Dear K&M
That looks excellent. A couple of suggestions:
- You might want to z-score age so it's roughly in the same range as the other variables, but this is not mandatory.
- Your second design (PEB-of-PEBs) is overly complicated, which might reduce statistical efficiency. You've correctly got a PEB for each group (PEB 1-4), including effects of time and confounds. Now you just need one more PEB (PEB-of-PEBs), with covariates for the overall mean and group differences - i.e., combine PEBs 5-8 into a single model.
I am hoping your much simpler first design will have the better (more positive) free energy :-)
Best
Peter
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From: SPM (Statistical Parametric Mapping) <[log in to unmask]> On Behalf Of <No name available>
Sent: Tuesday, May 2, 2023 1:34 AM
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Subject: [SPM] DCM Resting State 3-Between and 1-Within Factors
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Hi everyone,
I'm running DCM on some resting state data and hoping someone could help check the design matrices for the analyses below. Apologies for the lengthy message but we wanted to give you as much detail as possible and organized in a manner it was presented on the Wiki website.
Data: Resting State
4 ROIs (assuming full model): L and R Nucleus Accumbens (NACC), lateral habenula (LHAB) and ventral tegmental area (VTA)
Participants: Patients and Controls; Patients are further broken down down into two groups: treatment responders and non-responders
Time: All participants completed resting state scan pre and post treatment. Controls completed pre and post scan without intervention.
Separate DCM was fitted for each of these 6 experimental conditions for each subject. The names in the brackets are example variable names to store the DCMs for each condition 1. Responders Pre (GCM_R_Pre) 2. Responders Post (GCM_R_Post) 3. Non-Responders Pre (GCM_NR_Pre) 4. Non-Responders Post (GCM_NR_Post) 5. Controls Pre (GCM_HC_Pre) 6. Controls Post (GCM_HC_Post)
There are 24 responders, 20 non-responders and 23 controls with pre and post scans. Thus, we would need to mean center since we have an unbalanced design.
On the Wiki website we were able to find the hierarchical experimental design example for two groups, but since we have 3, we wanted to make sure that the PEB design below was correct. Here's the Option 1 on Wiki adapted to our data set.
1. Overall mean (all 1s)
2. Main effect of TwoGroup (1s for Patients, -1s for Controls, and then mean-centered) 3. Main effect of ThreeGroup (-1s for Responders, 1s for Non-Responders, 0s for Controls, and then mean-centered) 4. Main effect of Time (-1s for pre, 1s for post, and then mean-centered) 5. Interaction of TwoGroup x Time (the mean corrected main effects 2. and 4. element-wise multiplied) 6. Interaction of ThreeGroup x Time (the mean corrected main effects 3. and 4. element-wise multiplied)
and then we are also including the covariates:
Treatment type: CBT vs SSRI
Sex: Male vs Female
Age
7. Covariate 1. Treatment Type (1s for CBT, -1s for SSRIs, and 0s for controls; and then mean-centered) 8. Covariate 2. Sex (1s for Men, -1s for Women, and then mean-centered) 9. Covariate 3. Age (mean centered)
Attached is the design matrix of what these regressors would look like (look at the mean centered tab). Is the design matrix correct?
We would then fit this PEB models to all DCMS across subs and time points (in the right order to match the regressors we created):
GCM = {GCM_R_Pre; GCM_R_Post; GCM_NR_Pre; GCM_NR_Post; GMC_HC_Pre; GCM_HC_Post}; PEB = spm_dcm_peb(GCM, x);
We also wanted to compare the free energy between Option1 and Option 2 on Wiki and see which approach would be better for us.
Here's how we understand Option 2 (PEB-of-PEBs approach) should be set up and please correct us if we are wrong:
For patients we will have a design matrix X1 with regressors:
1. Main effect of patients
2. Effect of Time on Patients (-1 for pre, 1s for post; and then mean-corrected)
GCM_P = {GCM_P_pre; GCM_P_post};
PEB1 = spm_dcm_peb(GCM_P, X1);
For Healthy Controls we will have a design matrix X2 with regressors:
1. Main effect of controls
2. Effect of Time on Controls (-1s for pre, 1s for post; and then mean-corrected)
GCM_HC = {GCM_HC_pre; GCM_HC_post};
PEB2 = spm_dcm_peb(GCM_HC, X2);
For Responders we will have a design matrix X3 with regressors:
1. Main effect of responders
2. Effect of Time on Responders (-1s pre, 1s for post; and then mean-corrected)
GCM_R = {GCM_R_pre; GCM_R_post};
PEB3 = spm_dcm_peb(GCM_R, X3);
For Non-Responders we will have a design matrix X4 with regressors:
1. Main effect of non-responders
2. Effect of Time on Non-Responders (-1s pre, 1s for post; and then mean-corrected)
GCM_NR = {GCM_NR_pre; GCM_NR_post};
PEB4 = spm_dcm_peb(GCM_NR, X4);
We are assuming that if we wanted to include the three covariates we mentioned in Option 1 (treatment type, sex and age), they should be included in each of these individual design matrix X1-X4, correct?
In order to then assess all possible combinations, would the right third level PEBs be:
# Patients vs Controls
PEBs_a = {PEB1; PEB2};
PEB5 = spm_dcm_peb(PEBs_a; X5); where X5 is a 2x2 matrix with values [1 -1; 1 1]
# Responders vs Controls
PEBs_b = {PEB3; PEB2};
PEB6 = spm_dcm_peb(PEBs_b; X6); where X6 is a 2x2 matrix with values [1 -1; 1 1]
# Non Responders vs Controls
PEBs_c = {PEB4; PEB2};
PEB7 = spm_dcm_peb(PEBs_c; X7); where X7 is a 2x2 matrix with values [1 -1; 1 1]
#Responders vs Non-Responders
PEBs_d = {PEB3; PEB4};
PEB8 = spm_dcm_peb(PEBs_d; X8); where X8 is a 2x2 matrix with values [1 -1; 1 1]
If the PEBs 1-4 included covariates; would we need to change how design matrices X5-8 look?
Sorry for this long message - we are just trying to understand how to properly run the analysis.
Thank you so much in advance!
K&M
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