Hello everyone,
I am testing for statistical interaction between two variables in a logistic regression model and I am finding that from a biologically plausible level the interaction changes. However, I want to back up this finding statistically so I have an additional argument for stratification. Therefore I added a three way interaction as continuous1*continuous2*cut-off continuous2, with p=0.01, so fitting with my observation.
Can anybody tell me whether this is valid and perhaps provide me with some evidence (I am so far unable to find any papers)?
Tim,
Did you include all of the lower-order terms (all main effects and two-way interactions)? If not, you need to for the higher-order term to be interpretable. But if so, I'm somewhat surprised the model converged at all, as the cut-off continuous2 contains absolutely no information that continuous2 does not.
What are you hoping to show with that continuous2 X cut-off interaction? There may be a better way.
Pat
Hey Pat,
Yes all the lower order terms are in.
I want to show that there is a threshold for certain combined effects of the 2 variables, or for other endpoints a flip in the increase/decrease according to the interaction. I have valid reason to stratify based on previous analyses but would like to have a less biased approach.
Tim,
In that case, I suggest going to nonlinear (e.g., quadratic) effects of the predictors, rather than the cutoff. If you have a good a priori idea of where the cutoff is, piecewise regression might serve you well.
Pat
I take it your model is E(y) = x1*x2*f, where x1 and x2 are continuous variates and f is a factor with two levels: say 0 when x2
Thanks for your answer Peter. Considering that there is a specific threshold within my data I do feel that the interaction representss my data, however, I have further explored Pat's advice and now I have added the quadratic terms, and their product to the model and I now see that the lines diverge from approximately the breakpoint that I used as a cut-off for the continuous variables. It seems to fit very well.
Thanks again for your responses.
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