论文标题
在最大模拟的可能性估计中设计了正交到近似积分的正交
Designed Quadrature to Approximate Integrals in Maximum Simulated Likelihood Estimation
论文作者
论文摘要
混合多项式logit（MMNL）或概率模型的最大模拟可能性估计需要评估多维积分。准蒙特卡（QMC）方法，例如洗牌和炒烈孔序列和修改的拉丁高立方体采样（MLHS）是用于积分近似的主力方法。一些较早的研究探讨了稀疏的网格正交（SGQ）的潜力，但是这种近似遭受了负重。作为QMC和SGQ的替代方法，我们研究了最近开发的设计正交（DQ）方法。 DQ需要更少的节点才能获得与QMC和SGQ相同的准确性，它易于实现，确保权重阳性，并且可以在任何一般的多项式空间上创建。在蒙特卡洛研究中，我们在不同的数据生成过程中对QMC进行了基准测试，并具有不同的随机参数（3、5和10）和方差 - 稳定性结构（对角线和完整）。尽管DQ在对角线方差互动方案中显着优于QMC，但它也可以实现更好的模型拟合度，并在完整的方差 - 协方差方案中恢复具有更少的节点（即相对较低的计算时间）的真实参数。最后，我们在案例研究中评估了DQ的表现，以了解纽约市移动性服务的偏好。在用五个随机参数估算MMNL时，DQ获得了更好的拟合度和仅200个节点的参数的统计学意义，而1000 QMC绘制的参数则比QMC方法快五倍。
Maximum simulated likelihood estimation of mixed multinomial logit (MMNL) or probit models requires evaluation of a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as shuffled and scrambled Halton sequences and modified Latin hypercube sampling (MLHS) are workhorse methods for integral approximation. A few earlier studies explored the potential of sparse grid quadrature (SGQ), but this approximation suffers from negative weights. As an alternative to QMC and SGQ, we looked into the recently developed designed quadrature (DQ) method. DQ requires fewer nodes to get the same level of accuracy as of QMC and SGQ, is as easy to implement, ensures positivity of weights, and can be created on any general polynomial spaces. We benchmarked DQ against QMC in a Monte Carlo study under different data generating processes with a varying number of random parameters (3, 5, and 10) and variance-covariance structures (diagonal and full). Whereas DQ significantly outperformed QMC in the diagonal variance-covariance scenario, it could also achieve a better model fit and recover true parameters with fewer nodes (i.e., relatively lower computation time) in the full variance-covariance scenario. Finally, we evaluated the performance of DQ in a case study to understand preferences for mobility-on-demand services in New York City. In estimating MMNL with five random parameters, DQ achieved better fit and statistical significance of parameters with just 200 nodes as compared to 1000 QMC draws, making DQ around five times faster than QMC methods.
