Dear David, Thank you for the reference to Frank Harrell's excellent text. I will read up to correct my statistical deficiencies offline.
Thank you. On Sun, Oct 25, 2009 at 1:24 PM, David Winsemius <dwinsem...@comcast.net> wrote: > > On Oct 25, 2009, at 12:55 PM, Kyle Werner wrote: > >> David, >> >> Thank you for your reply. I am not using glm, but instead lrm. > > Does not matter. "lrm" is giving you the same output as would glm with a > logistic link. > >> I am >> consulting the documentation to try to parse out what the output >> "Model L.R." actually means: >> http://lib.stat.cmu.edu/S/Harrell/help/Design/html/lrm.fit.html >> ("model likelihood ratio chi-square") >> >> From my read of the documentation, it appears that the "Model L.R." >> output by lrm is not the deviance, but >> >> 2 * ln( [model deviance] / [null deviance] ) > > Believe it to be 2 * ln( [null deviance] / [model deviance] ), which is why > you and I differ as to sign. On page 183 Harrell formulates the L.R stat as: > > -2log(L at H0/ Lat MLEs) > >> >> This is why I believe I am correct to be talking about likelihood >> ratios instead of deviance, but I am unsure of this - which really >> relates back to the core of my question. Whether or not I have the >> sign wrong in the AIC formulation is dependent upon whether or not the >> - is incorporated into the calculation of the "Model L.R.", above, >> which is one part of my original question. >> >> The AIC formula is, generally, AIC = -2*ln(likelihood ratio) + 2k, >> with the best model (assuming the same observations) having the lowest >> AIC. I hope that my understanding of this fundamental formula is >> correct, but please let me know if not. > > I have offered my opinion as to your misunderstanding, and have suggested > specific references to what Harrell has written about the subject. > >> >> Thanks. >> >> On Sun, Oct 25, 2009 at 10:51 AM, David Winsemius >> <dwinsem...@comcast.net> wrote: >>> >>> On Oct 25, 2009, at 9:24 AM, Kyle Werner wrote: >>> >>>> I am trying to obtain the AICc after performing logistic regression >>>> using the Design package. For simplicity, I'll talk about the AIC. I >>>> tried building a model with lrm, and then calculating the AIC as >>>> follows: >>>> >>>> likelihood.ratio <- >>>> unname(lrm(succeeded~var1+var2,data=scenario,x=T,y=T)$stats["Model >>>> L.R."]) #Model likelihood ratio??? >>>> model.params <- 2 #Num params in my model >>>> AIC = -2*log(likelihood.ratio) + 2 * model.params >>> >>> You might want to check your terminology. A single model has a deviance. >>> You >>> construct a likelihood ratio as twice the logged ratio between two >>> likelihoods (deviances) (which then turns into a difference on the log >>> scale). And don't you have the sign wrong on that expression for AIC? I >>> thought you penalized (i.e. subtracted) for added degrees of freedom? >>> (There >>> is an implicit base model, so if you define AIC as a difference between >>> L1 + >>> 2p1 and L2+2p2 you would get (L1-L2) + (0 -2p2) = (LR - 2p2). See p 202 >>> of >>> Harrell's "Regression Modeling Strategies".) >>> >>>> >>>> However, this is almost certainly the wrong interpretation. When I >>>> replace var1 and var2 by runif(N,0,1) (that is, random variables), I >>>> obtain better (lower) AICs than when I use real var1 and var2 that are >>>> known to be connected with the outcome variable. Indeed, when I use >>>> GLM instead of LRM, the real model has a lower AIC than that with the >>>> predictors replaced by random values. Therefore, it appears that lrm's >>>> "Model L.R." is not actually the model likelihood ratio, but instead >>>> something else. >>>> >>>> Going to the Design documentation, lrm.fit states that "Model L.R." is >>>> the model likelihood-ratio chi-square. Does this mean that it is >>>> returning 2*log(likelihood)? If so, AIC becomes >>>> AIC = -[Model L.R.] + 2*model.params >>>> >>>> Can anyone confirm that this final formula for obtaining the AIC from >>>> lrm is correct? >>> >>> >>> I would not confirm it. What sources are you consulting? >>> >>> -- >>> David Winsemius, MD >>> Heritage Laboratories >>> West Hartford, CT >>> >>> > > David Winsemius, MD > Heritage Laboratories > West Hartford, CT > > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
