[R] how to define a geometric distribution for "glm"

[peter dalgaard]

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]]
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

-- 
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