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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?

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  • $\begingroup$ 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. $\endgroup$
    – Marius
    Mar 15 '12 at 3:57
  • $\begingroup$ @Marius: to clarify, are you suggesting boxcox() on the raw data, or on the transformed data? $\endgroup$
    – Michelle
    Mar 15 '12 at 6:18
  • $\begingroup$ 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. $\endgroup$ Dec 26 '14 at 8:42
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My experience with transformed data suggests that the correlation improves after transformation as well as the homoscedasticity and/or normality, although they are not necessarily all optimal for any single transformation. One simple answer may be to calculate correlation coefficients between the two models and their respective data sets. One can even test for the significance of difference of correlated correlation coefficients. Tests for homoscedasticity and density function type of residuals can also offer a means to evaluate them.

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