Johnson Timothy R
Department of Mathematics and Statistical Science, University of Idaho, Moscow, Idaho, USA.
Br J Math Stat Psychol. 2023 Feb;76(1):236-256. doi: 10.1111/bmsp.12292. Epub 2022 Nov 3.
Models for rankings have been shown to produce more efficient estimators than comparable models for first/top choices. The discussions and applications of these models typically only consider unordered alternatives. But these models can be usefully adapted to the case where a respondent ranks a set of ordered alternatives that are ordered response categories. This paper proposes eliciting a rank order that is consistent with the ordering of the response categories, and then modelling the observed rankings using a variant of the rank ordered logit model where the distribution of rankings has been truncated to the set of admissible rankings. This results in lower standard errors in comparison to when only a single top category is selected by the respondents. And the restrictions on the set of admissible rankings reduces the number of decisions needed to be made by respondents in comparison to ranking a set of unordered alternatives. Simulation studies and application examples featuring models based on a stereotype regression model and a rating scale item response model are provided to demonstrate the utility of this approach.
排名模型已被证明比用于第一/首选的可比模型能产生更有效的估计量。这些模型的讨论和应用通常只考虑无序的备选方案。但这些模型可以有效地应用于受访者对一组有序的响应类别进行排序的情况。本文提出引出与响应类别顺序一致的排名顺序，然后使用排名有序logit模型的一个变体对观察到的排名进行建模，其中排名分布已被截断到可接受排名的集合。与受访者只选择一个顶级类别的情况相比，这会导致更低的标准误差。并且与对一组无序备选方案进行排名相比，对可接受排名集合的限制减少了受访者需要做出的决策数量。提供了基于刻板印象回归模型和评级量表项目反应模型的模拟研究和应用示例，以证明这种方法的实用性。
