On 13 Jun 2003 04:24:44 -0700, [EMAIL PROTECTED] (dave martin) wrote: > [EMAIL PROTECTED] (akhan) wrote in message news:<[EMAIL PROTECTED]>... > > Is there any statistical metod which can be applied to test whether a > > non-linear model fit a dataset well or significantly? > > Fisher's F-test can be used to quantitatively compare two models of > data. > > The F-test can answer the question "Are these two models significantly > different at the X% level?".
This bothers me - that's not the way that I would describe the question. Down below: Clearly the two models are *different*, anyway, by a factor of 1/T. Does one have a lower residual? You can solve by least-squares, comparing predicted to observed, if the errors of prediction are of similar size across the range. But that's the non-assumption, for non-linear regression, isn't it? > > One model can be constant; i.e. assume that data scatter is entirely > random about the dependent variable mean & not dependent on the > independent variable(s) at all. > > Or one can see if adding another parameter to a fitting function makes > a significant difference. > Nested models; assessed by reduction of residuals of least squares, say, or by increase of Likelihood. > Or one can find out which of two arbitrary models best fits the data; > this is very useful for comparing two theories. AIC and BIC are keywords for looking up comparisons of non-nested models. > > As an example, alternate theories for chemical diffusivity D are: > > (1) D=(K)*exp(-Q/T) > (2) D=(K/T)*exp(-Q/T) > where K and Q are experimentally determined constants and T is > temperature. > > Given a set of (D,T) data the F-test can be used to see if there is a > significant difference between these two models. > The F-test is used, by theory and by custom, to test models that are *nested*, using the difference in d.f. as the numerator degrees of freedom. Here, that d.f. seems to be zero.... I'll try to find something in this library book I have on the topic. This does seem to be a curious example. I think I would show folks the F-test, assuming one d.f., as a 'demonstration' of the size of the difference. But these models are surely *different* in a way that seems pretty strong. I guess, I am accustomed to worrying more about whether a variable is *in* a model at all, instead of worrying about what form it takes. Biomedical data with subjective reports is usually not so definitive, not so well-measured as to select between models like that. -- Rich Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html "Taxes are the price we pay for civilization." Justice Holmes. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
