While I feel as though my competence with the GLM is improving, I actually don’t have much ‘conventional’ stats experience, so I often run into issues trying to translate between what users are trying to communicate, and a numerical expression of the model & hypothesis.
In this case, I’m stuck on “full multiple regression”. What I suspect this phrase is supposed to be referring to is that all variables of interest are being regressed against the data simultaneously within a single model. If this is the case, then it’s the inclusion of all three variables within your design matrix that is providing the “full multiple regression”. The problem then is that this provides no information about your hypothesis regarding how the data may fit this model.
If by “partial correlations” you mean how your measurement (e.g. FD / FC / FDC within FBA) varies as a function of a particular variable, specifically within a model that in fact regresses against all variables at once, then yes:
[0 1 0 0] will give you the rate of change of measurement variable as a function of explanatory variable 1; similarly
[0 0 1 0] for variable 2 and
[0 0 0 1] for variable 3.
-negative option allows you to test for both positive values of (rate of change of measurement variable as a function of explanatory variable), and negative values of that rate-of-change, within a single execution of
fixelcfestats. This is equivalent to e.g. running it once with contrast
[0 1 0 0], and then again with
[0 -1 0 0]; but doing it in a single execution is faster, as you only need to build the fixel-fixel connectivity matrix once. You however can’t yet test multiple distinct hypotheses within a single
fixelcfestats run; but that functionality is on its way.
Whether or not to de-mean variables in the design matrix can be context-dependent. Here, whether or not you de-mean influences the extent to which you can interpret directly the beta values that the GLM yields. However I might dodge that discussion for brevity this time around. The fundamental outcome of your experiment should not change depending on whether or not you de-mean; unless your explanatory variables vary wildly in magnitude (e.g. one variable has values of ~ 1e-6, another has values of ~ 1e+6), in which case demeaning the variables (& modulating to unity variance) may provide something akin to preconditioning for the GLM.
P.S. If, with Point 1, you were in fact referring to a hypothesis more akin to “Do any of these variables influence the observed measurement?”, then in GLM-speak this would be an F-test with matrix contrast. This is another capability that is not yet available in the public code but has been implemented and is on its way.