A Bayesian Vector Multidimensional Scaling Procedure for the Analysis of Ordered Preference Data
分析有序偏好数据的贝叶斯向量多维尺度方法AI 解读 ↓
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AI 根据所提供的论文材料归类：文本明确建模有序偏好类别、潜在效用及消费者购买意向，直接对应离散选择与偏好分析方向。
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分析有序偏好数据的贝叶斯向量多维尺度方法
- 研究问题
- 如何从有序类别偏好数据构建低维联合空间，解释潜在效用结构，并同时确定维度和量化参数不确定性？
- 方法与思路
- 作者建立贝叶斯向量多维尺度模型，直接建模整数类别数据，提供后验点与区间估计，并纳入相关数据的外部信息。
- 材料陈述的贡献
- 摘要称，该方法提供概率化维度选择、减少预处理需求，并在豪华SUV购买意向案例中与传统多维尺度方法比较。
- 阅读关注点
- 应核对有序类别的概率模型、空间表示的识别约束、维度选择准则，以及相关数据后验作为先验的实现方式。
- 阅读边界
- 仅据版本未注明的索引摘要；未说明比较指标和改善幅度，购买意向也不等同于实际购买行为，不能推断刊本变化。
原文摘要
Multidimensional scaling (MDS) comprises a family of geometric models for the multidimensional representation of data and a corresponding set of methods for fitting such models to actual data. In this paper, we develop a new Bayesian vector MDS model to analyze ordered successive categories preference/dominance data commonly collected in many social science and business studies. A joint spatial representation of the row and column elements of the input data matrix is provided in a reduced dimensionality such that the geometric relationship of the row and column elements renders insight into the utility structure underlying the data. Unlike classical deterministic MDS procedures, the Bayesian method includes a probability based criterion to determine the number of dimensions of the derived joint space map and provides posterior interval as well as point estimates for parameters of interest. Also, our procedure models the raw integer successive categories data which ameliorates the need of any data preprocessing as required for many metric MDS procedures. Furthermore, the proposed Bayesian procedure allows external information in the form of an intractable posterior distribution derived from a related dataset to be incorporated as a prior in deriving the spatial representation of the preference data. An actual commercial application dealing with consumers’ intentions to buy new luxury sport utility vehicles are presented to illustrate the proposed methodology. Favorable comparisons are made with more traditional MDS approaches.