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# Hessian singularity in a repeated measures analysis...

Hi, I'm running a GEE using Genmod on ordinal repeated measures data - but its telling me theat the hessian matrix is singular and that the output given is based on the last iteration...

I've done some reading around this, and I think its because my data matrix is evry sparse for some of the ordinal response choices (i.e. my ordinal scale runs from 0 - 10, but most people score it between 0 and 6 or 7 - with some, but very few people scoring above 7)...

So I was thinking that I could try two things - either I could (1) collapse my ordinal scale so that the upper boundaries get amalgamated - or (2) I could just forget the whole GEE approach - treat the data as continuous (I would have to do a fairly radical normalization transformation as my ordinal data looks like extreme poisson when you look at the frequency distribution) - and do a simple rANOVA instead...

So I guess my question is - it it best to use the GEE analysis with the dodgy hessian matrix, or to collapse my ordinal scale until the hessian matrix is ok in the GEE, or is it best to treat the data as continuous normal (after transform - which will never make it completely normal) - and do a simple rANOVA?

Thanks for any help with this tricky problem.

Dave
Posts: 2,655

## Re: Hessian singularity in a repeated measures analysis...

Dave,

I think collapsing the scores is probably the optimal direction, and I might get even more radical in collapsing in an effort to get relatively equal numbers in each collapsed category. For instance, suppose you had, for a representative time point:

Score Count
0_______22
1_______29
2_______46
3_______58
4_______17
5_______19
6_______12
7________6
8________3
9________1
10_______0

I would tend to break this into four categories: #1 0 to 1;
#2 2's
#3 3's
#4 greater than 3

Now if I had a particular interest in finding associations with the extremes, then maybe a bifurcation would be more useful, say 0 to 6 vs 7 and above.

I guess it really depends on what you hope to extract from your data. In any case, reducing the number of categories so that you aren't so sparse in the repeated sense should help with the Hessian matrix problem.

Steve Denham
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