[R] Estimate of intercept in loglinear model

[David Winsemius]

On Nov 7, 2011, at 12:59 PM, Colin Aitken wrote:

> How does R estimate the intercept term \alpha in a loglinear
> model with Poisson model and log link for a contingency table of  
> counts?
>
> (E.g., for a 2-by-2 table {n_{ij}) with \log(\mu) = \alpha +  
> \beta_{i} + \gamma_{j})
>
> I fitted such a model and checked the calculations by hand. I   
> agreed with the main effect terms but not the intercept.  
> Interestingly,  I agreed with the fitted value provided by R for the  
> first cell {11} in the table.
>
> If my estimate of intercept = \hat{\alpha}, my estimate of the  
> fitted value for the first cell = exp(\hat{\alpha}) but R seems to  
> be doing something else for the estimate of the intercept.
>
> However if I check the  R $fitted_value for n_{11} it agrees with my  
> exp(\hat{\alpha}).
>
> 	I would expect that with the corner-point parametrization, the  
> estimates for a 2 x 2 table would correspond to expected frequencies  
> exp(\alpha), exp(\alpha + \beta), exp(\alpha + \gamma), exp(\alpha +  
> \beta + \gamma). The MLE of \alpha appears to be log(n_{.1} * n_{1.}/ 
> n_{..}), but this is not equal to the intercept given by R in the  
> example I tried.
>
> With thanks in anticipation,
>
> Colin Aitken
>
>
> -- 
> Professor Colin Aitken,
> Professor of Forensic Statistics,

Do you suppose you could provide a data-corpse for us to dissect?

Noting the tag line for every posting ....
> and provide commented, minimal, self-contained, reproducible code.

-- 

David Winsemius, MD
West Hartford, CT