Ordinal regression: How important is parallel lines assumption?

[Bruce Weaver]

A colleague is planning a study where the main outcome variable has 5
ordered categories. After a fair bit of coaxing, I got him to provide
expected proportions falling into the 5 categories for Treatment and
Control groups. But when I take those proportions and work out the
odds ratio at each of the 4 cut-points, I get the following:

OR Cut
20.39 (1) v (4-5)
68.05 (1,2) v (3-5)
240.66 (1-3) v (4,5)
8.90 (1-4) v (5)

I'm rather new to ordinal regression myself, but I understand that the
"parallel lines" assumption means that these odds ratios should all be
more or less the same. Clearly, they are not. So...

1. Just how important is the parallel lines assumption? and
2. What are the options when it is violated pretty severely?
Multinomial logistic perhaps?

Thanks,
Bruce

--
Bruce Weaver
bwe...@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/Home
"When all else fails, RTFM."

[Ray Koopman]

If the expected proportions are values that he provided only under
duress and doesn't really believe are correct, then turn the problem
around: give him some proportions that are consistent with the model
and ask him whether they might equally well be the true values.

To generate such proportions, pick 4 cutpoints and get the
corresponding 5 category proportions in the standard logistic
distribution. Then add a constant to all the cutpoints, and get
another set of 5 category proportions. The odds ratios for the two
sets of proportions -- 12 v 345, etc -- will be constant; their log
will be the constant that you added to the cutpoints. The average
log(OR) in the data you gave is 3.695, so try that initially. That
leaves you with the 4 unknown cutpoints. You might initially try the
cutpoints implied by one of the two sets of proportions he gave you.

All that will take some playing around. Can he do it for himself,
once you show him what needs to be done?

On Mar 21, 8:33 am, Bruce Weaver <bwea...@lakeheadu.ca> wrote:
> A colleague is planning a study where the main outcome variable has 5
> ordered categories. After a fair bit of coaxing, I got him to provide
> expected proportions falling into the 5 categories for Treatment and
> Control groups. But when I take those proportions and work out the
> odds ratio at each of the 4 cut-points, I get the following:
>
> OR Cut
> 20.39 (1) v (4-5)
> 68.05 (1,2) v (3-5)
> 240.66 (1-3) v (4,5)
> 8.90 (1-4) v (5)
>
> I'm rather new to ordinal regression myself, but I understand that the
> "parallel lines" assumption means that these odds ratios should all be
> more or less the same. Clearly, they are not. So...
>
> 1. Just how important is the parallel lines assumption? and
> 2. What are the options when it is violated pretty severely?
> Multinomial logistic perhaps?
>
> Thanks,
> Bruce
>
> --
> Bruce Weaver

> bwea...@lakeheadu.cahttp://sites.google.com/a/lakeheadu.ca/bweaver/Home

[Ray Koopman]

On Mar 21, 12:39 pm, Ray Koopman <koop...@sfu.ca> wrote:
> ... The average log(OR) in the data you gave is 3.695, ...
Make that 3.726 . (I entered 68.05 as 60.05 .)

[Bruce Weaver]

Hi Ray. I should have mentioned that I did try something along those
lines. I.e., I started with the expected Control group proportions,
and plugged in a common odds ratio of 10. But the Tx group
proportions yielded by that were a long way from what he expects. The
reason for choosing 10 was that it was near the bottom end of the odds
ratios obtained using my colleague's estimates of the proportions--I
figured this was being conservative when it comes to estimating the
effect size. I've not tried it with an odds ratio nearer to
Exp(3.726), but will give that a try.

One of the resources I've been using, by the way, is Steve Simon's
page on sample size for an ordinal outcome:

http://www.childrens-mercy.org/stats/weblog2004/OrdinalLogistic.asp

Cheers,
Bruce

[Ray Koopman]

Steve's approach is an easier-to-follow version of what I was
suggesting. However, it just struck me that in ordinal logistic
regression using individual-level predictors, the "parallel lines"
assumption can not be tested by looking at the raw data.

The model is that the observed categorical y is quantized from an
unobserved continuous z = f(x) + e, where x is the set of predictor
scores, f is the regression function, and e is random error with a
standard logistic distribution. The distribution of y contains no
information about the validity of the assumed model.

[Adrian Sayers]

The parallel line assumption can be relaxed to non parallel lines.

see gologit2 in stata.

bw
A

--
To post a new thread to MedStats, send email to MedS...@googlegroups.com .
MedStats' home page is http://groups.google.com/group/MedStats .
Rules: http://groups.google.com/group/MedStats/web/medstats-rules

[Bruce Weaver]

Thanks Adrian, I'll check that out.

On Mar 22, 8:56 am, Adrian Sayers <adriansay...@gmail.com> wrote:
> The parallel line assumption can be relaxed to non parallel lines.
>
> see gologit2 in stata.
>
> bw
> A
>

[Ray Koopman]

If he does use gologit2 then he should remember that Brant's test
should play the same role here that Levene's test should in anova,
namely a minor bit part that may end up on the cutting-room floor.
If the sample size is large then Brant's test can detect trivial non-
parallelism that would not impair the usefulness of an analysis that
assumed parallelism. On the other hand, and unlike anova, if the
sample size is small than all results that do not use Firth-type
corrections should be regarded with suspicion.

As to what he should do if the non-parallelism is non-trivial,
consider the following excerpt from Agresti, 2002, Categorical Data
Analysis, p 282: "If a proportional odds model fits poorly in terms of
practical as well as statistical significance, alternative strategies
exist. These include (1) trying a link function for which the response
curve is nonsymmetric (e.g., complementary log-log); (2) adding
additional terms, such as interactions, to the linear predictor; (3)
adding dispersion parameters; (4) permitting separate effects for each
logit for some but not all predictors (i.e., partial proportional
odds); and (5) fitting baseline-category logit models and using the
ordinality in an informal way in interpreting the associations. For
approach(4), see Peterson and Harrell (1990), Stokes et al. (2000,
Sec. 15.13), and criticism by Cox (1995). In the next section we
generalize the cumulative logit model to permit extensions (1) and
(3)."