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# How to model hypergeometric distribution in PROC GLIMMIX ?

There is geometric distribution in PROC GLIMMIX. What about hypergeometric? As far as I understand it is the same as binomial but without replacement. Thank you in advance.

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‎08-07-2013 01:24 PM
Posts: 2,655

## Re: How to model hypergeometric distribution in PROC GLIMMIX ?

A hypergeometric distribution is not available in GLIMMIX, probably because it is really hard to fix marginal totals and still do REML.  Maybe future releases will make it available.  For now, the only way to fit a mixed model with a hypergeometric distribution would be to write the necessary code in PROC NLMIXED.

I'm curious as to how a hypergeometric distribution could be implemented in the context of mixed models, where anything that defined the marginal total would be a random variable, rather than a fixed sum.

Steve Denham

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‎08-07-2013 01:24 PM
Posts: 2,655

## Re: How to model hypergeometric distribution in PROC GLIMMIX ?

A hypergeometric distribution is not available in GLIMMIX, probably because it is really hard to fix marginal totals and still do REML.  Maybe future releases will make it available.  For now, the only way to fit a mixed model with a hypergeometric distribution would be to write the necessary code in PROC NLMIXED.

I'm curious as to how a hypergeometric distribution could be implemented in the context of mixed models, where anything that defined the marginal total would be a random variable, rather than a fixed sum.

Steve Denham

Contributor
Posts: 74

## Re: How to model hypergeometric distribution in PROC GLIMMIX ?

Steve,

I wanted to model hypergeometric distribution as my response variable is a characteristic of cells and there is no need to put them back in a vial. We consider cells with a certain characteristic and count their percent / proportion within a certain cell type. So the analyzed cell type might be considered as a subtype/subclass of cells.

Robin R. High wrote "[...] the hypergeometric distribution converges to the binomial, and then with the binomial, as n gets large and p gets small, so that the mean = n*p remains constant, the binomial converges to the Poisson ...  and, the Poisson converges to the normal.  So, if the event of interest is somewhat "rare" and the denominator is very large  (a "measure" of total size...), the binomial and poisson [...] will likely give you similar results, including fitted values". (I hope I cite correctly.)

As I understand correctly the denominator in my case is the number of cells of a type T. It ranges from 1000 to 3000 cells. The number of cells of interest t (the numerator) ranges from few decades (or less) to hundreds.

So, if the hypergeometric distribution is unavailable in PROC GLIMMIX now, I'll model the response variable as binomially distributed. Do I guess correct?

Posts: 2,655

## Re: How to model hypergeometric distribution in PROC GLIMMIX ?

Given everything you have, either a binomial as planned, or maybe even a beta, if all values are bounded away from zero and one.

Steve Denham

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