On Jan 11, 2023, at 1:20 AM, Riccardo (Jack) Lucchetti <p002264(a)staff.univpm.it&gt; wrote: ***This email is from an external source. Only open links and attachments from a Trusted Sender.*** > On Sat, 17 Dec 2022, Fred Engst wrote: > 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. There is a fair number of similar statistics available in the "extra" package, under the name "scores2x2". Have you checked if your proposed statistic is in there already?