MATLAB: Can the Fstatistic be used for nonlinear regression fit analysis if the underlying data is not normally distributed

non-normalnonlinearregression

The F-statistic seems to be used to check the 'goodness of fit' of non-linear regression models. I wanted to know if there was a normality assumption about the underlying data?

Sorry, to try to clarify: I know you can fit a nonlinear line to nonnormal data. My question is which statistical test(s) can be used to test the significance of the fit?

Best Answer

Yes. The F-statistic implicitly uses a normality assumption in there. To some extent, this is not terrible. Minor deviations from normality are not the end of the world. But if you want accurate predictions and care if a reported 95% is really the 95% statistic that was reported, then expect problems if for example, your noise is actually lognormally distributed. Of course, with lognormal (thus proportional) noise, then you want to log the model before fitting anyway.

Outliers in your data are a common corruption. Small outliers are not the end of the world. But large outliers are a common cause of problems. They often cause convergence problems in nonlinear least squares. And of course, they completely screw around with any statistical inferences you try to make.

If your residuals are purely lack of fit, then be VERY careful about believing any F-statistic. So if you have a nice quadratic curve, but use a straight line to fit it, then any F-statistic will be worthless (beyond telling you the fit is poor.) Statistics are meaningless in the face of lack of fit, since LoF describes a situation completely outside the universe of the model you have posed.

Related Solutions

MATLAB: Confidence and Prediction Bounds Documentation: How do the “confidence bounds for the fitted coefficients” relate to the “prediction bounds of a new function value”

After reading the chapter on predictions in Chatterjee and Hadi, I see the difference between confidence bounds on the parameters and confidence bounds on a prediction a little clearer. Confidence bounds on the parameters make a statement about an interval where the true (but unknown) parameters are located with a certain probability. Confidence bounds on a prediction, on the other hand, tell you in which interval a new observation (if sampled again) or a new regression fit (of the new samples) will probably lie.

So to answer my initial question, they are indeed different things from a statistical point of view.

MATLAB: How to tell a set of data is normally distributed

normplot(x)

And for formal tests, see lillietest and jbtest

(NB: these are all Statistics Toolbox functions. If you're doing this kind of statistical work, though, I assume you have that.)

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Related Solutions

MATLAB: Confidence and Prediction Bounds Documentation: How do the “confidence bounds for the fitted coefficients” relate to the “prediction bounds of a new function value”

MATLAB: How to tell a set of data is normally distributed

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