Yes, theta is the 'size' or overdispersion parameter. Sometimes
also denoted as k. Wikipedia discusses this parameterization in the
paragraph starting "In negative binomial regression ..." (but they call
this parameter r rather than theta or k).
You can also see this in MASS on google books:
https://www.google.ca/books/edition/Modern_Applied_Statistics_with_S/CzwmBQAAQBAJ?hl=en&gbpv=1&dq=venables+ripley+negative+binomial&pg=PA206&printsec=frontcover
This parameterization was added to R in version 1.3.0 ...
On 2023-09-15 2:27 a.m., Ivan Krylov wrote:
On Fri, 15 Sep 2023 01:51:27 +0000
"Sorkin, John" <jsor...@som.umaryland.edu> wrote:
What is theta, and how does it relate to the parameters of the
negative binomial distribution?
Plugging the p (the success probability) and the r (the number of
successes until the experiment is stopped) from the Wikipedia article
(where they are defined in terms of mean mu and variance sigma^2)
together with the variance from ?MASS::rnegbin (where it's defined as
mu + mu^2/theta) into Maxima and then solving for theta, I get:
solve(
[
p = mu / sigma^2,
r = mu^2/(sigma^2-mu),
sigma^2 = mu + mu^2/theta
],
[mu, sigma, theta]
);
[
mu = ((1-p)*r)/p,
sigma = sqrt(r-p*r)/p,
theta = r
]
That is, the theta from MASS seems to be equivalent to the number of
successes from the formulation in the Wikipedia article.
--
Dr. Benjamin Bolker
Professor, Mathematics & Statistics and Biology, McMaster University
Director, School of Computational Science and Engineering
(Acting) Graduate chair, Mathematics & Statistics
> E-mail is sent at my convenience; I don't expect replies outside of
working hours.
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