Comparing AIC of a model and its logit -transformed version

Hello All,
I would like to compare a model to its logit transformation using the AIC
values.

As a toy example
library(car)

seedrates <- data.frame(rate = c(50, 75, 100, 125, 150),
                        grain = c(21.2, 19.9, 19.2, 18.4, 17.9))
lm <- lm(grain~rate, data=seedrates)
logit.lm <- lm(logit(grain)~rate,data=seedrates)

AIC(lm, logit.lm )

In order to compare these two models using AIC we need to take into account
the JAcobian of the logit transformation.


Here
https://stats.stackexchange.com/questions/61332/comparing-aic-of-a-model-and-its-log-transformed-version

Prof. Ben Bolker mentioned how we can adjust the AIC in the presence of log
transformation by the multiplication of the likelihood by the corresponding
Jacobian to the AIC ... for the case of log{y(n)+1}, it is ?2 ??log{y(n)+1}

I was wondering in the case of logit transformation can I adjust the AIC by
multiplying the likelihood by logit{y(n)+1}.

Any help is greatly appreciated.

Kind regards,

Boby  Mathew

Dr. Boby Mathew
INRES, University of Bonn
Katzenburgweg 5
Phone: 0228732031
53115, Bonn,Germany.

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