Is simply including a covariate in a model (ANCOVA) enough for variance in the DV due to it to be factored away? Or do the higher order interactions of the covariate with the other factors of the model have to be modelled as well?
In some software (e.g. Statistica), you have to specifically ask what factorial effects you want to have tested, and it seems to make a huge difference in the results whether you just ask for the main effect of the covariate or also ask for its crossings with all other categorical IVs.
I suppose it's up to the researcher/situation if you would then decompose any of those computed interactions (it would presumably depend on whether you consider the covariate to be 'of interest' or not), but the question is, which specific interactions do you "ask for" in the first place? Is there a trade-off between how informative an effect would be if included in the model VS the cost it would then have on inference power?
Also, does the covariate (continuous) factor have the same 'status' among the other (categorical) factors, i.e. is it somehow less important to include covariate-related interactions than it is to include categorical-factor-related interactions? Or does the selection of the requested interactions simply depend on hypotheses rather than being a simple answer such as "all possible interactions should be requested"?
Thanks a lot for any help!