Correlated error term residual in logit regression: what are my options?

Question

I have estimated a model with many interactions of both continuous and factor explanatory variables. The model is to be used for prediction.

My model has performed reasonably in out-of-sample testing.

However, I have found that my errors are correlated.

I took my fitted values of y and ran several regressions like this:

$$y\sim \text{fitted}(y)\cdot \text{explanatory variable}$$

There were many instances where an explanatory variable already included in the model was significant.

What are some good techniques to resolve this issue?

Side note:
I have no strong a priori views on what the "true" model should look like.

Answer 1

With numerical predictors, maybe you can spline them? Their effect might not be linear ... include interactions. There is not much specific information in your post, so see some similar posts for more information: Model building and selection using Hosmer et al. 2013. Applied Logistic Regression in R and for treatin autocorrelation see How can I test for autocorrelated errors in logistic regression?, How to account for temporal autocorrelation in logistic regression with longitudinal data?, How to account for temporal autocorrelation in mixed effects logistic regression?