# [R] newbie polr() question

Prof Brian Ripley ripley at stats.ox.ac.uk
Tue Nov 27 07:59:16 CET 2007

```On Mon, 26 Nov 2007, Max wrote:

> Prof Brian Ripley explained :
>> On Mon, 26 Nov 2007, Max wrote:
>>
>>> Hi everyone, I'm trying to understand some R output here for ordinal
>>> regression. I have some integer data called "A" split up into 3 ordinal
>>> categories, top, middle and bottom, T, M and B respectively.
>>>
>>> I have to explain this output to people who have a very poor idea about
>>> statistics and just need to make sure I know what I'm talking about
>>> first.
>>>
>>> Here's the output:
>>>
>>> Call:
>>> polr(formula = Factor ~ A, data = a, Hess = TRUE, method = "logistic")
>>>
>>> Coefficients:
>>> Value        Std. Error  t value
>>> A -0.1259028 0.04758539  -2.645829
>>>
>>> Intercepts:
>>> Value Std. Error t value
>>> B|M -2.5872 0.5596 -4.6232
>>> M|T 0.3044 0.4864 0.6258
>>>
>>> Residual Deviance: 204.8798
>>> AIC: 210.8798
>>>
>>> I really am not sure what the intercepts mean at all. However, my
>>> understanding of the coefficient of A is that as the category
>>> increases, A decreases? If I have an A value of 10, how to I figure out
>>> the estimated probability that this score is in one of the three
>>> categories?
>>
>> Use predict(): see the book polr supports for examples (and the theory).
>
> I appreciate the reply, but have difficulty understanding what you mean
> by "the book polr supports"? :-?
>
> The manuals in R don't reference the polr() command, nor do they write
> about ordinal regression in R. (from what I can tell) The documentation
> of the polr() doesn't explain the output or the theory... I've done web

It _does_ describe both the theory and the use of predict(), on pages
204-5.

> searches on polr() and the MASS library and have found little of direct
> help to my question.

polr is in the MASS package (although you failed to mention that, or give
credit).  From library(help=MASS)

BundleDescription:   Functions and datasets to support Venables and
Ripley, 'Modern Applied Statistics with S' (4th
edition).
and from ?polr:

References:

Agresti, A. (2002) _Categorical Data._ Second edition.  Wiley.

Venables, W. N. and Ripley, B. D. (2002) _Modern Applied
Statistics with S._ Fourth edition.  Springer.

--
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 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

```