I have been running marginal homogeneity tests using Bhapkar's test via SAS Proc Catmod on 5x5 matrices of integer counts. (I have no problem with running Stuart-Maxwell instead, but there really isn't a proc to do that in SAS). Anyway both Bhapkar and Stuart Maxwell tests assume square matrices. These datasets represent the outputs from experimental designs, so sometimes one of the rows (or columns) contains all zeros, which is the same as a rectangular matrix as far as SAS is concerned.
Are any of you aware of a method of doing this test on rectangular matrices? (Or more accurately, a square matrix, where one column or row is all zeros)? I realize that that means a singular matrix (since a row of all zeros would mean a determant of zero). But there might be ways of working around that.
I suppose one way might be doing a 'generalized' or 'pseudo inverse' and plugging that in the formula where the inverse would belong.., but I don't know how to do that in SAS. If anyone has any code or methods to do that sort of thing, that might be useful.
I don't want to report a missing value, so at present I am imputing a 1 count in the category with all zeros to get a square matrix, then running Bhapkar's test on that. I'm not crazy about doing that, so would love to find a better way. I'm curious to what others of you might have done in similar situations.., let me know your experiences.
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