Date: Wed, 4 Jun 2008 14:43:39 -0500
Reply-To: Robin R High <rhigh@UNMC.EDU>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Robin R High <rhigh@UNMC.EDU>
Subject: Re: INTRACLASS CORR--PROC GLIMMIX
In-Reply-To: <20080529205840.DC65F1CE803@ws1-6.us4.outblaze.com>
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Tom,
A quick follow-up to my note from last week. One way to compute an "ICC"
(as suggested in Section 14.3.3 from Snijders and Bosker - "Multilevel
Analysis") is to apply the ratio:
tau^2 / (tau^2 + 3.29) for the "logit" link and
tau^2 / (tau^2 + 1) for the "probit" link and
where 3.29 is 3.1416^2/3 (i.e., pi^2/3) which is the variance of the
"logistic" distribution and 1 is the variance of the "standard normal".
Both of these formulas apply to the linear predictor (i.e, the logit) and
not to the actual proportions (which are non-linear transformations of the
logits), so at best, it would be a "pseudo" ICC. Most of us don't think in
terms of logits when working with 0/1 data (either collected independently
or in clusters), so this summary measure needs a qualifier or word of
caution. There are also the v and vcorr options on the RANDOM statement
in both MIXED and GLIMMIX that I have found helpful for examining the size
of variance components and resulting correlations from random effects
models. In either PROC, the ODS statements should always be applied to
look at them, as the output and datasets tend to quickly fill up the
output window otherwise, e.g.
ods output v=v vcorr=vcr;
ods exclude v vcorr;
proc glimmix data=exmp;
class e tr pos;
model rst = e pos / distribution=binary link=logit;
random tr(e) / solution v vcorr;
run;
proc print data=vcr(obs=8); var row col1-col8; run;
.. again these apply to the logits, so need that same "qualification"
before saying much, if anything, about clustering of the proportions.
Robin High
UNMC
Tom White <tw2@MAIL.COM>
Sent by: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
05/29/2008 04:00 PM
Please respond to
Tom White <tw2@MAIL.COM>
To
SAS-L@LISTSERV.UGA.EDU
cc
Subject
Re: INTRACLASS CORR--PROC GLIMMIX
Thank you Robin for this response--
So, just to double chcek with my original question:
Does GLIMMIX produce a single statistic (something like intraclass
corr coeff)
to tell me how much nesting is present in mydata set with binary
response variable?
Perhaps you say that the 'statistic' I'm looking for is the odds ratio?
This tells me how much nesting is present in my data?
Any papers that discuss this concept with binary response withing GLIMMIX?
Thank you.
Tom
----- Original Message -----
From: "Robin R High"
To: SAS-L@LISTSERV.UGA.EDU
Subject: Re: INTRACLASS CORR--PROC GLIMMIX
Date: Thu, 29 May 2008 15:41:51 -0500
Tom,
This is a topic about which I continually learn new things. When one
considers how the ICC is computed under the normal distribution model
(variance estimate is 'pooled' and assumed constant across grouping levels
which have different means);however, under the binary model, the variance
is a function of the mean, so constant variance is not part of the model;
computations for an ICC in this situation aren't the same.
In the random effects model, when one considers how the clustering is
accounted for (i.e., applied within the link function) it is more likely,
perhaps, that the results will be distorted and even incorrect if the
random effect is not included; that is, a model computed with GLIMMIX
that converges with a positive estimate for the random effect is likely to
be better than assuming conventional, esp. when the sample size is
relatively "large". It would also be interesting to compare this random
effects logistic regression with NLMIXED if appropriate (since it is based
on quadrature). And GLIMMIX has the odds and oddsratio options (among
others) which simplify interpretation.
Robin High
UNMC
Tom White
Sent by: "SAS(r) Discussion"
05/29/2008 02:38 PM
Please respond to
Tom White
To
SAS-L@LISTSERV.UGA.EDU
cc
Subject
INTRACLASS CORR--PROC GLIMMIX
Hello everyone,
I have this sort question:
From reading so far about PROC GLIMMIX, I undersand that it does not
produce an
intraclass corr coeff for binary dependent variable (i.e. logistic
regression).
Therefore, what statistic can I use in GLIMMIX to tell me whether or not
nesting
of my data makes a diference. If it does, then I will use multilevel
logistic--
if not, I will use conventional logistic.
Thank you.
T
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