Bayes Factors for Testing the Equality of Covariance Matrix Eigenvalues

Robert E. McCulloch and Peter E. Rossi
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Robert E. McCulloch: University of Chicago, Graduate School of Business
Peter E. Rossi: University of Chicago, Graduate School of Business

A chapter in Modelling and Prediction Honoring Seymour Geisser, 1996, pp 305-314 from Springer

Abstract: Abstract We use the methods of McCulloch and Rossi (1992) to construct a Bayes Factor for the hypothesis of the equality of eigenvalues of a covariance matrix. If the smallest s eigenvalues of a covariance matrix are equal, then we can think of the p dimensional sample data as arising from a reduced rank model. Tests of this sort are often used to identify the number of components used in a Principal Components analysis. The Bayes Factor approach requires specification of prior distributions for both the restricted and unrestricted covariance matrices. The problem of specifying a prior distribution on the restricted covariance matrix is solved via a projection method. We exploit the duality between sufficient statistics and parameters in exponential families to use the restricted MLE as a projection device. We illustrate this method with simulated and actual data. Our real data example addresses the question of the number of factors underlying stock return data.

Keywords: Monte Carlo; Factor Analysis; Nonlinear. (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2414-3_19

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DOI: 10.1007/978-1-4612-2414-3_19

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