In this paper, we apply a Bayesian perspective to sampling of alternatives for multinomial logit (MNL) and mixed multinomial logit (MMNL) models. We find three theoretical results -- i) McFadden's correction factor under the uniform sampling protocol can be transferred to the Bayesian context in MNL; ii) the uniform sampling protocol minimises the loss in information on the parameters of interest (i.e. the kernel of the posterior density) and thereby has desirable small sample properties in MNL; and iii) our theoretical results extend to Bayesian MMNL models using data augmentation. Notably, sampling of alternatives in Bayesian MMNL models does not require the inclusion of the additional correction factor, as identified by Guevara and Ben-Akiva (2013a) in classical settings. Accordingly, due to desirable small and large sample properties, uniform sampling is the recommended sampling protocol in MNL and MMNL, irrespective of the estimation framework selected.
翻译:在本文中,我们从巴伊西亚角度对多数值逻辑(MNL)和混合多数值逻辑(MMNL)模型的替代品进行取样,我们发现三个理论结果 -- -- 统一取样协议下McFadden的校正系数可在MNL中转移到巴伊西亚;二)统一取样协议最大限度地减少利益参数信息的损失(即后方密度的内核),从而在MNL中具有理想的小样本特性;三)我们的理论结果扩大到使用数据增强的巴伊西亚MMMNL模型。值得注意的是,在Bayesian MMNL模型中,抽样并不要求列入古典环境中Guevara和Ben-Akiva(2013年a)所查明的额外校正系数。因此,由于适当的小和大样本特性,统一的取样是建议在MNL和MMNL的取样协议,而不论选定的估计框架如何。