Dear SPMers,
In order to better understand the effects of correlated regressors in 1st level SPM design, I've played around with simulated regressors. My fMRI data consist of 200 resting state fMRI volumes. I have created 3 design matrices:
(A). A matrix consisting of two random regressors ("Rand1 "=rand(200,1)*10; "Rand2"= Rand1 + rand(200,1)).
(B). A matrix consisting of only the 'Rand1'.
(C). A matrix consisting of the "Rand1" and an with regard to "RAnd1" orthogonalized regressor "Rand2_orth".
Utmost surprisingly, when in the first model testing for the "Rand1" (i.e. [1 0] ) I obtained more significant and extended activations than testing for "Rand1" in the other two models. Since the two original regressors "Rand1" and "Rand2" are so highly correlated (R>0.994), I would expect that only very little BOLD variance were left to be attributed to each of the mutually orthogonal components of the regressors in model (A). And in the unlikely cases I still should find some significant effects, I would strongly expect that testing for the effects of "Rand1" in the later two models (B) and (C) I would yield much more significant results, since the shared variance is eliminated in the later cases. The fact that I found the opposit to be true made me have to test new models, using similar designs but with new random vectors. I replicated the first results of increased significance when controlling with a very correlated vector, and can not understand how this could be the case. After having digged in the SPM code etc I still don't have a clue. Do anyone see how adding a very correlated regressor can push the effects of a random regressor even above the significance threshold of FWE corrected cluster?
Any insight on this would be highly appreciated!
Pär
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