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Bayesian Factor Analysis and Model Selection

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概要 Factor analysis provides a useful tool for exploring the covariance structure among a set of observed random variables by construction of a smaller number of random variables called common factors. In... maximum likelihood factor analysis, the estimates of unique or error variances can turn out to be zero or negative, which makes no sense from a statistical point of view. In order to overcome the problem of these so-called improper solutions, we use a Bayesian approach by specifying a prior distribution for the variances of specific factors, i.e., we introduce a prior distribution for the parameters to prevent the occurrence of improper solutions. Crucial aspects of Bayesian factor analysis include the choice of adjusted parameters, in particular, the hyper-parameters for the prior distribution and also choosing an appropriate number of factors. The choice of these parameters can be viewed as a model selection and evaluation problem. We derive a model selection criterion for a Bayesian factor analysis model. Monte Carlo simulations are conducted to investigate the efficiency of the proposed procedures. A real data example is also given to illustrate our procedures.続きを見る

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登録日 2009.06.23
更新日 2018.01.24