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, School of Mathematics, King’s Buildings, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ. Tel: 0131 650 4877 E-mail: c.g.g.ait...@ed.ac.uk Fax : 0131 650 6553 http://www.maths.ed.ac.uk/~cgga The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. ______________________________________________ R-help@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.
