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I wonder if use of generalized linear models (GLMs) with transformed response variables is correct.

My particular case: I compared goodness of fit of several GLMs with response variable transformed and not, in addition to several error distributions for each case. Result is that the model with best fit (according to qq-plot, residual normality, homoscedasticity, etc...) is a GLM with response variable transformed by Box-Cox and inverse Gaussian errors (link=identity). Could I select this model?

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    $\begingroup$ Be wary of the possibility of overfitting here when you check many models & pick the best. $\endgroup$ – gung Jan 27 '16 at 16:51
  • $\begingroup$ Thanks @gung. ¿What do you think is the best method for evaluate overfitting of glms in R ? ¿cross validation with "boot" package? $\endgroup$ – Diego Salazar Tortosa Jan 27 '16 at 18:28
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    $\begingroup$ What did Box-Cox suggest? My prejudice is that a similar non-identity link (e.g.) is much easier to think about, as predictions are returned on the original scale. With a transformed scale, you would need to back-transform yourself, which is at least awkward. The main merit of Box-Cox is arguably not some slightly arbitrary power such as 0.1 or 0.42 but its pointing towards scales such as logarithmic or root. $\endgroup$ – Nick Cox Jan 27 '16 at 19:22

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