[R] Firths bias correction for log-linear models
sdfrost at UCSD.Edu
Thu Jan 12 21:54:11 CET 2006
Dear R-Help List,
I'm trying to implement Firth's (1993) bias correction for log-linear models.
Firth (1993) states that such a correction can be implemented by supplementing
the data with a function of h_i, the diagonals from the hat matrix, but doesn't
provide further details. I can see that for a saturated log-linear model, h_i=1
for all i, hence one just adds 1/2 to each count, which is equivalent to the
Jeffrey's prior, but I'd also like to get bias corrected estimates for other log
linear models. It appears that I need to iterate using GLM, with the weights
option and h_i, which I can get from the function hatvalues. For logistic
regression, this can be performed by splitting up each observation into response
and nonresponse, and using weights as described in Heinze, G. and Schemper, M.
(2002), but I'm unsure of how to implement the analogue for log-linear models. A
procedure using IWLS is described by Firth (1992) in Dodge and Whittaker (1992),
but this book isn't in the local library, and its $141+ on Amazon. I've tried
looking at the code in the logistf and brlr libraries, but I haven't had any
(successful) ideas. Can anyone help me in describing how to implement this in R?
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