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Prediction and Sufficiency in the Model Factor Analysis

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  • Ramses H. Abul Naga

Abstract

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.

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File URL: http://sticerd.lse.ac.uk/dps/darp/darp31.pdf
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Bibliographic Info

Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Distributional Analysis Research Programme Papers with number 31.

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Date of creation: Nov 1997
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Handle: RePEc:cep:stidar:31

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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

Keywords: Latent variables; factor analysis; sufficiency; prediction; exponential family of distributions; living standards analysis;

References

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  1. Chamberlain, Gary & Griliches, Zvi, 1975. "Unobservables with a Variance-Components Structure: Ability, Schooling, and the Economic Success of Brothers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(2), pages 422-49, June.
  2. Zimmerman, David J, 1992. "Regression toward Mediocrity in Economic Stature," American Economic Review, American Economic Association, vol. 82(3), pages 409-29, June.
  3. Wegge, Leon L., 1996. "Local identifiability of the factor analysis and measurement error model parameter," Journal of Econometrics, Elsevier, vol. 70(2), pages 351-382, February.
  4. Ramses H. Abul Naga, 1994. "Identifying the Poor: A Multiple Indicator Approach," STICERD - Distributional Analysis Research Programme Papers 09, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  5. Garratt, Anthony & Hall, Stephen G, 1996. "Measuring Underlying Economic Activity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(2), pages 135-51, March-Apr.
  6. van Praag, Bernard M S & Hagenaars, Aldi J M & van Eck, Wim, 1983. "The Influence of Classification and Observation Errors on the Measurement of Income Inequality," Econometrica, Econometric Society, vol. 51(4), pages 1093-108, July.
  7. Abul Naga, Ramses & Antille, Gerard, 1990. "Stability of robust and non-robust principal components analysis," Computational Statistics & Data Analysis, Elsevier, vol. 10(2), pages 169-174, October.
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