In article <[EMAIL PROTECTED]>, Rich Ulrich <[EMAIL PROTECTED]> wrote: >On 8 Oct 2003 12:15:17 -0500, [EMAIL PROTECTED] (Herman >Rubin) wrote:
>> In article <[EMAIL PROTECTED]>, >> Rich Ulrich <[EMAIL PROTECTED]> wrote: >> >On Wed, 8 Oct 2003 10:33:49 +0200, "Lughnasad" <[EMAIL PROTECTED]> >> >wrote: >[ snip a bit ] >ru > >Comment on the comment - >> >Since the multiple regression on a dichotomy is >> >mathematically identical to the problem of Fisher's >> >discriminant function, the multiple regression is pretty >> >robust for the job. You can do t-tests on dichotomous >> >variables and the tests will be pretty accurate, too, >> >and those are the same shape of residuals. >HR > >> This is the case if the INDEPENDENT variable is dichotomous. >It should be clear from the context that I am describing >the DEPENDENT ... >> The KEY assumption for any kind of validity of a linear >> regression is that the "errors" are uncorrelated with the >> independent variables. If this is not essentially the >> case, the results of a linear regression are decidedly >> biased. > ... and the *test* is not notably disturbed by bias. >There is an evident *meaning* to the LR coefficients : that >is one potential advantage of using Logistic with two groups, >instead of using Regression on 0/1 or Fisher's discriminant >function. I can't say that I am disturbed by 'bias' when I >don't have much notion of how to interpret the prediction >in any case. If you are testing for independence, this is correct. But in that case, there are other ways of looking at the problem. Besides, fixed significance tests do not make any sens from a decision standpoint. The point of a statistical analysis is to gain understanding. If the outcome is dichotomous, linear regression does not. <> Lack of homoscedasticity means that one can do <> better by using weights, and lack of independence of the <> errors means that one can get improvement in other ways, <> but lack of normality of the errors just means that the <> overused tests of significance, etc., are not quite right. >'not quite right' but still, pretty damned good. The LR >alternative tends to bomb [ perhaps I should say, 'fail to >achieve asymptotic properties' ] without warning; that >shortcoming makes 'not quite right' OLS into a competitive >alternative. OLS is robust, easier to read, and has useful >side-statistics. (LR is working to catch up.) It just means that you have to intelligently look at the problem when doing logistic regression. One is not just interested in testing for independence; other tests are not asymptotically correct for linear regression if the relationships are nonlinear. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
