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?
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Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucche...@univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
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