The likelihood for the geometric distribution is the same as for the binomial
distribution, except for the constant term, so estimates and LRT will be the
same. The properties of the estimator will be different, e.g. the estimate of p
is not unbiased, but asymptotically the likelihood procedures should work
(asymptotic in this case means a reasonably large total number of both successes
and failures, I suppose.)
So, if your geometric variate is called y, with the R convention of counting the
number of failures (not number of experiments), it should work with
glm(cbind(1,y) ~ whatever, family="binomial")
[The likelihood equivalence is fairly well-known in statistical theory as a
counterargument to the strong likelihood principle that all inference should be
based solely on the likelihood function.]
- Peter D.
> On 27 Oct 2014, at 22:29 , Amanda Li <amandali at uchicago.edu>
wrote:
>
> Hello,
>
> I was trying to apply "glm" to a dataset that assumes geometric
> distribution. I cannot use "glm.nb" in MASS package
(negative.binomial (1))
> because it tries to estimate this "1" while I am interested in
"p", the
> probability of success. Does anyone know how I can define a geometric
> distribution within "family" so that I can use glm assuming
geometric
> distribution to estimate "p"?
>
> I am not sure how "quasi" within the family works in this case
and I am not
> sure whether it can be used to assume geometric distribution.
>
> Thanks in advance for your help! I really appreciate it!
> Best regards,
> Amanda
>
> [[alternative HTML version deleted]]
>
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--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com