Dear Jeffrey,
In case the four runs were acquired with four separate fMRI sequences (= with the scanner stopping in between) you would model the runs as separate runs as well. fMRI is not quantified, so the average signal during run 1 might well be a different one than run 2, independent of brain activation, which is why one would go with four "intercepts"/"constants" within a model, one for each of the four runs.
Concerning your seemingly different results, of course it also makes a difference whether to include the motion parameters or not. Depending on head motion this might have a rather huge effect.
Leaving this aside, the design matrix is not unproblematic, as you seem to have very long "on" blocks, with the usual consequences: 1) signal within the low frequency range resulting in a trade-off with the high-pass filter (removing noise, but also signal vs. preserving signal, but also noise) 2) can the convolved boxcar function still be considered to be a reasonable predictor, given the long durations (> 60 s, at least if the TR is 2 s?), or are there changes over time. In addition, the two "on" periods of condition 1 seem to have a comparable length within a run, while the second trial/block for condition 2 seems to be much shorter than the first. If there are any deviances from the default predictors (which one might well expect for longer blocks) than the "on" condition might be affected to a larger extent than the "off" condition.
Best
Helmut
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