I have a linear model which doesn't have any particular issues with its assumptions (diagnostics plots look well). However it has a slighly skewed response (skewness approx. 0.5) and few skew independent variables. Now I would like to try to transform these skewed variables (as well as response) and see if the transformed model is better (that is if it explain response better). However, as far as I know I can't use neither R^2 statistic or AIC/BIC criterion to compare model with different data as they differ in variance. What should I do to compare the new, transform model with the old one? What criterion can I use?
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kjetil b halvorsen
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You might try "de-transforming" the predicted values for calculation of fit statistics. For example, if you fit to the log if the independent variable, that is log(IV), you can take the exponent of the model's predicted values as the "de-transform" for calculation of R-squared etc. – James Phillips Jul 06 '18 at 13:45
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First find a way to backtransform to the original scale, see https://stats.stackexchange.com/questions/115571/back-transforming-regression-results-when-modeling-logy or https://stackoverflow.com/questions/46392683/how-to-plot-transformed-regression-back-on-original-scale. But that will introduce bias, so some debiasing could do good. Maybe see https://www.sciencedirect.com/science/article/abs/pii/S0167629601000868. Then too compare backtransformed predictions and predictions on the original scale, maybe use crossvalidation. – kjetil b halvorsen Jul 07 '18 at 17:32