thank Nanny Wermuth for stimulating discussions and Kenneth A. Bollen for kindly providing us with the data-set.

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