Unrestricted Substitution Patterns
The mixed logit model can represent general substitution pattern because it does not exhibit logit's restrictive independence of irrelevant alternatives (IIA) property. The percentage change in the probability for one alternative given a percentage change in the mth attribute of another alternative is
where β m is the mth element of . It can be seen from this formula that "A ten-percent reduction for one alternative need not imply (as with logit) a ten-percent reduction in each other alternative." The relative percentages depend on correlation between the likelihood that respondent n will choose alternative i, L ni, and the likelihood that respondent n will choose alternative j, L nj, over various draws of β.
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