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Re: R^2 for linearized regression
Posted:
Jan 31, 2013 5:18 PM


By the way, this post by David Jones is fine, and my post does not contradict anything in it. I offered a slightly different angle on the same advice.
In the final paragraph, where he says, "From a theoretical point of view," I don't have a better single word for "theoretical," but I would prefer some statement like, "From a theoretical point of view that focuses on the validity and robustness of the statistical tests ...". His next sentence fixes that tiny problem.
 Rich Ulrich
On Thu, 31 Jan 2013 15:29:42 0000, "David Jones" <dajhawk@hotmail.co.uk> wrote:
[snip, original post] >====================================== > >It is important to be clear about how the value of R^2 that you use is >calculated when you use it. Just using values from individual fitting >modules may well not be enough. > >See http://en.wikipedia.org/wiki/Coefficient_of_determination > >You should try calculating R^2 directly from the sets of observed and >corresponding values predicted values, where >(i) "observed" is the original observations and "predicted" is either the >predictions from linear regression or the exponential of the predictions >from the regression model for the loged data (it is also possible to >include a "bias adjusted" version of the latter) >and >(ii) "observed" is the loged original observations and "predicted" is >either the predictions from linear regression on the loged data or the >logarithm of the predictions from the regression model for the original >data. > >This gives at least 4 values to compare. You can also try introducing an >additional linear regression step, for example where in (i) you could fit a >linear model for the observed data based on the exponentiated predictions >from the linear model for the loged observations. > >If you have time you could construct a pair of scatter plots of observed >versus predicted values in both original and transformed spaces. > >But there is no definite generally applicable answer to your question, >except hat you should definitely have a comparison of R^2 values calculated >for the same transformation of the observed data. From a theoretical point >of view , if the usual modelchecks for regression models suggest that the >transformed model is better then you should be using the R^2 calculated for >the loged data. But, if practical/realworld considerations suggest that >the "importance" of errors of prediction is equal on the nontransformed >scale, then R^2 calculated for the untransformed observations may be more >closely aligned to what you are trying to use the predictions for. > >David Jones



