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The simulated choice probabilities in Mixed Logit are approximated numerically from a multidimensional integral with a mixing distribution from a multivariate density function of the random parameters. Theoretically the order in which the variables are estimated should not matter; however, due to the inherent simulation ‘noise’ the magnitude of the estimated coefficients differs depending on the arbitrarily selected order in which the random variables enter the estimation procedure. This problem is exacerbated with a low number of draws or if correlation among coefficients is allowed. If correlation among the random parameters is allowed the variable ordering effects arise from simulation noise and from the Cholesky factorization used to allow for correlation. Ignoring the potential ordering effects in simulated maximum likelihood estimation methods seriously compromises the ability for replicating the results and can inadvertently influence policy recommendations. The simulation noise is independent of the number of integrating dimensions for random draws, but it increases for Halton draws. Hence, better coverage is achieved with Halton draws for small integrating dimensions, but random draws provide better coverage for larger dimensions.


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