Imagine I have a block design with three conditions and no “baseline” or “rest” periods, so my model contains a regressor for each block type. For each condition 3dDeconvolve will compute a t-value and a beta. I understand (I think) that these are marginal statistics, that is each t-value represents the significance of the effect compared to the model with only that effect removed. I’m confused about the baseline against which each beta is defined in this case. Looking, for example at page 5 of https://afni.nimh.nih.gov/pub/dist/doc/misc/Decon/3dDecon_Apr2007.pdf, it seems to suggest that the baseline would not include the the effects of the other two regressors. In the case like this where there is no implicit baseline, would each individual beta be relative to the model that included the combined effects of the other two regressors? I’m having some trouble reconciling these two ideas in my mind. Would the betas even be interpretable in such a case? I’d be very grateful for any help thinking about this.
In order to model this, there really must be a baseline condition. Otherwise there is no distinction between “equally active for all tasks” and “dead salmon” - we can only evaluate contrasts.
In your case, it is not really possible to get separate beta weights for all 3 conditions. One of them must be considered as a baseline, to which the others could be compared. The 3 possible basic contrasts (A-B, A-C, B-C) would then simplify (A-B, A, B), were condition C to taken as the baseline.
Does this seem reasonable?
Rick, thank for the fast reply! I understand the need for a baseline here and the ambiguity issue. The original study was designed only to look at relative differences between conditions and not activation levels for any one condition per se. Given that 3dDeconvolve will still produce a beta for each condition, can you help me understand how to think about what that means? Does it make sense to think of it as deviation from a voxel-wise mean that includes the other two conditions?
3dDeconvolve cannot produce a beta for each condition, one must be the baseline against which other would be compared.
For such a case you should declare some condition ‘C’ to be the baseline, and consider the 3 contrasts as those A-B, A and B betas (which would mean A-B, A-C, B-C, viewing condition C as the baseline).
I think this is essentially what you must do, regardless of the software.