On a couple different projects with a 0/1 outcome variable to predict, I have noticed that running the logistic regression (generalized, with binomial variance) checking the No Intercept box boosts the Generalized R Square substantially, about 25 or 30 percentage points. My latest model is for a rare event that is observed at about 1.2% in the experience period population. Predictive models with an intercept yield Generalized R Squares at about .60 to .67, while models without the intercept are at about .95 to .98. I do have some key variables that are highly predictive, so at first I thought the Gen R Squares above 90% seemed reasonable. But the confusion matrix shows more errors than I would like, even lowering the threshold to 2%-5%. I do like the idea that No Intercept implies a blind log-odds ratio for the constant term since Intercept=0, like flipping a coin, Probability =0.50. But perhaps these models are too easy to beat, inflating the Generalized R Square that depends on the likelihood ratios of (L0=intercept only model) to (LM fitted models with X predictors). Particularly if I know before hand (a priori) that the outcome event is rare. So, while it would be great to write a brief that has Generalized R Square about 95%-98%, I think it might be more prudent and practical if I use a model with an intercept that comes in at Gen R Square at 60%. Please respond back if you have any advise for me. Thanks!
