用于非对称选择响应的多项Probit模型
A Multinomial Probit Model for Asymmetric Choice Responses
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中文总结 AI 辅助
针对标准MNP模型无法捕捉非对称选择响应的问题，提出SMNP模型，通过协变量重参数化等方法解决识别与计算挑战，在消费者选择数据应用中提升了预测效果。
中文摘要 AI 辅助
标准多项Probit（MNP）模型设定对称的潜在效用分布，意味着选择概率对相同幅度的协变量正负偏移的响应是对称的。这一限制在实证选择场景中通常不符合实际，可能导致弹性和替代预测结果产生误导。我们提出一种偏斜多项Probit（SMNP）模型，通过为潜在效用设定多元偏态正态分布来捕捉非对称选择响应。该模型保留了MNP框架灵活的替代模式，引入了针对不同选项的偏度参数，且当偏度为零时可嵌套标准MNP模型。引入偏度会带来识别和计算挑战，因为偏度参数与MNP的尺度标准化相互作用，会破坏贝叶斯MNP估计中使用的条件高斯更新结构。我们通过协变量重参数化解决这些挑战，该参数化可从构造上确保识别和正定性，对识别后的参数空间采用可解释先验，并采用双重数据增强方案，生成了吉布斯采样器内的Metropolis-Hastings算法。数值实验和消费者选择数据的应用表明，SMNP模型能够恢复非对称选择响应，提高概率预测精度，并在价格弹性和替代模式方面产生具有经济意义的差异。
英文摘要
Standard multinomial probit (MNP) models specify symmetric latent utility distributions, implying that choice probabilities respond symmetrically to positive and negative covariate shifts of the same magnitude. This restriction is often implausible in empirical choice settings and can lead to misleading elasticity and substitution predictions. We propose a skewed multinomial probit (SMNP) model that captures asymmetric choice responses by specifying a multivariate skew-normal distribution for the latent utilities. The model preserves the flexible substitution patterns of the MNP framework, introduces alternative-specific skewness parameters, and nests the standard MNP model when skewness is zero. Introducing skewness creates identification and computational challenges because the skewness parameters interact with the MNP scale normalization and disrupt the conditional Gaussian updating structure used in Bayesian MNP estimation. We address these challenges through a covariance reparameterization that enforces identification and positive definiteness by construction, interpretable priors on the identified parameter space, and a double data-augmentation scheme that yields a Metropolis-Hastings within Gibbs sampler. Numerical experiments and applications to consumer choice data show that SMNP recovers asymmetric choice responses, improves probabilistic prediction, and produces economically meaningful differences in price elasticities and substitution patterns.
