Global maximum likelihood estimation procedure for multinomial probit (MNP) model parameters

This paper presents a procedure, named GAMNP, incorporating genetic algorithms (GAs) and non-linear programming (NLP) techniques to find the `global' maximum likelihood estimate (MLE) in multinomial probit (MNP) model estimation. The GAMNP estimation procedure uses GAs to search for `good' starting points systematically and globally through the possible solution areas that satisfy the property of positive definite variance-covariance matrix: the NLP algorithm is then used to fine-tune the solutions obtained from the GAs procedure. A numerical experiment was conducted to test the performance of the GAMNP estimation procedure based on an artificial data set with known parameter values, model specification, and error structure. The log-likelihood function value, parameter accuracy measures, and the CPU execution time were adopted as performance measures in this experiment. The experimental results indicated that the GAMNP estimation procedure is able to find the global MLE in MNP model estimation when the analyst does not have a priori expectations of the magnitudes of the parameters. The highlight, the importance of using systematic starting solution search procedures, like those used in genetic algorithms, instead of selecting starting solutions arbitrarily.