Abstract
In this paper we discussed the estimation of choice model with correlation and/or heteroscedasticity across alternatives when the number of alternatives was large. We examined the performance of randomly drawn choice set approach and Poisson regression approach. We designed 6 Monte Carlo experiments. 1000 observations with 30 alternatives each were generated for each experiment. We found that the randomly drawn choice set approach is only applicable to independent and homoscedastic alternatives. When there are correlated factors among alternatives, this approach can not get good fit for the correlated factors even when the number of draw is quite large. We proved theoretically and empirically that Poisson regression model can get the same estimates as some logit type models that showed heteroscedasticity and correlation across alternatives. Poisson regression model can also get estimates close to those of logit kernel model with less computing time.
