It is not clear to me what kind of experiment design you have: among the three critical conditions, does each condition have many repetitions/trials? Whether you should use AM1 or AM2 depends on the type of questions you'd like to ask regarding your data.

> In stim_times_AM1, it is assumed that "the change in FMRI signal as ABI changes is linearly
> proportional to the changes in the ABI values", what about AM2?

With AM2 you model trial-to-trial variability with two components: the effect corresponding to the average modulation values (sort of like main effect), and the modulation effect that accounts for trial-to-trial variability (like interaction or marginal effect).

> If we assume that the changed is not lineal, say it is a lg relationship, can we "marry" the
> transfered semantic distance(i.e. new index of semantic distance = lg(old semantic distance))
> to the onset time?

Sure you can define any specific nonlinear relationship and construct the modulation effect through transformation and marriage as you suggested.

> Does it matter if the semantic distance of some item is zero?

No, it doesn't as long as those zero values reflect the reality.

> When should we centered the semantic distance and when we don't have to?

The mean centering is automatically performed internally in the marriage step.

Gang