Abstract
Qualitative choice models are now widely used in economics. However, widely accepted measures evaluating the goodness of fit, predictive quality, or overall-success of such models do not exist, although many approaches have been suggested. Some measures are based on the likelihood-ratio test statistic, while others evaluate the residuals of the qualitative choice regressions, or use prediction-realization tables for analysis. Some measures are discussed in Amemiya (1981), Maddala (1983), Aldrich and Nelson (1984), Judge, Griffiths, Hill, Lütkepohl and Lee (1985) and Greene (1990), but these reviews are far from being complete.
A research draft on methods for the binary probit model covered by this paper was given at the First Munich Applied Econometrics Workshop in July 1989. This paper is an extended and completely revised version of it. I wish to thank Gerhard Arminger, Gebhard Flaig and François Laisney for many useful comments, John De New for excellent research assistance, and the German Science Foundation (DFG) for financial support. The paper was completed when I was visiting CentER, Tilburg University, in April 1990.
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References
ALDRICH, J. H., NELSON, F. D. (1984): Linear Probability, Logit, and Probit Models. Beverly Hills: Sage University Press.
AMEMIYA, T. (1980): “Selection of Regressors”. International Economic Review, 21, 331–354.
AMEMIYA, T. (1981): “Qualitative Response Models: A Survey,” Journal of Economic Literature, 19, 1483–1536.
ANDERSON, P., BAUER, R. K., FELS, E. (1954): On the Accuracy of Short-Term Entrepreneurial Expectations, mimeo.
BISHOP, Y. M. M., FIENBERG, S. E., HOLLAND, P. W. (1975): Discrete Multivariate Analysis, Cambridge, Mass., London, England
CRAGG, J. G., UHLER, R. (1970): “The Demand for Automobiles,” Canadian Journal of Economics, 3, 386–406.
CRAMER, H. (1946): Mathematical Methods of Statistics. Princeton
DHRYMES, P. J. (1986): “Limited Dependent Variables,” in Handbook of Econometrics, Vol. III, ed. by Z. Griliches and M. D. Intriligator, Amsterdam: North-Holland.
EFRON B. (1978): “Regression and Anova with Zero-One Data: Measures of Residual Variation,” Journal of American Statistical Association, 73, 113–121.
FOMBY, T. B., HILL R. C., JOHNSON, S. R. (1984): Advanced Econometric Methods. New York: Springer-Verlag.
GOLDBERGER, A. S. (1973): “Correlations Between Binary Choices and Probabilistic Predictions,” Journal of the American Statistical Association, 68, 84.
GOODMAN, L. A., KRUSKAL, W. H. (1954): “Measures of Association for Cross Classifications,” Journal of the American Statistical Association, 49, 732–764.
GOODMAN, L. A., KRUSKAL, W. H. (1974a): “Empirical Evaluation of Formal Theory,” Journal of Mathematical Sociology, 3, 187–196.
GOODMAN, L. A., KRUSKAL, W. H. (1974b): “More About Empirical Evaluation of Formal Theory,” Journal of Mathematical Sociology, 3, 211–213.
GREENE, W. H. (1990): Econometric Analysis. New York: Macmillan Publishing Company.
HAUSER, J. R. (1977): “Testing the Accuracy, Usefulness and Significance of Probabilistic Choice Models: An Information Theoretic Approach,” Operations Research, 26, 406–421.
HILDEBRAND, D. K., LAING, J. D., ROSENTHAL, H. L. (1974a): “Prediction Logic: A Method for Empirical Evaluation of Formal Theory,” Journal of Mathematical Sociology, 3, 163–185.
HILDEBRAND, D. K., LAING, J. D., ROSENTHAL, H. L. (1974b): “Prediction Logic and Quasi-lndependence in Empirical Evaluation of Formal Theory,” Journal of Mathematical Sociology, 3, 197–209.
JUDGE, G. G., GRIFFITHS, W. E., HILL, R. C., LÜTKEPOHL, H., LEE, T.-C. (1985): The Theory and Practice of Econometrics. New York: John Wiley and Sons.
KAWASAKI, S., MCMILLAN, J., ZIMMERMANN, K. F. (1983): “Inventories and Price Inflexibility,” Econometrica, 51, 599–609.
KAWASAKI, S., ZIMMERMANN, K. F. (1986): “Testing the Rationality of Price Expectations for Manufacturing Firms,” Applied Economics, 18, 1335–1347.
LAVE, C. A. (1970): “The Demand for Urban Mass Transportation,” Review of Economics and STATISTICS, 37, 320–323.
MADDALA, G. S. (1983): Limited-Dependent and Qualitative Variables in Econometrics. New York: Cambridge University Press.
MCFADDEN, D. (1973): “Conditional Logit Analysis of Qualitative Choice Behavior,” in Frontiers in Econometrics, ed. by P. Zarembka. New York: Academic Press, 105–142.
MCKELVEY, R., ZAVOINA, W. (1975): “A Statistical Model for the Analysis of Ordinal Level Dependent Variables” Journal of Mathematical Sociology, 4, 103–120.
MORRISON, D. G. (1972): “Upper Bounds for Correlation Between Binary Outcomes and Probabilistic Predictions,” Journal of the American Statistical Association, 67, 68–70.
NETER, J., MAYNES, E. S. (1970): “Correlation Coefficient with a 0,1 Dependent Variable,” Journal of the American Statistical Association, 65, 501–509.
Theil, H. (1966): Applied Economic Forecasting, Amsterdam.
VEALL, M. R., ZIMMERMANN, K. F. (1990a): Evaluating Pseudo R2’s for Binary Probit Models, mimeo. Forthcoming 1993: Quality Er Quantity. International Journal of Methodology.
VEALL, M. R., ZIMMERMANN, K. F. (1990b): Goodness of Fit Measures in the Tobit Model, mimeo.
VEALL, M. R., ZIMMERMANN, K. F. (1992a): “Pseudo R2’s in the Ordinal Probit Model,” Journal of Mathematical Sociology, 16, 333–342.
VEALL, M. R., ZIMMERMANN, K. F. (1992b): “Performance Measures from Prediction — Realization Tables,” Economics Letters, 39, 129–134.
ZIMMERMANN, K. F. (1986a): “On Rationality of Business Expectations: A Micro Analysis of Qualitative Responses,” Empirical Economics, 11, 23–40.
ZIMMERMANN, K. F. (1986b): “Multivariate Micro Prediction Analysis of Qualitative Models,” in Methods of Operations Research, 53, ed. by K. W. Gaede, K. Ritter and H. Schneeweiß, 683–696.
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Zimmermann, K.F. (1993). Goodness of Fit in Qualitative Choice Models: Review and Evaluation. In: Schneeweiß, H., Zimmermann, K.F. (eds) Studies in Applied Econometrics. Contributions to Economics. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-51514-9_3
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