Three categorical variables A, B, C each have three levels 1, 2, 3. I have two 3x3 contingency tables of count data for A vs B and A vs C. These tell me, for example, that there are 7 instances where A=1 and B=1 and 10 instances where A=1 and C=1. I would like to know the joint distribution of B x C, or at least understand it better, but I'm stuck!
Looking at chi-squared results for the two (marginal) contingency tables, it seems that there is some association between A and B, but that the data is consistent with no association between A and C. It is likely that there is some association between B and C.
If I assume that there is no association between A and C, I've got 18 observations (3 x 3 x 2) and only 15 parameters (constant plus 3 x 2 first order + 4 x AB interactions + 4 x BC interactions) in a loglinear model. This means I should be able to fit a model, I guess, but I don't know how!
Does anyone have any pointers? I know very little about Generalised Estimating Equations but, given this marginal data structure, perhaps they could help somehow? Or am I hoping for too much to be able to unravel the data to such a degree?
Any help appreciated! Thank you,
Dominic Muston.
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