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Abstract for:

Prediction and Sufficiency in the Model Factor Analysis

Ramses H.  Abul Naga,  November 1997
Paper No' DARP 031: | Full paper (pdf)
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Keywords: Latent variables; factor analysis; sufficiency; prediction; exponential family of distributions; living standards analysis

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This Paper is published under the following series: Distributional Analysis Research Programme
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We contrast two approaches to the prediction of latent variables in the model of factor analysis. The likelihood statistic is a sufficient statistic for the unobservables when sampling arises from the exponential family of distributions. Linear predictors, on the other hand, can be obtained as distribution-free statistics. We provide conditions under which a class of linear predictors is sufficient for the exponential family of distributions. We also examine various predictors in the light of the following criteria: (I) sufficiency, (ii) mean-square error, and (iii) unbiasedness and illustrate our results with the help of Chinese data on living standards.