Thanks, Cyril and Bas!
Things are getting MUCH clearer now that I stopped thinking of the derivatives as being time-shifted canonical HRFs and started thinking of them as actual derivative functions : )
Making sure I finally got this right:
- Using derivatives might result in more statistical power for detecting an amplitude-based effect because the error term of the linear equation predicting the BOLD response might have diminished by taking out temporal and dispersion variance effects from the error term. It also allows for the direct testing of onset- and duration- effects by contrasting the temporal and dispersion derivatives, respectively.
- To test the A-B contrast (amplitude of the BOLD response in condition A versus condition B), the following contrast would apply: (1 0 0 -1 0 0).
- If I'm interested in the regions that showed latency or dispersion effects in the BOLD response for the A-B contrast, then I should test contrasts with the temporal (0 1 0 0 -1 0) or dispersion derivatives (0 0 1 0 0 -1). That is, regions that showed different onsets or durations in cond A vs. cond B will be revealed.
Last question: I want to use derivatives in the analysis of a blocked-design dataset (These data were acquired with a 2-shot EPI, and I am aware that my effectively double TR (2.529*2=5.058s) might have repercussions on the HRF, hence my wanting to use derivatives). How can I test for and deal with potential colinearity problems? If in this case I am *not* interested in latency or duration effects, is it correct to think that colinearity might no add much to my model, but would not be a problem for testing for amplitude effects?
Revisiting differential calculus (almost) made my day..