s-news
[Top] [All Lists]

Goodness of fit for negative binomial

To: s-news@wubios.wustl.edu
Subject: Goodness of fit for negative binomial
From: Wim Kimmerer <kimmerer@sfsu.edu>
Date: Fri, 04 Aug 2006 11:53:59 -0700
Hello S-newsers. I am trying to fit some data to a negative binomial distribution: I have ~70 sets of count data and want to fit each set separately, mainly to determine the extent to which the zeros are in excess of expectations, but also to assure myself that the NB is the correct distribution to describe these data, which should be distributed as an overdispersed Poisson (with the possible exception of extra zeros).

(Note re NB: There are two ways of formulating it, one appropriate to Bernoulli trials and the other to continuous distributions. The parameter names used in the various formulations are different, and I have not found a place where these are explained very well. For example, rnbinom (Splus) has r and p, and rnegbin (MASS) has mu and theta. Unlike r, theta can take non-integer values.)

I calculated the parameter mu (the mean) and calculated theta using theta.ml (MASS). However, the ks.gof function using negbinom has ONLY the discrete formulation, so that can't be used. It is easy enough to calculate the expected distribution from these parameters and then run the Kolmogorov-Smirnov test, but I have read that this test should be used against an expected distribution with KNOWN parameters, not with parameters calculated from the data.

So given that I have to get the parameters from the data, is my only choice for testing goodness of fit to simulate? If so, I assume I could simply calculate the KS statistic repeatedly using samples from the NB distribution with the estimated parameters and see whether my sample KS statistic falls within 95% of the values. Is there a better way to do this?

Thanks....

======================
Dr. Wim Kimmerer
Research Professor of Biology
Romberg Tiburon Center
San Francisco State University
3152 Paradise Drive
Tiburon CA 94920
Ph. (415) 435-7143
Fax (415) 435-7120
http://online.sfsu.edu/~kimmerer/
<Prev in Thread] Current Thread [Next in Thread>