# Compare fits of model to transformed and untransformed response

I want to compare data that proportions among three different groups e.g.:

 ID Group Prop.Nitrogen
1    A     0.89
2    A     0.85
3    B     0.92
4    B     0.97


Following Wharton and Hui (doi:10.1890/10-0340.11) I though I'd see if these data would be better dealt with using a logit transformed.

When I look at diagnostic plots for linear models on the transformed and un-transformed data they look very similar with no obvious problems, and there are only small differences in estimated parameters. However, I'd still like to be able to say something about how well the model fits the transformed and untransformed versions of the data - I know I can't compare AIC values directly. Is there a correction and I can make to examine this? Or should I be taking a different approach?

• You might want to try a Box-Cox transformation (boxcox() in the MASS library), although I'm not sure whether it can deal with logit transforms. Mar 15 '12 at 3:57
• @Marius: to clarify, are you suggesting boxcox() on the raw data, or on the transformed data? Mar 15 '12 at 6:18
• What about transforming the data and the fitted values to the subject-matter-relevant scale (so you will have a unified scale) and then calculating AIC for all the competing models you have? You would have to calculate AIC values manually for models that were originally fit on a different scale but I don't think this could be a problem. Dec 26 '14 at 8:42