I am fitting regression models using closely related and highly collinear critical variables.
I have used a few collinearity-reduction techniques, such as:
- variable selection.
Nevertheless, there is scope for further reduction.
Since my primary goal is to perform do inference on the variables, dimensionality reduction and variable selection are not the best options for me, because they make the variables and the models harder to interpret or even outright uninterpretable. Sadly, regularization is not an option for me given the specific type of regression model and the specific software package I am using.
Are there any other collinearity reduction methods that preserve as much information as possible while keeping the information contained in each of the critical variables distinct?