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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)
colonus
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1 Answers1

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Anyway you would not be able to measure the effect of the "group" variable on people choices as there is no variability at the task-level (both alt_1 and alt_2 systematically take the same "group" value). Instead you will need to specify interaction effects between the "group" variable and "rating". This interaction effect will capture the marginal effect of moving from one reference level of "group" to another level on preferences for rating. This is what you try to do in mlogit with "rating:group" but your probably need to check that "group" is automatically converted into a factor variable - Otherwise you can manually crate dummy variables based on "group".

Nicolas K
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