Most of the various kinds of pseudo-R2s are attempts at providing the
equivalent of the "variance explained" interpretation of the OLS R2. The
other interpretation of R2 is the proportional reduction in errors when
predicting the dependent variable or PRE. This is a measure of the
predictive capability of the model and can be calculated for other models
as well - the ssc post-estimation command -pre- will calculate this for
common model types (logit, ologit, mogit, poisson and the like). Some
don't like it because for some models it can actually be negative if the
model is worse than predicting the mode (for example with logit or probit
models that model a rare phenomenon). Nevertheless, I think it is useful
to know how the model improves prediction capability - this might in fact
be one of the more important measures of a model, yet it doesn't seem to be
widely used.
I prefer the plain old Pseudo-R2 (the proportional improvement in the
log-likelihood) for pseudo-R2s, since it is available for all models and is
easily calculated and understood. It is somewhat analogous to the pre, in
that it measures the improvement of the log-likelihood instead of the
reduction of errors.
