Mixed Logit: An Overview with Applications
by Kenneth Train

Mixed logits provide a highly flexible and easily estimated 
generalization to standard logit. We describe their properties 
and estimation, illustrating the concepts with two applications
-- one with cross-sectional data on vehicle choice and the other 
with panel data on recreation demand. We describe user-friendly, 
free software that is available for estimation and forecasting. 
Among the results, we show that any random utility model can be 
approximated arbitrarily closely by a mixed logit, and we use this 
concept to motivate the specifications in the two applications. 
Statistical tests of the mixing distribution are described and 
applied. Using Monte Carlo methods, the accuracy of the mixed 
logit simulator is compared with the GHK probit simulator; we
find that the mixed logit simulator is more accurate for 
a given amount of computer time while the GHK probit simulator 
is more accurate for a given number of draws. The substitution 
patterns and willingness-to-pay estimates from mixed logits are 
compared with those for standard logits. The substitution 
patterns are found to be far more realistic with a mixed logit, 
and the estimates of willingness-to-pay are similar to those 
obtained with standard logit.