Comments on goodness-of-fitmeasures in binary choice models by frank windmeijer

Why study Pseudo-R²,s for limited dependent variable models? After all, even in the much clearer ordinary least squares case, R² is a poor guide to model selection, at least when used by itself, because it never decreases and typically increases whenever an independent variable is added. There are even cases where R² will tend to one when there is no relationship among the (nonstationary) variables whatsoever (Granger and Newbold, 1974). Surely applied researchers would not want to bother with such a statistic in the limited dependent variable case, particularly when the intuitive explainedvariation- to- total- variation interpretation is no longer available.