[R] Poisson Regression

[Viechtbauer Wolfgang (STAT)]

I think it's useful to realize that this approach still implies that the \phi_{i}'s are entered as fixed effects into the model (as opposed to treating the \phi_{i}'s as random effects); it's just that the iterative algorithm to obtain the maximum likelihood estimates is faster when using 'eliminate = Subject' (and the output doesn't show the estimates for these nuisance parameters).

Since the number of parameters then rises linearly with the number of subjects, this may be a case where maximum likelihood theory breaks down, that is, a Neyman-Scott problem. See:

Neyman, J., & Scott, E. L. (1948). Consistent estimates based on partially consistent observations. Econometrica, 16(1), 1-32.

Maybe somebody more familiar with this could shed some light on this.

Best,

--
Wolfgang Viechtbauer
Department of Methodology and Statistics
School for Public Health and Primary Care
Maastricht University, P.O. Box 616
6200 MD Maastricht, The Netherlands
Tel: +31 (43) 388-2277
Fax: +31 (43) 361-8388
Web: http://www.wvbauer.com


----Original Message----
From: r-help-bounces at r-project.org
[mailto:r-help-bounces at r-project.org] On Behalf Of Michael Friendly
Sent: Thursday, October 14, 2010 14:56 To: Antonio Paredes
Cc: r-help at r-project.org
Subject: Re: [R] Poisson Regression

> On 10/13/2010 4:50 PM, Antonio Paredes wrote:
>> Hello everyone,
>>
>> I wanted to ask if there is an R-package to fit the following
>> Poisson regression model
>>
>> log(\lambda_{ijk}) = \phi_{i} + \alpha_{j} + \beta_{k} i=1,\cdots,N
>> (subjects) j=0,1 (two levels) k=0,1 (two levels)
>>
>> treating the \phi_{i} as nuinsance parameters.
>>
>> Thank you very much
>
> You can use the gnm() function in the gnm package with eliminate= to
> get
> rid of parameters for each subject.
> Something like
>
> gnm( lambda ~ Row + Col, eliminate = Subject, family=poisson,
> data=myData)
>
> where Row, Col, Subject are suitable *factors*.  This is equivalent to
>
> gnm( lambda ~ -1 + Subject Row + Col, family=poisson)
> except that Subject parameters aren't estimated explicitly.  See
> vignette("gnmOverview")
>
>
> --
> Michael Friendly     Email: friendly AT yorku DOT ca
> Professor, Psychology Dept.
> York University      Voice: 416 736-5115 x66249 Fax: 416 736-5814
> 4700 Keele Street    Web:   http://www.datavis.ca
> Toronto, ONT  M3J 1P3 CANADA
>
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