I am carrying out a logistic regression with $24$ independent variables and $123,996$ observations. I am evaluating the model fit in order to determine if the data meet the model assumptions and have produced the following binned residual plot using the arm
R
package:
Obviously there are some bad signs in this plot: many points fall outside the confidence bands and there is a distinctive pattern to the residuals. My question is - can I attach these issues to specific assumptions of the logistic regression model? For instance, can I say that there is evidence of non-linearity in the independent variables or of heteroscedasticity? If not, are there other diagnostics I can produce to help identify where the problem lies?
Based on Daniel's answer, it appears that the main issue is I was using residuals on the logit scale but expected values on the response scale. If I reproduce the plot with the residuals also on the response scale it looks like this:
which is much more believable.