Pseudo-R2 Measures for Some Common Limited Dependent Variable Models

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 consistently well under our criterion. We also very
briefly discuss Pseudo-R2 measures for count data, for duration
models and for prediction-realization tables.