A time model for 2nd-level GLM analysis

jip-rem is a random-effects or mixed-effects model for functional imaging data. It attempts to faithfully follow the summary-statistics described here:

Worsley KJ, Liao CH, Aston J, Petre V, Duncan GH, Morales F, Evans AC (2002) A general statistical analysis for fMRI data. Neuroimage 15:1-15.

In this approach, a 1st-level analysis is done for each subject (or run, or session, or …), and then group results are analyzed using a second-level GLM that requires as input for each subject:

- the “effect size”, or the value of the GLM condition of interest (where a condition is a GLM parameter or some combination),
- the first-level variance for the condition of interest,
- the degrees of freedom from the first level.

For neuro-imaging data, the above input boils down to 3-dimensional maps of GLM parameter values and errors, plus a single degrees-of-freedom parameter. This is exactly the information stored in the “signal change” files of type “S-condition.nii” by the first-level programs, jip-glm and jip-srtm (also, "BP-condition” files store this information for SRTM). In each such file, the first map is value of the condition, and the second map is the error. The degrees of freedom parameter is stored in the file header.

Why not simply concatenate subjects and perform a single large GLM analysis across all subjects? The first-level analysis captures the variance within each subject (or run or session or ….) but not the cross-subject variance. The latter variance is a “random effect” across subject, and this generally exceeds the fixed-effects variance, so inferences should account for the larger variance. Nice features of the Worsley approach include

- This is a summary statistics approach that efficiently uses results of 1st-level analyses, so there is no need to perform a global analysis after adding each additional subject.
- The method provides for a true random-effects analysis, or a “mixed-effects” analysis that allows one to boost the effective degrees of freedom by spatially regularizing the random-effects variance assuming that it resembles the spatial structure of the fixed-effects variance, which is well known.

Overall, the method appears to offer a good compromise between “efficiency, generality, validity” (Worsley et al., 2002).