# [R] polr question

Prof Brian D Ripley ripley at stats.ox.ac.uk
Sun Mar 12 09:10:00 CET 2000

```On Sat, 11 Mar 2000, Troels Ring wrote:

> Dear friends.
> Do Polr in Mass change the sign of the coefficients ? Example (McCullagh 1980)

No, but there are at least three conventions here.  The simplest way to
interpret a polr model is as a discretized linear model with a logistic
error distribution, and that is what polr does.  So think of the
coefficients as being those of the variation with x of the (mean, mode) of
the underlying logistic, and the intercepts as the breakpoints for the
discretization.

> options(contrasts=c("contr.treatment","contr.poly"))
> library(Mass)

(Um, it's MASS, and you are only getting away with this on Windows.
Don't trust what is displayed in Explorer by default.)

> freq <- c(19,29,24,497,560,269)
> yy <- ordered(gl(3,1,6))
> z4 <- polr(yy~x,weights=freq)
> > z4
> Call:
> polr(formula = yy ~ x, weights = freq)
>
> Coefficients:
>         x2
> -0.6026492
>
> Intercepts:
>        1|2        2|3
> -1.1111584  0.7600705
>
> Residual Deviance: 2955.49
> AIC: 2961.49
>
> - since as specified the logit for the non-carrier for being in the
lower categories is higher ?

I don't see any mention of a carrier here, nor of x?  But if you had
the table

y=    1   2   3
x=0   19  29  24
x=1  497 560 269

I can reproduce your results, and the larger x does tend to give a lower
response.  (That does seem the natural sign for the x coefficient to me.)

Note that glm will give the same sign (apart from the intercepts) as polr:

> glm(yy ~ x, weights=freq, family=binomial)

Call:  glm(formula = yy ~ x, family = binomial, weights = freq)

Coefficients:
(Intercept)            x
1.0258      -0.5142

> glm((yy>2) ~ x, weights=freq, family=binomial)

Call:  glm(formula = (yy > 2) ~ x, family = binomial, weights = freq)

Coefficients:
(Intercept)            x
-0.6931      -0.6753

The sign of the intercepts are different, as you need to subtract the
breakpoint to get a zero-breakpoint model.

> as also got from Lindsey's library:

[...]

I think that has one of the other conventions, which are logistic models
for P(Y <= k | x)  or P(Y > k | x).

--
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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```