Dear Soroor



> 1. In this situation, is the uncertainty of ECs considered in average connections? or just each effective connection (expectation of estimated parameters) is averaged across all participants?



Yes, the uncertainty is taken into account. This means that more confidently estimated ECs will have a greater impact on the group-level result than less confidently estimated ECs.



> 2. The average of each connection in the PEB analysis is different from the average of connections calculated in the t-test analysis (two-sample t-test), Is the reason for this difference not removing outliers in the PEB analysis?



I think you may be conflating three things here - the form of the model, whether classical or frequentist statistics are used, and whether a single-level or multi-level (hierarchical PEB) model is used.



Regarding the form of the model, a two-sample t-test implies a general linear model (GLM) has been used with two regressors in the design matrix - parameters from group 1 and parameters from group 2. You said that in your PEB model, you just have a single regressor, encoding the group average, because you only have one group. So your model is more like a one-sample t-test than a two-sample t-test. However, the PEB approach differs from conducting a classical (frequentist) one-sample t-test by hand or in external software such as SPSS, in a few respects:



- Each DCM estimates a multivariate normal distribution over the parameters. In PEB, this full distribution - both effect sizes and uncertainty (covariance) is conveyed to the group level, which a classical t-test would miss.



- The PEB model is a hierarchical random effects model, with DCMs at the first level (within-subject) and a GLM at the between-subjects level. The model says that across subjects, there is some (normally distributed) effect size, and the individual subjects' connection strengths inherit from this. The model estimates both this between-subject variability (random effects) and the regression parameters. Hence, you'll get a different result than simply conducting a one-sample test.



- Bayesian statistics are used rather than classical statistics. You will get posterior probabilities for different candidate PEB models that you compare. That's different from a classical p-value (which is the probability that your effects are unlikely under the null hypothesis that parameters are exactly zero.)



I hope that helps,

Peter



-----Original Message-----

From: SPM (Statistical Parametric Mapping) <[log in to unmask]> On Behalf Of Soroor Sh

Sent: 31 August 2023 08:37

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Subject: [SPM] PEB analysis



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Dear experts,



The benefit of PEB analysis compared to other classical tests such as the t-test is the consideration of the uncertainty of estimated ECs (variance) in addition to the expectation of each ECs parameter (strength of ECs).

I used PEB analysis for ECs which was estimated by spDCM (for a rs-fMRI study) and I didn't define any covariate so the design matrix just has a column of ones; therefore, I get the average connectivities in the PEB analysis. now I have a couple of questions:



1. In this situation, is the uncertainty of ECs considered in average connections? or just each effective connection (expectation of estimated parameters) is averaged across all participants?



2. The average of each connection in the PEB analysis is different from the average of connections calculated in the t-test analysis (two-sample t-test), Is the reason for this difference not removing outliers in the PEB analysis?



Kind regards,

Soroor