[R] Modeling Binary x Binary Interactions with mlogit (and interpretation)

[Marcel Gerds]

Dear R community,

I am using the mlogit package to analyze discrete choice data. Apart 
from a main effects model, I want to estimate interactions between the 
attributes of the choice set (e.g. the existence of a certain attribute) 
and some subject-specific data (like gender or income).
Studying the mlogit documentation, I found no hint on how to do it. In 
the literature there is only the case discussed how alternative-specific 
variables can be combined. In my case, the alternatives are of no 
interest, meaning I am using a purely generic model.
So far, I tried to model these interactions by simple multiplying the 
variables.

Example:
mlogit.model <- mlogit(CHOICE ~ ATR1+ATR2+ATR3 + ATR1*GENDER + 
ATR1*GENDER + ATR1*GENDER| -1, data=data_ml)

Here, gender is subject-specific.

I get results like the following:

---
Coefficients :
                                            Estimate
ATR1_yes                          0.779116
ATR2_ yes                         2.257905
ATR3_ yes                        1.141625
GENDERfem                     -14.026649
ATR1_yes :GENDERfem     0.094709
ATR2_ yes:GENDERfem    -0.076223
ATR3_ yes:GENDERfem    0.117373
---

I present only the coefficients here. However, when I change the 
reference level to male, the coefficients of the interactions effects 
just change sign.

I have two questions in this regard:

1.) Is the modeling of such interactions effect feasible in the mlogit 
setting?
2.) I have some problem understanding the changing sign of the 
coefficients when I change the reference level. This would imply that 
females always prefer the opposite of males. Clearly, this cannot be. I 
imagine that I am misinterpreting this issue and I would be grateful for 
any help on this.

Best regards,
Marcel

-- 
Marcel Gerds, M.Sc.
University of California
Department of Agricultural and Resource Economics
233 Giannini Hall
Berkeley, CA 94720

Tel.:  +1 510-643-2202
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E-Mail: marcel.gerds at berkeley.edu
web:    www.marcel-gerds.de