Convolution terms [X * Y] ?

[jimbobodoll]

Hello there,

I was wondering if some kind person could help me with a query I have regarding these terms as applied to statistics.

Presume that I have N individuals within a group (so non-independent group members), and want to represent the statistical interaction of two measures which are each measured at the individual level.

Would it at all be valid to use a convolution term instead of a multiplication term to take into account the non-independence of the units whilst still assessing the interaction of the two measures?

I'm not supposing multiple groups here, so traditional Multi-level/Hierarchical regression approaches wouldn't be appropriate... Also, I'm quite prepared to accept that cross-correlation (or something more similar) might be more appropriate!

I've been thinking about this for over 18 months now! If you have any suggestions/comments, then I'd be delighted to hear them!

Thanks ever so much,

James