MSL for Mixed Logit Model Estimation - On Shape of Distributions
M V Sørensen, O A Nielsen, CTT, Technical University of Denmark, DK
The use of Mixed Logit models (or Hybrid Logit) has grown rapidly during the past five years as research has demonstrated the applicability of the model and especially the software/purpose specific code has become available. In general, the method of Maximum Simulated Likelihood (MSL) is applied, although this only optimises the parameters of the a priori assumed distribution of the distributed terms. Only few of the analyses so far, has dealt with the interesting question of which distributions to apply. And the distribution to be assumed for the coefficients is generally assumed prior to the estimation.
This paper describes a study of extensive model estimations on synthetic data with known distribution. Several different distributions and combinations of distributions have been tested. These included fixed coefficients, normal distributed random coefficients, lognormal distributed random coefficients, bi-modal distributed random coefficients and combinations hereof (e.g. one normal and one lognormal distributed random coefficients), and finally, a normal disturbance added in addition to the Gumbel residual.
The correct distribution did come out as significant in a MSL testing. However, in several cases other distributions did turn out to be significant.
The paper will conclude with guidelines on how to include error components in demand estimation and how to compare models that only differ in assumed distribution of the random coefficients.
Association for European Transport