[R] polr (MASS) link functions

From: I M S White <iwhite_at_staffmail.ed.ac.uk>
Date: Mon 11 Jul 2005 - 21:37:32 EST


When we analyse ordered categorical data, with categories I<II<III, should we expect an equivalent analysis if the ordering is changed to I>II>III ? Not with a cloglog link (see example below). However, I suspect the cloglog analysis on the reordered categories is equivalent to a loglog analysis on the original ordering. Perhaps for consistency polr should include a loglog link? Or warn that a different answer is available, possibly more appropriate?

Cheese tasting example from McCullagh and Nelder:

> library(MASS)
> frqs <- c(0,0,1,7,8,8,19,8,1,

+ 6,9,12,11,7,6,1,0,0,
+ 1,1,6,8,23,7,5,1,0,
+ 0,0,0,1,3,7,14,16,11)

> Y1 <- ordered(rep(1:9,4))
> Y2 <- ordered(rep(9:1,4))
> trt <- factor(rep(c("A","B","C","D"),each=9))
> fit1 <- polr(Y1 ~ trt, method="clog",weight=frqs)
> fit2 <- polr(Y2 ~ trt, method="clog",weight=frqs)
> print(fit1)

Call:
polr(formula = Y1 ~ trt, weights = frqs, method = "clog")

Coefficients:

     trtB trtC trtD
-1.809487 -0.879997 0.987389

Intercepts:

        1|2 2|3 3|4 4|5 5|6 6|7 -2.50668784 -2.04055560 -1.42592187 -0.80166219 -0.01722569 0.55135471

        7|8 8|9
 1.55688848 2.84302173

Residual Deviance: 725.2341
AIC: 747.2341
> print(fit2)

Call:
polr(formula = Y2 ~ trt, weights = frqs, method = "clog")

Coefficients:

      trtB trtC trtD
 1.9513455 1.1033902 -0.9588354

Intercepts:

       1|2 2|3 3|4 4|5 5|6 6|7 7|8 -1.3832854 -0.5216350 0.4225419 0.9994969 1.8317538 2.5777980 3.4532818

       8|9
 4.4026602

Residual Deviance: 718.0052
AIC: 740.0052



I.White
University of Edinburgh
Ashworth Laboratories, West Mains Road
Edinburgh EH9 3JT
Tel: 0131 650 5490 Fax: 0131 650 6564
E-mail: iwhite@staffmail.ed.ac.uk

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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Mon Jul 11 21:45:57 2005

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