# Rank responses based on the Bradley-Terry model with the quasi-Newton accelerated MM method

### Description

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.

### Usage

1 |

### Arguments

`data` |
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. |

### Value

The rank.btqn returns the associated values in the first line and the ranks of the responses in the second line.

### Author(s)

Hsiuying Wangwang@stat.nctu.edu.tw,Yu-Chun Linrestart79610@hotmail.com

### References

Hunter DR (2004). MM algorithms for generalized Bradley-Terry models. The Annals of Statistics, 32, 384-406.

### See Also

`rank.btmm`

,`rank.btnr`

,`rank.L2R`

,`rank.LN`

,`rank.gs`

,`rank.wald`

### Examples

1 2 3 4 5 6 7 8 9 10 | ```
## 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)
``` |

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