# How can root mean square error be used to predict logistic regression model accuracy?

The problem which I have at hand consists of a logistic regression model for risk evaluation that has been made on some credit card data of Quarter-1'12 (Jan'12 - Mar'12). Now I use the same model to evaluate risk for the data of Quarter-2'12(Apr'12-Jun'12). I want to devise an accuracy score that gives an insight into how "accurately" my model fits the new data (Quarter -2 data).

I have used Hosmer Lemeshow Statistic and Balanced Accuracy Method till now but none served the purpose. What further can be done in this regard?

• The mean square error in the predict probability for binary outcome case is the Brier score, which is a proper scoring rule. Optimizing proper scoring rules corresponds to finding predicted probabilities that are well calibrated to the actual probabilities in the data. Is this the kind of "accuracy" you are looking for?
– user44764
Jul 1, 2014 at 14:10
• @Matthew I am looking for a measure that can ensure logistic regression model (made on an older data) fitting a new data-set. I want it to alert me when the model is not predicting accurately so that I can re-model my regression model to new data-set. What I meant by accuracy is that a new score should be able to indicate the error between observed (values of new data-set) and predicted values (by the model trained on older data-set) Jul 2, 2014 at 7:52
• Lots of options since what you're looking for isn't very specific. There is the brier score I mentioned, or any other proper scoring rule. Also look at this thread.
– user44764
Jul 2, 2014 at 13:52

If I understand correctly, the situation is that you have an estimated logistic regression model that you use in production. So you need a system of quality control that can tell you if the model start to perform worse.

One possibility could be to calculate a running Brier score, you could on the same plot indicate the expected Brier score assuming the model is correct and calibrated. That should give a reference value. There might be some ideas in this stored search.

The Brier score is a proper scoring rule, you could also choose to use some other proper scoring rule.

• how is the mean squared error different to brier score? Oct 19, 2020 at 15:17