On Thu, Aug 30, 2012 at 7:54 PM, Lorenzo Cordani <[log in to unmask]> wrote:
> Dear all,
>
> I’m analyzing data from an fMRI experiment with 17 subjects and one within-subject factor with 6 levels (“WITHIN”). I also want to include 2 covariates of interest in my model (one I call “score” and one not varying over the levels, which is “age”). I’m using SPM5, if this is of importance.
>
> I checked the relevant posts on this matter and I think I understood roughly which way to go, but I still have some questions and would welcome any input you can give me on this.
>
> 1) I first performed a 1st-level analysis for each subject with one regressor for each level of “WITHIN” plus 6 motion regressors. From this analysis I get number-of-sessions*6 beta-images of interest. Now I can calculate a t-contrast for each condition to obtain the weighted sum of parameters for each condition (one con.img for WITHIN 1, one for WITHIN 2 etc).
> First question: Some of my subjects are missing one session. Do I have to adjust my contrasts for these subjects?
>>>> Yes. Instead of weighting each run with the value of 1 for each session, weight each session by 1/n where n is the number of runs. A more complicated approach would be to weight each run by the proportion of trials in the run e.g. if you have 10 trials in one run and 60 trials over all, you would weight that run by 10/60.
>
> 2) Now, as I understand the second level is a bit more complicated: Basically, I should do a one-way repeated measures ANCOVA with 2 covariates (a mixed model, because I have both within-subject and between-subjects effects, the covariates). So, as SPM doesn’t partition the residual variance for each effect I cannot evaluate the statistics for each effect in one model, right?
> Some posts in the list have suggested splitting up the model, each having the adequate error term, to test for the different effects.
>>>> This is correct, you need to partition the error; however, this is not easily done with repeated measures. If you look at different programs, the ANCOVA results will vary.
>
> a) I would use flexible factorial to model one ANCOVA design with 1 “WITHIN” factor, 1 “subjects” factor (because it is a repeated measures design) and 1 “score” covariate (the covariate with different values per condition). I wouldn’t include “age” in this model, because it’s collinear with the subject factor, right?
> Then, I would include the main effect for “subjects”, the main effect for “WITHIN” and the interaction WITHIN *score (under the “covariate” and “interaction with factor” option) in the model.
> This results in a matrix with 17 regressors for “subjects”, 6 regressors for “WITHIN” and 6 additional regressors (I guess each-level-of-WITHIN *score?). Is this ok?
> And how do I test for the WITHIN*score interaction? zeros(1,23) -2.5 -1.5 -0.5 0.5 1.5 2.5 ?
>>>> You really need a mixed regression model to properly answer this question. I wouldn't trust SPM with what you are trying to do. Could you try and simplify the model to answer your question? Perhaps computing the slope across your 6 conditions and then correlate that with the slope of the scores for each subject?
>
> b) For the main effect of “score” I use a second design: I would take the averaged parameter estimates for all conditions from the 1st-level (beta1+beta2+betam)/m), resulting in one contrast image per subject. Then I’d do a one-sample t-test in the 2nd-level with the “score” covariate.
> Is this how I can test for “score” and can I also test for “age” in this model this way?
>>>> This would work because its purely a between-subject design.
>
> And what about WITHIN *age? I’ve read it’s tricky to include covariates like age, but I don’t want to just leave it out. Any way how to deal with it?
>>>>> When your using a simple model like a GLM, then you need to simplify the question. As I said above, you could compute the slope across conditions at the first level and then ask if it correlates with age in a one-sample t-test with a covariate. In this way, you've removed the within-subject factor from the model and it implicitly is an interaction condition and age because the input is the condition effect.
>
> I also recently found a poster online that was on display in the HBM 2011 in Quebec (“Repeated measures Designs overestimate between-subject effects in fMRI packages using one error term”) by McLaren, Schultz, Locascio, Sperling and Atri. In this study the authors used in-house flexible factorial scripts using the correct error terms for within- and between-subject effects. I wonder if they are available, because I think they could be useful for my kind of design.
>>>> http://nmr.mgh.harvard.edu/harvardagingbrain/People/AaronSchultz/GLM_Flex.html
It won't do repeated-measure designs with covariates though.
>
> Thanks for your help
>
> Best regards
>
> Lorenzo Cordani
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