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DARP Paper
Prediction and Sufficiency in the Model Factor Analysis
Ramses H. Abul Naga
November 1997
Paper No' DARP 031:
Full Paper (pdf)

Tags: latent variables; factor analysis; sufficiency; prediction; exponential family of distributions; living standards analysis

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.