Dynamic paired comparison models with stochastic variances
Dynamic paired comparison models with stochastic variances
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DOI：
10.1080/02664760120059219
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发表时间：
2001-08-01
影响因子：
1.5
通讯作者：
Glickman, ME
中科院分区：
文献类型：
--
作者：
Glickman, ME
在配对比较实验中，一个单位的价值或优点是通过与其他单位的比较来衡量的。当随着时间的推移收集成对的比较结果时，单元的优点可能会改变，假设数据遵循非线性状态空间模型通常是方便的。假设一个固定的(未知的)自回归方差的典型的成对比较状态空间模型不考虑优点突然改变的可能性。例如，在对人类发展中的认知能力进行建模时，这是一个特别值得关注的问题；认知能力不仅会随着时间的推移而变化，而且可能会突然变化。对于配对比较数据，我们探索了传统状态空间模型的一种特殊扩展，它允许状态方差随机变化。这种类型的模型最近被开发并应用于对金融数据进行建模，但可以看出在对配对比较数据进行建模时具有适用性。还推导了一种过滤算法，当比较的对象数量很大时，该算法可以用来代替基于似然的计算。给出了在国家橄榄球联盟比赛结果和国际象棋比赛结果中的应用。
In paired comparison experiments, the worth or merit of a unit is measured through comparisons against other units. When paired comparison outcomes are collected over time and the merits of the units may be changing, it is often convenient to assume the data follow a non-linear state-space model. Typical paired comparison state-space models that assume a fixed (unknown) autoregressive variance do not account for the possibility of sudden changes in the merits. This is a particular concern, for example, in modeling cognitive ability in human development; cognitive ability not only changes over time, but also can change abruptly. We explore a particular extension of conventional state-space models for paired comparison data that allows the state variance to vary stochastically. Models of this type have recently been developed and applied to modeling financial data, but can be seen to have applicability in modeling paired comparison data. A filtering algorithm is also derived that can be used in place of likelihood-based computations when the number of objects being compared is large. Applications to National Football League game outcomes and chess game outcomes are presented.