Discrete Choice Model with Alternative-Specific Variables that do not vary across individuals

[tortillita de camarones]

Hello all,

I got a dataset with different choices for several individuals. I also have different individual characteristics, as well as alternative specific characteristics. The problem is that these alternative-specific characteristics do not vary across individuals, so I cannot include them in conditional logit models (asclogit command in Stata).

My question is: do a discrete choice model allowing alternative-specific variables that do not vary across individuals exist?

For helping the case, this is an example of the dataset i have:

id chosen alternative alternative_price gender income
1 0 1 10 1 500
1 1 2 20 1 500
1 0 3 30 1 500
2 1 1 10 0 750
2 0 2 20 0 750
2 0 3 30 0 750
3 0 1 10 0 250
3 0 2 20 0 250
3 1 3 30 0 250

Where id is an individual identifier; chosen =1 when individual i chooses that alternative; alternative_price is the price of each alternative (look is the same for every individual); gender is 1 if the individual is a woman 0 otherwise; and income is individual income (note that varies across individuals but not within individuals).

Thank you very much.
Best

[Hong Il Yoo]

In your example, price is perfectly colinear with alternative-specific constants (ASCs) so without making further assumptions you can't disentangle ASCs from the price coefficient. You can include (1) one ASC and the price variable or (2) two ASCs and no price variable. But both model specifications are simple reparameterizations of each other and substantively the same: one is just as good (or bad) as the other.

If your data comes from an unlabelled choice experiment, you may use that feature of your experiment as the identifying assumption: you can estimate a model with the price variable and no ASC.