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How, if at all, can one compare the "fit" of a simple linear vs. non-linear regression model to observed data?

I apologize if I didn't search long/hard enough for the answer, but I cannot find anything concrete.

-Patrick

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What software are you using? – Michelle Jan 26 '12 at 23:39
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Can you share your purpose in comparing the fit of the different models? To develop a predictive model? To describe a particular data set? To provide evidence for or against a particular theory? You might choose different comparison approaches depending on your purpose. – Anne Z. Jan 27 '12 at 3:05
Anne, at this point it is simply for description. I would like to quantitatively be able to say that a non-linear fit is preferred. – Patrick Jan 28 '12 at 17:21
Michelle, I use R. – Patrick Feb 3 '12 at 17:20
Would using AIC/BIC or the LogLik be sound statistically to make a choice between non-linear and linear models on the same dataset? – user9974 Mar 19 '12 at 23:33

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Perform cross-validation on each model on a development set to find the best hyper-parameters / accuracy estimate for each. Then check that the accuracy estimates are still valid on some held out data that you did not use during the model selection / parameter tuning phase.

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