[Gretl-users] Some suggestions on the "Number of cases ’correctly predicted'" from a logit/probit outputs

Hi Jack, Allin, Sven and all others on the gretl team, As you know, "Number of cases ’correctly predicted’" in a logit/probit model can be miss-leading even in a 50/50 split case. What we should be comparing is not zero ‘correctly predicted’, but rather random assignments based on sample mean. If a sample is 50/50 split, a random assignment would get 50% "correctly predicted", in theory. If our model's 'correctly predicted' is 70%, we are only 20 percentage points higher than a model based on random assignment, representing an improvement over the random assignment model by only 40%. Thus, I would like to propose an alternative output from gretl, i.e. the “Extra number of cases 'correctly predicted' over random assignment” (or something like that), call this dot_R-square perhaps. Dot_R-saure = (Y_hat_model - Y_hat_random) / (1-Y_hat_random) where Y_hat_model = sum(Y_hat_model_i=Y_i)/N Y_hat_random = Y_hat^2 + (1-Y_hat)^2 Y_hat is the sample mean Y_hat_model_i = Pro(Y_i = 1) >Y_hat Pro(Y_i = 1) >Y_hat = 1, if Pro(Y_i = 1) >Y_hat is true Unlike the McFadden R-squared, the interpretation of this is fairly straight forward, i.e. the percent that our model is better off than a model based on random assignment. Best, Fred