Is plotting the log_odds vs independent variables an appropriate way to check the linearity in logistic regression with multiple predictors?
I feel the assumption should be that linearity between dependent and an independent variable exists when other independent variables are kept constant. But since in the data other independent variables are also varying, is such a scatter plot appropriate way of checking linearity?
The trouble with your plan is that you don’t know the log-odds. You can predict the log-odds through some method like what you suggested in the comments by grouping your time series by month, but then you’re comparing your predictions to other predictions. Even setting aside the influence of multiple features, if your plot shows nonlinearity, it will be a challenge to untangle if that is because of regression misspecification or because of an error from your other method of predicting.