tailieunhanh - Train_Discrete Choice Methods with Simulation - Chapter 6

6 Mixed Logit Choice Probabilities Mixed logit is a highly flexible model that can approximate any random utility model (McFadden and Train, 2000). It obviates the three limitations of standard logit by allowing for random taste variation, unrestricted substitution patterns | P1 GEM IKJ CB495-06Drv P2 GEM IKJ QC GEM ABE CB495 Train KEY BOARDED T1 GEM August 20 2002 12 37 Char Count 0 6 Mixed Logit Choice Probabilities Mixed logit is a highly flexible model that can approximate any random utility model McFadden and Train 2000 . It obviates the three limitations of standard logit by allowing for random taste variation unrestricted substitution patterns and correlation in unobserved factors over time. Unlike probit it is not restricted to normal distributions. Its derivation is straightforward and simulation of its choice probabilities is computationally simple. Like probit the mixed logit model has been known for many years but has only become fully applicable since the advent of simulation. The first application of mixed logit was apparently the automobile demand models created jointly by Boyd and Mellman 1980 and Cardell and Dunbar 1980 . In these studies the explanatory variables did not vary over decision makers and the observed dependent variable was market shares rather than individual customers choices. As a result the computationally intensive integration that is inherent in mixed logit as explained later needed to be performed only once for the market as a whole rather than for each decision maker in a sample. Early applications on customer-level data such as Train et al. 1987a and Ben-Akiva et al. 1993 included only one or two dimensions of integration which could be calculated by quadrature. Improvements in computer speed and in our understanding of simulation methods have allowed the full power of mixed logits to be utilized. Among the studies to evidence this power are those by Bhat 1998a and Brownstone and Train 1999 on cross-sectional data and Erdem 1996 Revelt and Train 1998 and Bhat 2000 on panel data. The description in the current chapter draws heavily from Train 1999 . Mixed logit models can be derived under a variety of different behavioral specifications and each derivation provides a particular interpretation. .

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