Hi,
I've several followup naive questions to this old post on categorical parametric modulators, which I think has been touched on other previous posts, but just to be certain...
Would you ever enter each of the four task loads as separate parametric modulators (if yes, what would be the advantage of this) -- or in this case, is it no longer parametric modulation and they should be entered as stick functions as the usual separate regressors, and it's the contrast definitions that test for linear effects, for example? How would you test of quadratic effects then ([-9 -3 0 3 9]?)?
If your going to have separate PM, then I would just model each "load" as a separate condition. I'm not sure where you get 5 columns from though. You now have 4 conditions, the linear effect would be [-1.5 -.5 .5 1.5]. The quadratic (x^2) effect would be [2.25 .25 .25 2.25]. The cubic (x^3) would be [-3.375 -.125 .125 3.375].
In cases where the categories do not fall into an obvious scale (so rather than "task load" we're dealing with "different picture types"), but I'd like to find out which "order" on a scale they would go, is it kosher to enter several parametric modulation definitions in the same model where I vary the numbers assigned to the categories, effectively putting them in different orders on a scale? Or should they be modelled as separate regressors and use contrast definitions to test different orders on a scale?
I would model them as separate conditions. Ordinal tests cannot be computed with a single contrast unless you assume a linear relationship across the 4 conditions. To find the order, you would compare 1v2 and 2v3 and 3v4. If 1v2 is not significant, it will be hard to argue that the order is 1 2 3 4 compared to 2 1 3 4.
A linear relationship (e.g. -1.5 -.5 .5 1.5) does not mean that condition 2 has to be larger than condition 1 and smaller than condition 3. For example: -2 -2 1 2, would yield a contrast of 3+1+.5+3=7.5. Changing the order of the contrast would yield the same or smaller value. Thus, you'd have to find the contrast that had the highest magnitude to know the order. This might not be the same as the contrast with the largest t-statistic though. If you have 2 contrasts that have similar value, it will be hard to argue for one order over the other order.
Thanks a lot in advance,
g