Rich Ulrich <[EMAIL PROTECTED]> wrote on 6/17/03 3:02:20 PM: >As we have said several times, >"Adding one more parameter", if that is what you are >doing, gives a nested model, where the F-test is proper >and well-known (given: other assumptions).
I agree & point out that I'm not adding one more parameter, rather, I'm using a different model. See Bevington, "Data Reduction and Error Analysis for the Physical Sciences", McGraw-Hill, 1969. p196 ff. In particular, p200 ff briefly discuss the derivation of the nested form to which you refer. It seems to me that adding one parameter is a special case of using a different model. Note that I'm not using the special difference form of the F test; in my case the numerator and denominator are the reduced chisquares for the two models. As another example of comparing models, say I'm faced with determining thermal properties from temperature distribution data in a cooling sphere. One model is that the temperature distribution is parabolic while another model is a cosine function; there is only one parameter in each model. I suggest that the F-test can in fact be used to see if these two models can be distinguished from the data (to paraphrase R Dodier, Is the dataset sufficiently large to distinguish between the two models?). I agree about the need for independent numerator and denominator. Is that requirement somehow relaxed when using the nested model with one additional parameter approach? >have a test, so it lends itself to the AIC or BIC -- those >are attempts at borrowing the logic of the >(somewhat-similar) nested tests. I looked into the AIC & BIC approaches as soon as you suggested them. They look useful. I've not yet seen how one can ascribe a level of confidence to a difference in AIC measures. I'd appreciate it if you'd provide a pointer to such a discussion. >I think that the AIC and BIC differ mainly in how much >they penalize extra degrees of freedom. > PS I find the weight ascribed to additional degrees of freedom in a chisquare or F-test disquieting. It somehow doesn't seem fair to give as much weight to an additional data point as one gives to an additional parameter which operates on all the data. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
