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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.

Suggested Citation

  • Ramses H. Abul Naga, 1997. "Prediction and Sufficiency in the Model Factor Analysis," STICERD - Distributional Analysis Research Programme Papers 31, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  • Handle: RePEc:cep:stidar:31
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    File URL: http://sticerd.lse.ac.uk/dps/darp/darp31.pdf
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    References listed on IDEAS

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    1. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626.
    2. Garratt, Anthony & Hall, Stephen G, 1996. "Measuring Underlying Economic Activity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(2), pages 135-151, March-Apr.
    3. 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.
    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. Zimmerman, David J, 1992. "Regression toward Mediocrity in Economic Stature," American Economic Review, American Economic Association, vol. 82(3), pages 409-429, June.
    6. 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 422-449, June.
    7. 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.
    8. 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 1093-1108, July.
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    More about this item

    Keywords

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

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • I3 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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