PSEUDO‐R² MEASURES FOR SOME COMMON LIMITED DEPENDENT VARIABLE MODELS

Abstract

A large number of different Pseudo-R2 measures for some common limited 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-R2 to use, if the estimation is in the context of an underlying latent dependent variable model, a case can be made for basing the choice on the strength of the numerical relationship to the OLS-R2 in the latent dependent variable. As such an OLS-R2 can 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-R2 measure due to McKelvey and Zavoina scores consistentiy well under our criterion. We also very briefly discuss Pseudo-R2 measures for count data, for duration models and for prediction-realization tables.

Distribution of Barnacle GeeseBranta leucopsisin Relation to Food Resources, Distance to Roosts, and the Location of Refuges

“…AIC was used to compare OLS and spatial autoregressive models. Since the OLS models report goodness of fit using R 2 , whereas the spatial autoregressive models use pseudo R 2 , they are not directly comparable (Veall & Zimmermann 1996). The spatial dependence of the two model residuals was also compared using Moran's I scatterplots.…”

Fears and realisations of employment insecurity

“…Useful surveys are presented by Windmeijer (1995) and Veall and Zimmermann (1996) amongst others. Table 4 reports two such R 2 measures.…”

“…This is of the 'explained variation class' of measures in that it mimics the standard R 2 in OLS since it can be interpreted as the ratio of explained sum of squares to the total sum of squares (Veall and Zimmermann, 1996). Simulations suggest that this measure most closely approximates the OLS R 2 for the underlying (unobserved) latent variable model (Hagle and Mitchell, 1992;Windmeijer, 1995) and hence it is an attractive choice.…”

Early childhood behaviours, schooling and labour market outcomes: estimates from a sample of twins

“…13 The χ 2 tests of whether the data for males and females could be pooled and a single equation estimated indicated that these samples should be examined separately. Veall and Zimmermann 1996). Absolute value of 't' statistics in parentheses.…”

“…However, the partial effect is very small, being around one percentage point. Note: The McFadden R 2 is calculated as 1 -(l m /l o ), where l m = the maximised log-likelihood value of the model and l o = the log-likelihood value if the non-intercept coefficients are restricted to zero (see Veall and Zimmermann 1996). Absolute value of 't' statistics in parentheses.…”