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Alternative Measures of the Explanatory Power of Multivariate Probit Models with Continuous or Ordinal Responses

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  • Martin Spieß
  • Gerhard Tutz

Abstract

In this paper R2-type measures of the explanatory power of multivariate linear and categorical probit models proposed in the literature are reviewed and their deficiencies are discussed. It is argued that a measure of the explanatory power should take into account the components which are explicitely modeled when a regression model is estimated while it should be indifferent to components not explicitely modeled. Based on this view three different measures for multivariate probit models are proposed. Results of a simulation study are presented designed to compare two measures in various situations and evaluate the BCa bootstrap technique for testing the hypothesis that the corresponding measure is zero and to calculate approximate confidence intervals. The BCa bootstrap technique turned out to work quite well for a wide range of situations, but may lead to misleading results if the true values of the corresponding measure is close to zero.

Suggested Citation

  • Martin Spieß & Gerhard Tutz, 2002. "Alternative Measures of the Explanatory Power of Multivariate Probit Models with Continuous or Ordinal Responses," Discussion Papers of DIW Berlin 291, DIW Berlin, German Institute for Economic Research.
    • Handle: RePEc:diw:diwwpp:dp291
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    References listed on IDEAS

    as
    1. McElroy, Marjorie B., 1977. "Goodness of fit for seemingly unrelated regressions : Glahn's R2y.x and Hooper's r2," Journal of Econometrics, Elsevier, vol. 6(3), pages 381-387, November.
    2. Glahn, Harry R, 1969. "Some Relationships Derived from Canonical Correlation Theory," Econometrica, Econometric Society, vol. 37(2), pages 252-256, April.
    3. Carter, Richard A. L. & Nagar, Anirudh L., 1977. "Coefficients of correlation for simultaneous equation systems," Journal of Econometrics, Elsevier, vol. 6(1), pages 39-50, July.
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    Keywords

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    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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