I would like to use a logistic regression for estimating the parameters of the logit function by using the maximum likelihood estimate. This amounts to minimizing the log-loss function, instead of minimizing another loss function such as squared error.
To assess a model's predictive power I want to employ this strategy to the training set. This is essentially minimizing the log-loss cost function with respect to the parameters of the model. But now I can use a different loss function to assess predictive performance such as briers score? Or log-loss as was used in the parameter estimation? Or it doesn't matter since these are two two loss functions are answer different questions of model fitting and performance checking?
It would seem I want to find the model's parameters in which it finds the minimum of a loss function, then the same loss function is used to assess predictive performance of the model.
Source: Defining predictive vs estimation beginning of intro https://www.ine.pt/revstat/pdf/rs070102.pdf