Mixed logit

Mixed logit is a fully general statistical model for examining discrete choices. It overcomes three important limitations of the standard logit model by allowing for random taste variation across choosers, unrestricted substitution patterns across choices, and correlation in unobserved factors over time.^[1] Mixed logit can choose any distribution $f$ for the random coefficients, unlike probit which is limited to the normal distribution. It is called "mixed logit" because the choice probability is a mixture of logits, with $f$ as the mixing distribution.^[2] It has been shown that a mixed logit model can approximate to any degree of accuracy any true random utility model of discrete choice, given appropriate specification of variables and the coefficient distribution.^[3]

^ Train, K. (2003) Discrete Choice Methods with Simulation
^ Hensher, David A. & William H. Greene (2003). "The Mixed Logit Model: The State of Practice," Transportation, Vol. 30, pp. 133–176, at p. 135.
^ McFadden, D. and Train, K. (2000). “Mixed MNL Models for Discrete Response,” Journal of Applied Econometrics, Vol. 15, No. 5, pp. 447-470.

[dca-1] Train, K. (2003) Discrete Choice Methods with Simulation

[2] Hensher, David A. & William H. Greene (2003). "The Mixed Logit Model: The State of Practice," Transportation, Vol. 30, pp. 133–176, at p. 135.

[mt-mnl-3] McFadden, D. and Train, K. (2000). “Mixed MNL Models for Discrete Response,” Journal of Applied Econometrics, Vol. 15, No. 5, pp. 447-470.

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