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Dear Will (et al)

I have re-run my simulation taking into account your suggestions, but a model that is not the true model is still the very clear winner (using both FFX and RFX). Specifically I’ve done the following:

Simulated data for 10 subjects (three 5-min runs each) using spm_dcm_generate.m
TR = 0.240 sec
TE = .025 sec
A = [-1 0 0 0;  0 -1 0 0;  .1 .9 -1 .1;  .9 .1 .1 -1]
B = all zeros
C = [.8 .1; .2 .8; 0 0; 0 0]
SNR = 5
transit = [.98 .98 .98 .98] (from Table 1 of Friston et al, 2003)
decay  = [.65 .65 .65 .65]
epsilon = .05

Again, I included just three models in model space. The first was the one used to generate the data. The second was the “opposite” model in which the intrinsic connections pointed the other direction and the direct inputs entered in the opposite pair of regions. The third was the union of those two models.

Again, the third model (union model) is the very, very clear winner. However, during estimation, the EM procedure often had to go through all 64 steps allowed (and did not always report “convergence”). This makes me wonder if the EM procedure did not settle on the optimum estimates for each model.

Perhaps examining the parameter estimates, as you suggested, will help clarify this? You said to make sure they were close to the true values, especially for those different between models. I’ve checked this for the true model and the winning alternative model, using BPA to get a quick look at the estimates. A diagram of this is attached (thickness = magnitude, red = negative, dotted = post.prob < 90%). It seems that they were not always the same as the true values, but often close. The hemodynamic parameter estimates are farther from the "truth" and priors, but they are similar across models.

Also, I ran Dr. Friston’s spm_dcm_fmri_check.m inputting the DCM_avg.mat file created using BPA for each model. Both models explained a very large amount of the variance and yielded no “red-flags”. 

(By the way, I also followed your recommendation to check that the true parameters “are within the range of the priors” – which seems unlikely to be the problem given your recent discussion with Martin. Nevertheless, they are.)

Thank you in advance for any guidance or suggestions. I’d be happy to follow-up with more details.

Becky