What are temporal basis function models? How do they fit in?
Basis function models are a sort of transition step, representing the continuum between the standard, canonical-HRF, GLM analysis, and the unconstrained FIR model analysis. The standard analysis assumes an exact form for the HRF you’re looking for; the FIR places no constraints at all on the HRF you get. But sometimes it’s nice to have some kinds of constraints, because it’s possible (and often happens) that the unconstrained FIR will converge on a solution that doesn’t “look” anything like an HRF. So maybe you’d like to introduce certain constraints on the type of HRFs you’ll accept. You can do that by collapsing the design matrix from the FIR a little bit, so each column models a certain constrained fragment of the HRF you’d like to look for – say, a particular upslope, or a particular frequency signature. Then the beta weight from the basis function model represents the effect size of that part of the HRF, and you can multiply the fragment by the beta weight and sum all the fragment
