On Extending the Bradley-Terry Model to Accommodate Ties in Paired Comparison Experiments
On Extending the Bradley-Terry Model to Accommodate Ties in Paired Comparison Experiments
复制标题
关于扩展 Bradley-Terry 模型以适应配对比较实验中的平局
DOI：
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发表时间：
1970
期刊：
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通讯作者：
R. Davidson
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文献类型：
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作者：
R. Davidson
摘要本研究将Bradley-Terry配对比较模型推广到不允许表达偏好的情况。一个新的模型的开发和它的性能相比，由Rao和Kupper提出的模型。参数的最大似然估计使用迭代过程，在弱假设下，单调收敛到似然方程的解。值得注意的是，对于平衡配对比较实验，从最大似然估计获得的排名与从得分系统获得的排名一致，该得分系统为胜利分配两分，平局分配一分，失败分配零分。结果表明，等偏好假设的似然比检验具有与Rao-Kupper模型相同的渐近效率。给出了两个例子，其中之一介绍了一组数据的不平衡配对比较实验。拟合优度检验的初步应用表明，建议…
Abstract This study is concerned with the extension of the Bradley-Terry model for paired comparisons to situations which allow an expression of no preference. A new model is developed and its performance compared with a model proposed by Rao and Kupper. The maximum likelihood estimates of the parameters are found using an iterative procedure which, under a weak assumption, converges monotonically to the solution of the likelihood equations. It is noted that for a balanced paired comparison experiment the ranking obtained from the maximum likelihood estimates agrees with that obtained from a scoring system which allots two points for a win, one for a tie and zero for a loss. The likelihood ratio test of the hypothesis of equal preferences is shown to have the same asymptotic efficiency as that for the Rao-Kupper model. Two examples are presented, one of which introduces a set of data for an unbalanced paired comparison experiment. Initial applications of the test of goodness of fit suggest that the propos...