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Re: st: Help please re Ocratio
"Anders Alexandersson" <email@example.com>
Re: st: Help please re Ocratio
Thu, 1 Nov 2007 09:14:23 -0400
> Anders Alexandersson <firstname.lastname@example.org> wrote:
> > Jon Heron (ALSPAC) <Jon.Heron@bristol.ac.uk> would like an extra bit
> > of clarification about the continuation ratio model:
> >> It sounds like, if I want to fit an ocratio model and then examine
> >> the individual pairs of effects I either fit two logistics
> >> 1 [=1] versus 2 & 3[=0]
> >> 2 [=1] versus 3 [=0]
> >> and compare with an ocratio on an outcome ordered 1,2,3
> >> or fit two logits
> >> 1 [=0] versus 2 & 3[=1]
> >> 2 [=0] versus 3 [=1]
> >> and compare with an ocratio with outcome ordered the other way i.e.
> >> 3,2,1
> >> If this is the case, and a quick experiment with Stata suggests it
> >> is, and since the continuation ratio model is not reversible (unlike
> >> proportional odds), how do I decide which one to do?
> >> I guess the former
> > I think that the answer depends on what you want to compare. Bender and
> > Benner (2000, 681) suggest that a "forward" continuation ratio model
> > (your option 1) seems useful if the response Y represents "survival
> > times". For example, you want to compare short survival times versus
> > high survival
> > times. In contrast, a "backward" (or reverse) continuation ratio model
> > (your option 2) seems useful if Y represents "disease status". For
> > example, you want to compare bad disease vs mild disease. Bender and
> > Benner illustrate the backward continuation ratio model.
> > It is also important to distinguish between "stopping" and
> > "continuation" continuation ratio models. I find the terminology in the
> > documentation for R's function vgam() by Yee helpful, see
> > http://www.stat.auckland.ac.nz/~yee/VGAM/. I try to summarize the four
> > models here:
> > continuation ratio Probability, j = 1,2
> > -------------------- --------------------
> > a. forward stopping P[Y=j|Y>=j]
> > b. reverse stopping P[Y=j+1|Y<=j+1]
> > c. forward continuation P[Y>j|Y>=j] = a with reversed signs
> > d. reverse continuation P[Y<j+1|Y<=j+1] = b with reversed signs
> > It seems to me that logistic regression and Rory Wolfe's -ocratio-
> > estimates (a). Logistic regression assumes equal slopes on original
> > data, or unequal slopes on expanded data. In comparison, -ocratio-
> > assumes equal slopes only but you can test this assumption, and the
> > sign of the slope is opposite but that is easy to handle. It seems
> > that Maarten Buis's -seqlogit- estimates (c).
> > How to estimate version (b) or (d) of the continuation ratio model in
> > Stata, or how to extend the continuation ratio model(s) as a
> > mixed-model? For mixed-model version, the literature (e.g, Grilli
> > 2005) suggests the use of logistic regression on expanded data, but I
> > have not had a chance to try this nor have I found an example to
> > replicate. Any suggestions?
> > References
> > ----------
> > Bender, R., Benner, A. 2000. Calculating ordinal regression models in
> > SAS and S-Plus. Biometrical Journal 42(6): 677-699.
> > Grilli, L. 2005. The random-effects proportional hazards model with
> > grouped survival data: a comparison between the grouped continuous
> > and continuation ratio versions. Journal of the Royal Statistical
> > Society, Series A. 168(1): 83-94
Jon Heron found my answer helpful, but I missed something obvious:
To estimate the reverse versions of the continuation ratio models, you
simply reverse the values of y before you run the estimation command.
So, Stata can fit all four versions of the continuation ratio models.
I'll be happy to provide examples if Jon or someone else is
I also made mistake about R: There is no such thing as the vgam() function.
I meant to refer to the R function vglm() in the package VGAM. Well,
Statalist is a discussion list for Stata and statistics, not focusing
I still don't know exactly how to estimate the continuation ratio
model on multilevel data but Grilli (2005) gives an outline. This
issue is also discussed in the GLLAMM book,
http://www.stata.com/bookstore/glvm.html, on pages 378-381.
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