difference in predictions approach to contrasts

[Ryan Jarrett]

Hi regression modeling strategists,

 

I have a quick question about the “difference in predictions” approach to testing contrasts, as it relates to question 4 of the homework (chapter 9). As I understand it, the approach is to calculate the predicted response at multiple different values of interest in order to essentially recreate the response profile for a set of covariates. For example, in our case we would have two curves, corresponding to treatments B and C, which are quadratic in age. My question: do we need to evaluate the predicted values at multiple points in order to test the hypothesis of equivalence of treatment B and treatment D at a single point (i.e. age =30), or is the technique used primarily to reconstruct the response profiles for the purpose of future testing and/or viewing the effect of different drugs over a range of values?

 

If it seems that I am off base in my approach, please let me know.

 

Thanks!

Ryan

[Frank Harrell]

The general answer is that you have to evaluate the contrasts (differences in predictions) at a set of covariate values for covariates that are allowed to interact with the factor of interest, when the particular value of those covariates is not conditioned upon.  The chunk test for no effect over the entire set of covariate settings you varied is a simultaneous test of all differences equalling zero.  When there is only one value of a covariate the chunk test simplifies to a 1 d.f. test.  Let us know if that doesn't get you further.