Bill Rising posted earlier this week:
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Hello folks,
Has anyone out there tried mimicking the ordinal logistic regression
results from the insomnia example given the second edition of Agresti's
book on Categorical analysis?
I was trying to learn to use the gllamm package for Stata using Agresti,
because his datasets are all on the web
http://www.stat.ufl.edu/~aa/cda/sas/sas.html
(and because I have the book).
As one might guess from the URL, SAS is the package he used to get the
results in his book.
I'm stuck trying to mimic table 12.7 on page 514, where he compares
estimates for a model using ordinal logistic regression (aka cumulative
logit) for some insomnia data (found in table 11.4 on p.462).
When I use Stata's ologit command to try to match his ML estimates, I
instead match his marginal GEE estimates.
If I try to mimic his use of ML random intercept models, using gllamm
using 'binomial' as the family and 'ologit' as the link, I get similar
but different coefficients.
Stata's ologit command matches his estimates for the mental impairment
example on page 279, so it cannot be that there is something which causes
the ologit and his ml cumulative logit models to be off all the time.
Is there any reason to worry about the slightly different results from
time to time? Does anyone know whether SAS computes these models
differently? Perhaps I'm missing a nuance about ML estimation vs. some
other method of fitting the models?
Any hints would be much appreciated,
Bill
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There's nothing about it in the errata
(www.stat.ufl.edu/~aa/cda/errors.pdf), but it's possible that the Marginal
ML and Marginal GEE columns are transposed. There is an online manuscript
by David Clayton in which a GEE estimate for the interaction term is 0.677
with a working correlation matrix estimated from the data, and 0.701 when
independence is assumed between the baseline and posttreatment occasions.
Those two numbers don't clarify the situation in the textbook, but the
manuscript does go on to indicate that Alan Agresti has published at least
an empirically weighted least squares (EWLS) estimated model of this
dataset. I don't have access to it, but Alan Agresti's paper cited in the
manuscript seems to be a survey of applicable methods, so it might also
report Marginal ML estimates for this dataset that can be checked against
those in his textbook.
D. Clayton, Repeated ordinal measurements: a generalised estimating
equation approach. 1995. Available at
www.mrc-bsu.cam.ac.uk/pub/publications/submitted/david_clayton/ordcat2.ps
A. Agresti, A survey of models for repeated ordered categorical response
data. _Statistics in Medicine_ 8:1209-24, 1989. (Cited in the online paper
above.)
Joseph Coveney
P.S. Does anyone know what the reception has been of David Clayton's GEE
implementation for repeated ordinal data? There is nothing on the method in
the Stata directory of his website (he used S for the manuscript); the
accompanying readme file states that the manuscript was conditionally
accepted by _Applied Statistics_, but abandoned. The manuscript (or an
earlier version of it) has been cited in a review article
(www.imbs.mu-luebeck.de/reports/paper24.pdf) primarily in the context of how
difficult convergence can sometimes be with GEE models of repeated ordered
categorical data, but this has been my experience with random effects
maximum likelihood methods, too, with ordinal data.
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