Estimate of intercept in loglinear model

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,