[R] summary(polr.object)

[ripley@stats.ox.ac.uk]

On Tue, 25 Feb 2003, Tord Snall wrote:

> Dear all, 
> 
> I have used polr in MASS but I am uncertain about the summary(polr.object)
> interpretation and would be happy for help on that. This is my summary:
> 
> > summary(shade.polr)
> 
> Re-fitting to get Hessian
> 
> Call:
> polr(formula = as.ordered(shade) ~ as.factor(objekt), data = sof, 
>     weights = as.numeric(frek))
> 
> Coefficients:
>      Value Std. Error    t value 
>  2.1699520  0.3681840  5.8936612 
> 
> Intercepts:
>     Value   Std. Error t value
> 2|3 -2.2975  0.2656    -8.6500
> 3|4  2.8737  0.3296     8.7175
> 
> Residual Deviance: 347.5964 
> AIC: 353.5964 
> 
> 
> The ordered variable thus has 3 levels. The independent as.factor(objekt)
> has two levels.
> 
> Is t=5.8936612 for a test of difference in the ordered response between the
> two groups, and is the p-value for the two-sided test thus 
> 2* (1-pt(5.8936612, df=shade.polr$df.residual))
> 
> Why is the p-value not reported? Is there a special reason that would be
> good to know?

Like glms. there is no exact p-value.  R is unwise to report them for 
binomial and Poisson glms: S-PLUS is more sanguine here.

> Furthermore is t = -8.6500 in 
> 2|3 -2.2975  0.2656    -8.6500
> for a test of difference in the proportion of twos and threes between the
> two levels of the independet factor?
> 
> Is the p-value: 2* (1-pt(8.6500, df=shade.polr$df.residual))?

Not quite.  It's between categories to the left of the line and to the 
right of the line, at the base value of the regressor.  In your case that 
is between proportions of 2 vs 3,4 at the base value of object (assuming 
you are using treatment contrasts).

Also, use a normal reference distribution: there is no real evidence that 
I know of for the accuracy of a t distribution.

As ever, MASS the package supports MASS the book and the details are in 
the latter.

-- 
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