Designed quadrature to approximate integrals in maximum simulated likelihood estimation

Summary Maximum simulated likelihood estimation of mixed multinomial logit models requires evaluation a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as Halton sequences and modified Latin hypercube sampling are workhorse for integral approximation. Earlier studies explored the potential sparse grid quadrature (SGQ), but SGQ 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 space. We benchmarked against in Monte empirical study. outperformed all considered scenarios, practice ready, has become method