regrouping to satisfy proportional odds

[Juliet Hannah]

All,

Does anyone have references regarding the following.

If proportional odds is not satisfied by some metric (score test,
graphical approaches), it is reasonable
to regroup the outcome so that PO is satisfied.

Thanks,

Juliet Hannah

[Frank Harrell]

I saw a paper on this but could not find it in my bibliographic database.  In general, the only time grouping will help is if there are levels of Y that are in the wrong order.

Note that the test for PO in SAS (invented by a former PhD student of mine Bercedis Peterson) was shown by Peterson to be anti-conservative.  A better way to assess PO is through partial residuals plots using different Y cutoffs, or fitting a sequence of binary models for all cutoffs of Y and plotting the log odds ratios against the cutoff.  For the latter here's an example using R:

require(rms)

y <- as.factor(mydata$y)

Y <- as.numeric(y) - 1

ncut <- length(unique(Y)) - 1

p <- ...  # total no. of coefficients less intercepts

Coef <- matrix(NA, ncol=p, nrow=ncut,

               dimnames=list(paste('>=', levels(y)[-1],sep=''),

                 NULL))

for(k in 1:ncut) {

  f <- lrm(Y >= k ~ x1 + x2 + ..., data=mydata)

  Coef[k,] <- coef(f)[-1]

}

colnames(Coef) <- names(coef(f))[-1]

round(Coef, 3)

Also see the plot.xmean.ordinaly function.

Frank

[Juliet Hannah]

Frank,

Thanks for the response.

In case it was not clear, what I meant was collapsing categories if PO
is not satisfied. For example,
if we have outcomes 1, 2, 3, 4, 5: collapse some adjacent groups such
as 4, and 5 and reexamine if
PO is satisfied.

Do you find this practice reasonable?

I would rather stick with PO if possible rather than trying to find
software to fit partial PO models or
multinomial models.

Thanks,

Juliet

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[Frank Harrell]

That situation is exactly what my post was intended to answer.

Frank

On Wednesday, April 11, 2012 9:19:11 AM UTC-5, Juliet wrote:

Frank,

Thanks for the response.

In case it was not clear, what I meant was collapsing categories if PO
is not satisfied. For example,
if we have outcomes 1, 2, 3,  4, 5: collapse some adjacent groups such
as 4, and 5 and reexamine if
PO is satisfied.

Do you find this practice reasonable?

I would rather stick with PO if possible rather than trying to find
software to fit partial PO models or
multinomial models.

Thanks,

Juliet