Re: Ordinal logistic regression vs. multiple regression with ordinal outcome?

"John Uebersax" <jsuebersax@xxxxxxxxx> wrote in
news:1155847681.043865.71330@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:

Thanks for your reply.

David Winsemius wrote:

Wouldn't these just be the same as the reasons to use LR in
preference to ordinary multiple regression for a dichotomous DV?

Yes and no--there's a question of degree here, i.e., how many
categories there are.
10 ordered categories is different than just 2.

Agreed. Pseudo-continuous is the term I have heard. I have heard dissent
to this position, however. My take: If you end up estimating 9 separate
models when one would do, you have created more trees and less forest.

WHY LOGISTIC REGRESSION IS NEEDED
One might try to use OLS regression with categorical DVs. There are
several reasons why this is a bad idea:
1. The residuals cannot be normally distributed (as the OLS model
assumes), since they can only take on one of several
values for each combination of level of the IVs

ok

That was actually the one I was least comfortable with. See below.

2. The OLS model makes nonsensical predictions, since the DV is not
continuous - e.g., it may predict that someone does
something more than 'all the time'.

Interesting. I'm not sure the issue is one of nonsensical
predications, as much as that the DV is upper- and lower-censored,
while the predicted values aren't.

I think that is a distinction without a difference. If the predicted
probability of an event or of class membership is greater than 1.0 or
less than 0, then non-sense has been predicted.

Wouldn't the same thing happen if the DV is continuous, but has a
natural 0--I mean one where there can be no negative values by
definition?

Agree. Could happen if you were modeling counts on a linear scale.

3. For nominal DVs, the coding is completely arbitrary, and for
ordinal DVs it is (at least supposedly) arbitrary up to a
monotonic transformation. Yet recoding the DV will give very
different results.

I don't agree with this part. One should only consider OLS with an
ordered-category DV if one has reason to believe the categories are
more-or-less evenly spaced (or one uses something like a probit
re-scaling to make them so).

I think what that author was saying (and I will be eventually agreeing
with you) is that ordinal DVs are less susceptible to restrictive
assumption of linearity. I think OLR may be just as susceptible to
forcing a linear relationship if there is "really" non-linearity on the
log(odds) scale. I would think the careful analyst would check a
multinomial odds model first,especially in those situations where the
form of the relationship had not been established by prior work.

I would add a couple of advantages that were not offered in that
citation:

4. Form of the link function in logistic regression means that
multiplicative predictions are made under the situation of joint
increments in the linear predictor from 2 or more IVs. In cardiovascular
and many other medical models, this has been shown to be a more accurate
summarization of the data than an additive model. The advantage is not
inherent in logistic regression but merely represents a good match
between biological reality and the form of the model. Same applies to
Poisson regression and Cox proportional hazards models.

5. For purposes of inference, the observed fact that variances seem to
increase at higher levels of linear predictors in medical data means that
linear models are more susceptible to failing the homoschedasticity
assumption. I would replace number 1. above with 5., since normality is
less crucial to inferential validity than homoschedasticity.

--
David Winsemius
.

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