I'm a regression troglodyte too, but I recall reading about your kind of
problem.  If you had all categorical variables, the problem you describe
falls within the "multivariate log linear analysis" framework (Bishop,
Feinberg, Holland, Mosteller, and Light, /Discrete Multivariate
Analysis/).   In your description, the key thing seems to be that none
of the variables is distinguished as the dependent variable.  Today I
did some googling and I find the documentation on this much more
understandable that it used to seem to me.  Sites like this describe it
within the glm framework

http://www.uwsp.edu/psych/cw/statmanual/glmloglinear.html
http://online.sfsu.edu/~efc/classes/biol710/loglinear/Log%20Linear%20Models.pdf

Now, granted, those are for categorical variables, and I have not
answered your desire to include a continuous variable.  The loglinear
folks seem to want you to categorize your continuous variable.

pj

Franzese, Robert wrote:

>Apologies for what is no-doubt a remedial (& awkwardly phrased b/c I'm
>going to use terms to mean some things possibly different from their
>statistical meaning) question, but can someone point me to appropriate
>tests for/measures of independence in the distribution of a population
>across categories on multiple categorical variables? That is, we have a
>population of, say, people, normalized to 1. I want to test/measure the
>independence of the allocation of shares of that population across, say,
>k categorical variables, each with j>=2 or more categories. Then, to
>complicate matters, I would like to allow some of the variables to be
>continuous rather than categorical, but would like a measure/test that
>could include those continuous variables with the others in gauging
>independence in the allocation of population across the variables.
>
>
>
>E.g., suppose each individual in a population has a score on variables
>A, B, C, and D. A is continuous, and B, C, & D are categorical. B has
>two categories, C has 3, and D has 4. I want a measure/test of the
>independence of an individual's score on each variable to his/her score
>on the others. Does a measure/test/gauge exist that could compare such
>independence of the distribution of those individuals' values on those
>variables to the same measure (possibly for other variables) in another
>population?
>
>
>
>This must be a generic problem that demographers, biologists, and
>numerous others have already thought about & probably solved, probably
>long ago, right? It's probably in (M)AN(C)OVA, i.e.,
>(insert-string-of-letters-here)OVA, somewhere, but I didn't come to
>stats from that route (I'm one of those Neanderthal
>regression/econometrics types), so my ignorance is showing.
>
>
>**********************************************************
>
>


--
Paul E. Johnson                       email: [log in to unmask]
Dept. of Political Science            http://lark.cc.ku.edu/~pauljohn
1541 Lilac Lane, Rm 504
University of Kansas                  Office: (785) 864-9086
Lawrence, Kansas 66044-3177           FAX: (785) 864-5700

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