Technical Note—An Expectation-Maximization Method to Estimate a Rank-Based Choice Model of Demand
提出一种期望最大化方法，仅用销售交易和产品可得性数据估计顾客偏好，结合基于排名的离散选择模型和伯努利到达过程，实现简单高效的极大似然估计。
We propose an expectation-maximization (EM) method to estimate customer preferences for a category of products using only sales transaction and product availability data. The demand model combines a general, rank-based discrete choice model of preferences with a Bernoulli process of customer arrivals over time. The discrete choice model is defined by a probability mass function (pmf) on a given set of preference rankings of alternatives, including the no-purchase alternative. Each customer is represented by a preference list, and when faced with a given choice set is assumed to either purchase the available option that ranks highest in her preference list, or not purchase at all if no available product ranks higher than the no-purchase alternative. We apply the EM method to jointly estimate the arrival rate of customers and the pmf of the rank-based choice model, and show that it leads to a remarkably simple and highly efficient estimation procedure. All limit points of the procedure are provably stationary points of the associated incomplete data log-likelihood function, and the output produced are maximum likelihood estimates (MLEs). Our numerical experiments confirm the practical potential of the proposal. The online appendix is available at https://doi.org/10.1287/opre.2016.1559 .