I have to pull through a regression on a set of probabilities (so values between 0 and 1). Those probabilities are related to a binary variable, which I have to forecast exactly.

My code basically uses a logit transformation to make the probability data "wider" and then calculate the betas and the forecasts (based on out-of-sample information); then it makes a logit transformation and gives 1 or 0 to the forecasts if their value is over or below 0.5.

The R squared and other performance measures tell me that the regression works fine for in-sample data but those forecast really tell me another story (they float around 0.52-0.55).

Has anybody got any suggestion about this problem or how to better my procedure?

P.S. I already tried logistic regression (always with the >0.5 classification method) but I obtained same results.

  • $\begingroup$ Is this time series data I assume? If so, are you accounting for time trends and stationarity? $\endgroup$ – robin.datadrivers Apr 15 '15 at 15:34
  • 2
    $\begingroup$ You might consider beta regression as a formal alternative to your inverse logit approach. But from your description my feeling is that this won't substantially change the results. Might be worth trying, though. $\endgroup$ – Achim Zeileis Apr 15 '15 at 15:37
  • $\begingroup$ The timespan is quite short so the effect should not be very important, anyway I'll give a try to removing them. I never heard of Beta Regression but I'll look straight at that . $\endgroup$ – Stefano R. Apr 15 '15 at 15:53

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