Pseudo-R Measures for Some Common Limited

A large number of different Pseudo-R measures for some common limited 2 dependent variable models are surveyed. Measures include those based solely on the maximized likelihoods with and without the restriction that slope coefficients are zero, those which require further calculations based on parameter estimates of the coefficients and variances and those that are based solely on whether the qualitative predictions of the model are correct or not. The theme of the survey is that while there is no obvious criterion for choosing which Pseudo-R to use, if the estimation is in the context of an underlying latent 2 dependent variable model, a case can be made for basing the choice on the strength of the numerical relationship to the OLS-R in the latent dependent variable. As such an OLS-R can 2 2 be known in a Monte Carlo simulation, we summarize Monte Carlo results for some important latent dependent variable models (binary probit, ordinal probit and Tobit) and find that a Pseudo-R measure due to McKelvey and Zavoina scores consistently well under our criterion. 2 We also very briefly discuss Pseudo-R measures for count data, for duration models and for 2 prediction-realization tables. Acknowledgements: We thank John DeNew for excellent research assistance. Useful comments were provided by Deb Fretz, Colin Cameron, Frank Windmeijer, the participants at seminars at McGill and McMaster University, three anonymous referees and the editor. The authors are responsible for all errors and shortcomings. The former author thanks the Alexander von Humboldt Foundation and the Social Sciences and Humanities Research Council of Canada. The second author acknowledges support by the German Science Foundation. 2