This work concerns the estimation of recursive route choice models in the situation that the trip observations are incomplete, i.e., there are unconnected links (or nodes) in the observations. A direct approach to handle this issue could be intractable because enumerating all paths between unconnected links (or nodes) in a real network is typically not possible. We exploit an expectation–maximization (EM) method that allows dealing with the missing-data issue by alternatively performing two steps of sampling the missing segments in the observations and solving maximum likelihood estimation problems. Moreover, observing that the EM method could be expensive, we propose a new estimation method based on the idea that the choice probabilities of unconnected link observations can be exactly computed by solving systems of linear equations. We further design a new algorithm, called decomposition–composition (DC), that helps reduce the number of systems of linear equations to be solved and speed up the estimation. We compare our proposed algorithms with some standard baselines using a dataset from a real network, and show that the DC algorithm outperforms the other approaches in recovering missing information in the observations. Our methods work with most of the recursive route choice models proposed in the literature, including the recursive logit, nested recursive logit, or discounted recursive models.

这项工作涉及在行程观察不完整的情况下递归路径选择模型的估计，即观察中存在未连接的链接（或节点）。处理此问题的直接方法可能很棘手，因为枚举真实网络中未连接的链接（或节点）之间的所有路径通常是不可能的。我们利用期望最大化(EM) 方法，该方法允许通过交替执行对观察中的缺失部分进行采样和解决最大似然估计问题的两个步骤来处理缺失数据问题。此外，观察到 EM 方法可能很昂贵，我们提出了一种新的估计方法，该方法基于可以通过求解线性方程组来精确计算未连接链接观测值的选择概率的想法。我们进一步设计了一种新的算法，称为分解-合成(DC)，这有助于减少要求解的线性方程组的数量并加快估计速度。我们使用来自真实网络的数据集将我们提出的算法与一些标准基线进行比较，并表明 DC 算法在恢复观察中丢失的信息方面优于其他方法。我们的方法适用于文献中提出的大多数递归路径选择模型，包括递归逻辑、嵌套递归逻辑或折扣递归模型。