Robust conjoint analysis by controlling outlier sparsity
Robust conjoint analysis by controlling outlier sparsity
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DOI：
10.5281/zenodo.42366
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发表时间：
2011-12
期刊：
影响因子：
--
通讯作者：
G. Mateos;G. Giannakis
中科院分区：
文献类型：
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作者：
G. Mateos;G. Giannakis
偏好测量 (PM) 在营销、医疗保健和生物行为科学领域有着悠久的历史，这些领域通常使用联合分析。 PM 的目标是从可能受到异常值污染的表达偏好数据（购买模式、调查、评级）中了解个人或一组个人的效用函数。对于度量联合数据，基于ℓ0-（伪）范数正则化回归和最小修剪平方估计器之间的巧妙连接，开发了鲁棒的partworth估计器。这种联系表明基于凸松弛的高效求解器，这自然会导致包含 Huber 最优 M 类的一系列稳健估计器。通过调整正则化参数来识别离群值，这相当于控制沿着最小绝对收缩和选择算子解的整个鲁棒路径的离群值向量的稀疏性。对于基于选择的联合分析，开发了一种新颖的分类器，能够在模型拟合和复杂性之间实现理想的权衡，同时控制鲁棒性并揭示存在的异常值。还研究了考虑非线性效用和消费者异质性的变体。
Preference measurement (PM) has a long history in marketing, healthcare, and the biobehavioral sciences, where conjoint analysis is commonly used. The goal of PM is to learn the utility function of an individual or a group of individuals from expressed preference data (buying patterns, surveys, ratings), possibly contaminated with outliers. For metric conjoint data, a robust partworth estimator is developed on the basis of a neat connection between ℓ0-(pseudo)norm-regularized regression, and the least-trimmed squared estimator. This connection suggests efficient solvers based on convex relaxation, which lead naturally to a family of robust estimators subsuming Huber's optimal M-class. Outliers are identified by tuning a regularization parameter, which amounts to controlling the sparsity of an outlier vector along the entire robustification path of least-absolute shrinkage and selection operator solutions. For choice-based conjoint analysis, a novel classifier is developed that is capable of attaining desirable tradeoffs between model fit and complexity, while at the same time controlling robustness and revealing the outliers present. Variants accounting for nonlinear utilities and consumer heterogeneity are also investigated.