Abstract
For multivariate probit models, Spiess and Tutz suggest three alternative performance measures, which are all based on the decomposition of the variation. The multivariate probit model can be seen as a special case of the discrete copula model. This paper proposes some new measures based on the value of the likelihood function and the prediction-realization table. In addition, it generalizes the measures from Spiess and Tutz for the discrete copula model. Results of a simulation study designed to compare the different measures in various situations are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aldrich, J.H., Nelson, F.D.: Linear Probability, Logit, and Probit Models. SAGE, Thousand Oaks (1984)
Ashford, J.R., Sowden, T.: Multi-variate probit analysis. Biometrics 26, 535–546 (1970)
Bishop, Y.M.M., Fienberg, S.E., Holland, P.W.: Discrete Multivariate Analysis: Theory and Practise. MIT Press, Cambridge (1980)
Cohen, J.: A coefficient of agreement for nominal scales. Educ. Psychol. Meas. 20, 37–46 (1960)
Cox, D.R.: Analysis of Binary Data. Chapman & Hall, London (1989)
Cragg, J.G., Uhler, R.: The demand for automobiles. Can. J. Econ. 3, 386–406 (1970)
Estrella, A.: A new measure of fit for equations with dichotomous dependent variables. J. Bus. Econ. Stat. 16, 198–205 (1998)
Goodman, L.A., Kruskal, W.H.: Measures of association for cross-classification. J. Am. Stat. Assoc. 49, 732–764 (1954)
Joe, H.: Multivariate Models and Dependence Concepts. Chapman and Hall, London (1997)
Joe, H., Hu, T.: Multivariate distributions from mixtures of max-infinitely divisible distributions. J. Multivar. Anal. 57, 240–265 (1996)
McFadden, D.: Conditional logits analysis of qualitative choice behavior. In: Zarembka, P. (ed.) Frontiers in Econometrics, pp. 105–142. Academic Press, New York (1973)
McKelvey, R.D., Zavoina, W.: A statistical model for the analysis of ordinal level, dependent variables. J. Math. Soc. 4, 103–120 (1975)
Molenberghs, G., Lesaffre, E.: Marginal modelling of correlated ordinal data using a placket distribution. J. Am. Stat. Assoc. 89, 633–644 (1994)
Moran, P.A.P.: Partial and multiple rank correlation. Biometrika 38, 26–32 (1951)
Nelsen, R.B.: An Introduction to Copulas. Springer, New York (1999)
Sklar, A.: Fonctions de répartition à n dimensions et leur marges. Publ. Inst. Stat. Univ. Paris 8, 229–231 (1959)
Spiess, M., Keller, F.: A mixed approach and a distribution free multiple imputation technique for the estimation of multivariate probit models with missing value. Br. J. Math. Stat. Psychol. 52, 1–17 (1999)
Spiess, M., Tutz, G.: Alternative measures of the explanatory power of general multivariate regression models. J. Math. Soc. 28, 125–146 (2004)
Tschuprow, A.A.: Grundbegriffe und Grundprobleme der Korrelationstheorie. Teubner, Leipzig (1925)
Veall, M.R., Zimmermann, K.F.: Pseudo-R2 in the ordinal probit model. J. Math. Soc. 16, 333–342 (1992a)
Veall, M.R., Zimmermann, K.F.: Performance measures from prediction-realization tables. Econ. Lett. 39, 129–134 (1992b)
Veall, M.R., Zimmermann, K.F.: Pseudo-R2 measures for some common limited dependent variable models. J. Econ. Surv. 10, 241–259 (1996)
Xu, J.J.: (1996) Statistical modelling and inferences for multivariate and longitudinal discrete response data. Ph.D. thesis, Department of Statistics, University of British Columbia
Yule, G.U.: On the methods of measuring association between two attributes. J. R. Stat. Soc. 75, 579–642 (1912)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Meinel, N. Comparison of performance measures for multivariate discrete models. AStA Adv Stat Anal 93, 159–174 (2009). https://doi.org/10.1007/s10182-008-0078-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10182-008-0078-x