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

"John Uebersax" <jsuebersax@xxxxxxxxx> wrote in news:1155808696.803566.154640@xxxxxxxxxxxxxxxxxxxxxxxxxxx:

I have a basic question about Ordinal Logistic Regression (OLR),
which is logistic regression with an ordered-category outcome
variable.

Please excuse any incorrect statements below--it is my very
ignorance about logistic regression that prompts the question.
I believe there's a simple answer, and perhaps someone can
supply a concise one. (Also, I hesitate to mention this, but
experience suggests I should: no rambling, speculative replies,
please!)

It seems to me OLR assumes something like one of the following:

1. The odds of going from one outcome level to the next higher
one are constant (or proportional?) for each pair of
adjacent outcome levels.

Or possibly:

2. The odds of going to outcome level j from *any* lower
outcome level is constant for all levels j (cumulative
logit?)

Halpin at the University of Limerik says 1. is the adjacent category
model and 2. is the continuation-ratio model:
http://teaching.sociology.ul.ie/SSS/lugano/node74.html

Since we are not implying any real transition, I wonder if the words
"going to" might be replaced by "being above" or "being in". There appears to be
a third option and is the one described in several web citations as
being used by Stata and SAS:
3. The odds (or I think more likely the log(odds)) of being above
a particular level, The proportional odds model per Halpin:

http://staff.washington.edu/glynn/olr.pdf#search=%22ordinal%20logistic%20regression%22

http://teaching.sociology.ul.ie/SSS/lugano/node75.html

Whichever the case (but it appears more applicable in case 1),
how different is that from assuming that the outcome variable
levels are evenly spaced in the first place--i.e., an interval
level of measurement. But in that case, why not just use
ordinary multiple regression?

Wouldn't these just be the same as the reasons to use LR in preference
to ordinary multiple regression for a dichotomous DV? Copied from:
http://www.nesug.org/html/Proceedings/nesug05/an/an2.pdf#search=%22ordinal%20logistic%20regression%22
----quote-----
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
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'.
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.
-------end quote-----------

I hope that was sufficiently not(rambling).
--
David Winsemius
.