Dear Zhi
> 1. What is the size of smoothing kernal should I take during time series extraction? I found that the size of the smoothing core will influence the significance of the estimated parameters, especially the ROIs are very close to each other in anatomy. On my case, I found the modulatory connectivity from the left dorsolateral cortex to the left caudate is significant when a 8mm-FWHM Gaussian kernal was applied, however, its significance disappeared when a 5mm-FWHM Gaussian kernal was applied. I checked the mask of ROIs, the individual caudate mask was very close to the individual thalamus mask. And the modulatory connectivity from the left dorsolatoral cortex to the left thalamus was significant no matter what the size of smoothing kernal is. I am wandering that if the significant connectivity between the left dorsolateral cortex and the left caudate was caused by the connectivity between the left dorsolateral cortex and the left thalamus?
Short answer - use whatever smoothing kernel gives you the best results in your initial GLM analysis. Slightly longer answer - by matched filter theorem, you want the size of the kernel to match the spatial extent of the effect you want to detect. You don't know how big the true effect is, so you can do an informal model comparison to determine the optimal kernel that maximises your t-statistic. Also note that the more smoothing you add, the less confident you can be about your anatomy. Also, if you are using voxel-wise family-wise error connection, be careful not to reduce the smoothing too much- FWE correction is only appropriate if the estimated smoothness of the data (FWHM given at the bottom of the SPM results table) is at least 3 times the voxel size.
> 2. How should I define the design matrix X in PEB? If I have one group, and I just want to investigate the group effect, the X should be a N*1 vector, right? if I have two groups, for example, 6 subjects with 3 in each group, should I set the X matrix as following form?
1 1
1 1
1 1
1 -1
1 -1
1 -1
Yes.
> If I have more than two groups, how should I set the X matrix then? In addition, if I have other covariates such as gender and age, if the following X matrix is correct?
> The second column denotes group, while the third column denotes gender and the last column denotes age. Sorry I did not found the example of the X matrix setting, hence I could not understand it intuitively. For example, I am still not clear about the meaning of 'mean-correct' during the X matrix setting, the mean of group?
> 3. Another question regarding the design matrix X is that if I would like to investigate the difference between two experimental conditions on the same connectivity, between groups, which mean a 2 (between group) x 2 (within group) deign, should I set the deign matrix as the PEB example on the effect of treatment? LIke:
Lots of people are asking questions of this sort, so I have added a section to the SPM Wiki which should hopefully clarify all this - https://en.wikibooks.org/wiki/SPM/Parametric_Empirical_Bayes_(PEB)#Example_design_matrices
If anything remains unclear, please let me know.
> 4. Finally, according to my understanding, we need to use posterior probability or free energe to threshold the parameters, but which threshold should we take, more than 90 or 95 or even 99? How could I get the parameter estimation from each subject, still I need to use 'spm_dcm_bmr' to get them, PEB will not derive the individual averaging parameters across models, is that correct? In addition, how to interprete the results of PEB in investigate the effects of covariates. For example, I found a main effect of gender on a certain connectivity, the result seemed to be a parameter coefficient 0.565, what's the meaning of this coefficient, and how could I know if the males showed greater connectivity than females or vice versa?
Regarding thresholding, no, this is not necessary. It's just to focus the reader's eye on the most probably effects. With Bayesian statistics, you have a probability for each effect - there's no p-value and no concept of significance. So report all parameters' probabilities, and focus your discussion on the most probable ones (e.g. Pp > 0.9 or Pp > 0.95).
With regards to interpreting the parameters, if this isn't resolved after reading the Wiki page above, I recommend reading the recent tutorial paper, which goes through a worked example in detail: https://github.com/pzeidman/dcm-peb-example . As you'll see, the PEB scheme is like doing an ANOVA on your DCM connectivity parameters, so the PEB parameters have the same meaning as the parameters of the underlying DCM. Feel free to ask more questions if needed.
Best
Peter
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