Hi,
I got some questions about assumption and interpretation of conditional logistic regression. It seems that two of my variables (let says N and O) have non-linear effects. In fact, their effects look parabolic, so I transform O and N into quadratics variables (now N+N2 and O+O^2) in my model. The variable O (now became O+O^2) is the most interesting variable in my model and I want to look for interaction of this variable with some others including variable N (now became N+N^2).

The questions are:

1) Is the transformation necessary (what does the transformation do to the variable/model) for the assumption and how do I interpret quadratics terms after (O+O^2)?

2) How do I put interaction between a quadratic and a simple variable (O^2:O:X, O^2:X + O:X, etc.)?

3) How do I put interaction between two quadratics variables in the model (O^2:N^2:O:N, O:N+ O^2:N + O:N^2: O^2:N^2, etc.)

4) How do I interpret these quadratics interactions?