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Re: st: Help please re Ocratio


From   "Anders Alexandersson" <andersalex@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Help please re Ocratio
Date   Thu, 1 Nov 2007 09:14:23 -0400

> Anders Alexandersson <andersalex@gmail.com> 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
interested.

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
on R.

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.

Anders Alexandersson
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