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 June 21, 2012 06:03AM
Hi,
I have a naive question (sorry if the answer is obvious). Let me say that I have a design with one factor A with three modalities A1, A2, and A3. During the experiment, subjects were presented with stimuli belonging to the three categories. There were 10 exemplars for each factor (that is a example). I run a GLM analysis, and get the statistical maps.
Now I discover that the 10 exemplars are not equivalent, and may fall into two categories B1 and B2 that potentially result in different cortical activations and/or interact with the first factor. Therefore, I now have orthogonal two factors A and B, and the stimuli fall into six categories, A1B1, A1B2, A2B1, A2B2, A3B1, A3B2.
So I split design matrices and run another GLM analysis.
Now I want to verify that both analyses are coherent, so I compute the following "contrasts": A1B1+A1B2, A2B1+A2B2, A3B1+A3B2 that I compare to main statistics of A1, A2, and A3 in the first analysis.
Statistical maps look similar between the two analyses, but there are some differences. Things get more different (although the patterns are still qualitatively similar) when I use the individual results in a group analysis.
My understanding is that if inputs of the GLM analysis were simple measures (say from a behavioral experiment), both analyses should be exactly similar (sums of squares are additive, or am I wrong?).
However, things are here not so simple, because the input is a canonical response function fitted to the BOLD response, and the fitting might be different depending on what model is fitted to what data. So I checked the fitted responses, and they indeed look a little bit different (again, overall pattern look very similar). Even though the signal is (of course) similar, the model, and the fitted responses are different. I am not quite sure why, but it looks like when there are, for instance, two successive stimuli B1 and B2, the second model will try to fit two independent gamma functions for B1 and B2, while the first analysis tries to fit the addition of two successive gamma functions. Therefore the models are slightly different.
So here are my questions:
- Is my interpretation correct, and in this normal ?
- Which model is more correct ? I know the rule "any potential source of effect should be included in the model", but what if it turns out that the second variable has no significant effect? Should I remove it from the model, since the first model seems to have a little bit more statistical power ?
- How could I be sure that both analyses are coherent and that I have not make a mistake somewhere ?
Thanks !
Guillaume
Subject Author Posted

Guillaume Lemaitre June 21, 2012 06:03AM

#### Re: Additivity in GLM analysis

Gang June 21, 2012 05:31PM

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