Date: Thu, 7 Apr 2005 19:22:38 +0200
Reply-To: "A.J. Rossini" <blindglobe@gmail.com>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: "A.J. Rossini" <blindglobe@GMAIL.COM>
Subject: Re: Biased prob. estimates in random logistic regression?
In-Reply-To: <c6na515picqn8e0npjtt3vrudd7afikd9p@4ax.com>
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This might be related to the general problems with subject-specific
estimates in generalized linear mixed effects models that have a
non-identity link. There is always a bias, due to the link function
transforming the random effect.
I believe there were some papers by Neuhouse and others in Biometrics
or a similar journal in the early 90s that discussed this in more
detail.
On Apr 7, 2005 6:49 PM, Chris Maloof <cjmaloof@gmail.com> wrote:
> On 7 Apr 2005 01:21:09 -0700, Oliver.Kuss@medizin.uni-halle.de (Oliver
> Kuss) wrote:
>
> >Hi Chris,
> >I think you are expecting too much of the model and the estimation
> >method.
> >I ran your simulation (with your original code, that is, with the
> >random intercept) a hundred times and got a mean estimated p of 0.910
> >(Min: 0.872, Max: 0.942) for ItemType=0 and a mean estimated p of
> >0.178 (Min: 0.141, Max: 0.236) for ItemType=1. These are are very good
> >estimates for the data you have. Is the observed difference to the
> >true values of 0.9 and 0.2 really relevant?
> >Remember that you have only 30 observations to estimate the random
> >effect, very large fixed effects (separation might become an issue)
> >and a very complicated likelihood function (that can only be maximized
> >by numerical integration!), so in my opinion PROC NLMIXED is doing a
> >very good job here.
> >
> >Oliver
> >
> It's not the magnitude of the difference that bothers me, but the
> fact that for any data set, the predicted mean is apparently always in
> the same direction away from the *observed* mean toward 0 or 1. It
> seems like bias rather than random, unavoidable error, and that makes
> me think that there ought to be something I can do to improve the
> match, or some other way to look at the output.
>
> (One person has suggested PREDICT rather than ESTIMATE statements,
> which seems to slightly reduce the magnitude of the error if I use
> PREDICT intercept+rand_subj out=mydata;
> .)
>
> In my actual data the discrepancy between observed and adjusted means
> varies from .011 to .032, again always in the same direction;
> unfortunately, this is quite a lot because the observed means only
> vary between .83 and .96.
>
> Thanks for your time and effort! If this is the best that can be done
> with NLMIXED, that's annoying but good to know.
>
> Chris
>
--
best,
-tony
"Commit early,commit often, and commit in a repository from which we can easily
roll-back your mistakes" (AJR, 4Jan05).
A.J. Rossini
blindglobe@gmail.com
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