The use of heuristic optimization algorithms to facilitate maximum simulated likelihood estimation of random parameter logit models

The maximum simulated likelihood estimation of random parameter logit models is now commonplace in various areas of economics. Since these models have non-concave simulated likelihood functions with potentially many optima, the selection of "good" starting values is crucial for avoiding a false solution at an inferior optimum. But little guidance exists on how to obtain "good" starting values. We advance an estimation strategy which makes joint use of heuristic global search routines and conventional gradient-based algorithms. The central idea is to use heuristic routines to locate a starting point which is likely to be close to the global maximum, and then to use gradient-based algorithms to refine this point further to a local maximum which stands a good chance of being the global maximum. In the context of a random parameter logit model featuring both scale and coefficient heterogeneity (GMNL), we apply this strategy as well as the conventional strategy of starting from estimated special cases of the final model. The results from several empirical datasets suggest that the heuristically assisted strategy is often capable of finding a solution which is better than the best that we have found using the conventional strategy. The results also suggest, however, that the configuration of the heuristic routines that leads to the best solution is likely to vary somewhat from application to application.