When the variation range of attribute independent variables is large in the Multinomial Logit (MNL) model, using the point elasticity value at the original value of the attribute independent variable to approximate the actual elasticity leads to a non-negligible first-order remainder error in the predicted change range of the choice probability. To address this issue, the first-order Lagrange remainder of the actual elasticity is derived based on the first-order Taylor formula of the mode choice probability function, and the maximum value and the extremum point of the absolute value of the first-order remainder are obtained. Then, given the error limit of the remainder-point elasticity ratio, within the neighborhood of the original value of the attribute independent variable, with the constraint that the upper limit of the absolute value of the first-order remainder-point elasticity ratio does not exceed the error limit, the analytical form of the applicable neighborhood for predicting the change range of the choice probability is systematically derived when using the own- and cross-point elasticity values to approximate the actual elasticity, which fully ensures the prediction accuracy of the change range of the choice probability. Finally, through numerical experiments, by taking three alternative modes of bus, car, and bicycle, and by using the bus fare as the attribute independent variable, the correctness of the theoretical derivation of the applicable neighborhood is verified.

在多项Logit (MNL)模型中, 属性自变量变动幅度较大情况下, 采用属性自变量原值处点弹性值近似实际弹性时, 预测选择概率变化幅度存在不可忽略的一阶余项误差。针对这一问题, 首先基于方式选择概率函数的一阶Taylor公式, 推导出实际弹性的一阶Lagrange余项, 并求得一阶余项绝对值的最大值及最值点; 然后在给定余项–点弹性比误差限的情况下, 在属性自变量原值邻域, 以一阶余项–点弹性比绝对值上限不超误差限为约束, 系统地推导出采用自身及交叉点弹性值近似实际弹性时, 预测选择概率变化幅度的适用邻域解析形式, 充分保证选择概率变化幅度的预测精度; 最后通过数值实验, 选取公交车、小汽车和自行车3种备选方式, 以公交票价为属性自变量, 验证了适用邻域理论推导的正确性。