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 at staffmail.ed.ac.uk