Hi, I have a question regarding the interpretation of contrasts among
main effect coefficients when the same parametric modulator (PM) is
also included in the model for both main effects. Given the following
estimated coefficients (two conditions and the same PM for both):
A AxPM B BxPM
My understanding is that A reflects the the effect of the condition
that is NOT modulated by the PM (i.e., the effect of A cleaned of any
variability due to the PM). Same for B, of course. My questions:
1. How should I interpret the contrast among A and B ([1 0 -1 0]). Can
this be interpreted as differences among A and B that cannot be
attributed to differences among the PM?
2. If not, then what is the appropriate interpretation?
3. If not, would the appropriate model be a single predictor
estimating the general effect of A and B (so, A+B) with two PMs
modeling (1) the differences among A and B and (2) the PM in the
original model. I understand that, in this case, the first effect
would actually need to be entered last given serial orthogonalization
Thanks very much for any tips.
Department of Psychology
University of California, Los Angeles