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: [EMAIL PROTECTED] ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html