I have a panel data for 453 groups over a period of 6 years. The objective is to use the previous year properties (predictors) of a group to predict an outcome of 0/1. After fitting a conditional fixed effects logit model I got a McFadden's R-square of 0.243. I calculated the predicted probabilities using Hosmer, Lemeshow, and Sturdivant 2013 eq. 7.4 shown in the picture attached. After getting these predicted probabilities, I get a brier score of 0.32. However, If I calculate the brier using simple prediction based on historical data, i.e. I only look at the number of positive outcomes in the past years without taking into account the predictors of the model, I get a better brier score of 0.22. Is this considered normal? Is it a property of the logit model to have limited predictability?
Any insight is appreciated.
Any insight is appreciated.
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