# interaction with a mixed logistic regression using mlogit on choice data

What is the best way to analyse interactions in choice data between an individual specific variable and an alternative specific variable?

I have designed a discrete choice experiment in which participants are asked to make several dichotomous choices (4 choice sets per participant) between different optione (air conditioners). Each options has two varrying attributes: price and energy star rating. The attributes are randomly drawn from a preset distribution. Furthermore, participants receive framed messages (2 framed message groups plus control group: eg. money: "save money with more energy stars" and impress: "impress with more energy stars"). These varry randomly between-participants and are displayed above each choice set. The reference group for the group variable is the "control" group.

The data-frame is cleaned and has the following format:

##  id   instance   alt    group     price   rating    choice
#    1          1     1    impress     600        3         1
#    1          1     2    impress     450        2         0
#    1          2     1    impress     500        2         0
#    1          2     2    impress     650        4         1
#    1          3     1    impress     700        5         0
#    1          3     2    impress     550        4         1
#    1          4     1    impress     560        4         1
#    1          4     2    impress     580        4         0
#    2          1     1    money       300        1         1
#    2          1     2    money       450        2         0
#    2          2     1    money       600        4         1
#    2          2     2    money       550        3         0
#  ...
#    3          1     1    control     500        2         0
#    3          1     2    control     650        3         1
#    3          2     1    control     400        2         1
#    3          2     2    control     550        3         0
#  ...
#    4          1     1    money       500        2         0
#    4          1     2    money       650        3         1
#    4          2     1    money       400        2         1
#    4          2     2    money       550        3         0
#  ...


I am manly interested in the interaction effect of the group variable with the rating variable. Since the choice options are unlabelled and attributes are randomly drawn, I am not interested in the main effects of the group variable. I was planning on using the mlogit() function, but have not found anything on how to model the interaction.

Would the following be the correct way to proceed?

library(mlogit)
dce_df <- mlogit.data(dce, choice = "choice", shape = "long", alt.var = "alt", id.var = "id")
m <- mlogit(choice ~ price + rating + rating:group, data = dce_df)