I am wondering whether someone could help me out with a GLM with orthogonalized parametric regressors mentioned below.

In our event-related fMRI experiment, there are three conditions: 'A', 'B', and 'C'. The design is ABC-delay-ABC-delay etcetera. Because of the nature of the experiment, the trials A, B, and C are in fixed order and very close together and inevitably highly correlated (r= 0.3-0.5).

Modelling this in a 'classical' GLM with one regressor for each condition we get some results. However, as we are in the end only interested in the difference between conditions, e.g. A and C, there is an alternative way of modelling this, using orthogonalized regressors. In this approach, the onset time of all conditions (all trials together) is firstly modelled as one single regressor. Then, using the parametric modulations in SPM5, you can add orthogonalized regressors based on the difference of two conditions of interest, e.g. A-C.

E. g., regressor 1 will then be

1 1  1 0 0 0 0 0 1 1  1 0 0 0 0 0 ...

and (orthogonalized parametric) regressor 2 will be the difference of interest:

1 0 -1  0 0 0 0 0 1 0 -1 0 0 0 0 0 ...

You can do a similar thing for differences between other conditions.

This way, the regressors in your model are fully orthogonal so you got rid of the high correlation between them. Using this orthogonalized GLM approach, we get somewhat different results compared to the 'classical' GLM.

According to some literature, we thought that the orthogonalized model would have some advantages. However, as we cannot explain the differences between the two approaches we are not sure whether the GLM with orthogonalized parametric regressors is a valid approach or not.

Could someone please provide some helpful suggestions or comments on this orthogonalized model?