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I have one question concerning the mlogit command in Stata and/or R. In the model I’m working on the individuals don’t face the same choice set each other; for example I have 10 alternatives but for some customers the choice set is reduced to 8. Is it possible to take this into account when I use mlogit? Thank you very much for your attention

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Use MNP. For implementation see this question:

If the choice set varies from one observation to another, use the syntax, cbind(y1, y2, y3) ~ x1 + x2, in the case of a three choice problem, and indicate unavailable alternatives by NA. If only the most preferred choice is observed, y1, y2, and y3 are indicator variables that take on the value one for individuals who prefer that choice and zero otherwise. The last column of the response matrix, y3 in this particular example syntax, is used as the base category.