Designed Quadrature to Approximate Integrals in Maximum Simulated Likelihood Estimation

摘要: Maximum simulated likelihood estimation of mixed multinomial logit (MMNL) or probit models requires evaluation a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as shuffled and scrambled Halton sequences modified Latin hypercube sampling (MLHS) are workhorse for integral approximation. A few earlier studies explored the potential sparse grid quadrature (SGQ), but this approximation suffers from negative weights. As an alternative to QMC SGQ, we looked into recently developed designed (DQ) method. DQ fewer nodes get same level accuracy is easy implement, ensures positivity weights, can be created on any general polynomial spaces. We benchmarked against in Monte study under different data generating processes with varying number random parameters (3, 5, 10) variance-covariance structures (diagonal full). Whereas significantly outperformed diagonal scenario, it could also achieve better model fit recover true (i.e., relatively lower computation time) full scenario. Finally, evaluated performance case understand preferences mobility-on-demand services New York City. In estimating MMNL five parameters, achieved statistical significance just 200 compared 1000 draws, making around times faster than methods.