Maximum Likelihood Estimation in Mallows’s Model Using Partially Ranked Data
Maximum Likelihood Estimation in Mallows’s Model Using Partially Ranked Data
复制标题
使用部分排序数据的 Mallows 模型中的最大似然估计
DOI：
10.1007/978-1-4612-2738-0_6
复制
发表时间：
1993
期刊：
影响因子：
--
通讯作者：
L. Beckett
中科院分区：
文献类型：
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作者：
L. Beckett
考虑一个来自总体的样本，其中每个个体的特征都在于项目上的排名，但样本中的个体只能获得有关排名的部分信息。问题是在给定部分排名数据的情况下估计排名的人口分布。本文提出使用 EM 算法来获得 Mallows 排名分布模型中参数的最大似然估计。讨论医疗应用，其中项目是疾病或发育过程的表现，排名是它们随着时间的推移首次出现的顺序，部分排名是通过对受试者的横截面或在几个指定时间的观察得出的。这些方法是针对 65 岁及以上社区人口的纵向研究进行说明的，其中的迹象是不同身体活动损伤的自我报告。
Consider a sample from a population in which each individual is characterized by a ranking onkitems, but only partial information about the ranking is available for the individuals in the sample. The problem is to estimate the population distribution of rankings, given the partially ranked data. This paper proposes use of an EM algorithm to obtain maximum likelihood estimates of the parameters in Mallows’s model for the distribution of rankings. Medical applications are discussed where the items are manifestations of a disease or a developmental process, the ranking is the sequence in which they first appear over time, and the partial ranking results from observation of the subjects cross-sectionally or at a few specified times. The methods are illustrated for a longitudinal study of a community population aged 65 years and older, where the signs are self-reporting of impairment in different physical activities.