Rank responses based on the Bradley-Terry model with the quasi-Newton accelerated MM method
Adopt the Bradley-Terry model to rank responses in a single response question or in a multiple response question with the quasi-Newton accelerated MM method. This method associates each response with a value 'gamma', and use this value to rank responses.
A m x n matrix dij, where dij = 0 or 1. If the ith respondent selects the jth response, then dij = 1, otherwise dij = 0.
The rank.btqn returns the associated values in the first line and the ranks of the responses in the second line.
Hunter DR (2004). MM algorithms for generalized Bradley-Terry models. The Annals of Statistics, 32, 384-406.
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## This is an example to rank three responses in a multiple response question when ## the number of respondents is 1000. In this example, we do not use a real data, ## but generate data in the first three lines. A <-sample.int(2,1000,replace=TRUE,prob=c(0.37,0.63))-1 B <-sample.int(2,1000,replace=TRUE,prob=c(0.65,0.35))-1 C <-sample.int(2,1000,replace=TRUE,prob=c(0.5,0.5))-1 D <-cbind(A,B,C) data <-matrix(D,nrow=1000,ncol=3) ## or upload the true data rank.btqn(data)