Date: Tue, 23 Jun 2009 06:32:13 -0700 shiling99@YAHOO.COM "SAS(r) Discussion" Shiling Zhang http://groups.google.com Re: Deviance versus log likelihood To: sas-l@uga.edu text/plain; charset=ISO-8859-1

You may check out Chap 16 "Binary Dependent Variable" in John Neter "Applied Linear Regression Models" 2nd edition. or Chap 4 "Hypothesis Testing and Goodness of Fit" in J. Scott Long "Regression Models for Categorical and Limited Dependent Variables".

In short the 'logistic" model is directly extended from a reguler linear regression or in a GLM format in John's book. As he pointed out three problems(actually two problems) which are violated usually regression assumptions. The hard problem is nonconstant error variance. Autualy, the error also depends on betas. In order to make usual chi-square work, the grouping data is needed(Hosmer and Lemeshow) because the natures of error structure of Bernoulli distribution <===> while Var(y(i) - p(i))=p(i)(1-p(i)), but Var(y-phat (i))<>phat(i)(1-phat(i)).

The binary depenent variable model is constructed as a latent variable model in Long's book. I think it is a easy way to understand. It is obvious that variance component in link fuction is not identifiable. So the variance is set at its standard value.

HTH

On Jun 22, 8:41 pm, Bminer <b_mi...@live.com> wrote: > On Jun 22, 6:05 pm, shilin...@yahoo.com wrote: > > > > > > > You should use -2(LL_reduced - LL_full) which is distributed as > > chi-square df=# of variables reduced. > > The error term in logistic or probit model is not useful. The > > distribution of Deviance_reduced - Deviance_full is not known. The > > definitions of both terms are different. You should not expect they > > would be equal to one another. > > > HTH > > > On Jun 21, 3:17 pm, Bminer <b_mi...@live.com> wrote: > > > > I am used to testing constraints on parameters (two nested models) in > > > logistic regression as either: > > > > Deviance_reduced - Deviance_full > > > or > > > -2(LL_reduced - LL_full). Both give the same value to compare to > > > critical values of chi-square. > > > > Using genmod and a normal error, identity link model the two values > > > above are not the same. Why? > > > > Which should be used in a likelihood ratio test? > > > Thanks! > > Hi Thanks for the reply. But, I see many authors saying to subtract > deviances or to compute deviance_full - deviance_reduced / scale. Here > is an example (look under Analysis of Deviance)http://www.unc.edu/courses/2006spring/ecol/145/001/docs/lectures/lect... > > Its confusing because if you run a logistic regression with genmod, > deviance_full - deviance_reduced is the same exactly as -2(LL_reduced > - LL_full). If you run normal error with identity link, they are not.- Hide quoted text - > > - Show quoted text -

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