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I’m using DCE with unlabelled alternatives, 9 choice set with 3 alternative each (2 option and Optout alternative), described with 4 attributes.

I've started with a conditional logit (with only alternative specific constants).

mydata$ASC<-ifelse(mydata$alt==3, 1, 0)#To create the ASC for the optout alternative.
mydata<-mlogit.data(mydata,choice = 'Y', shape = 'long',varying = c(5:8,48), 
                     id.var = 'Indiv', chid.var = 'CASE', alt.var = 'alt')#To prepare the data for mlogit.
CLM<-mlogit(Y~ 0+ ASC+ x1+x2+x3+ x4, data=Tlemcen)

Then, I wanted to add individual specific variables (characteristics of decision makers). Since alternatives are unlabelled, I use interaction between alternative and individual specific variables. 

mydata$gender.f<-as.factor(mydata$gender)#define gender as factor variable.
MNL<-mlogit(Y~ 0+ x1+x2+x3+ x4+x1:gender.f+x2:gender.f+ x3:gender.f+ x4:gender.f, data=mydata)

I have notice however, that the parameters estimate of the attributes variables change when I add those interactions.

enter image description here

So I have some questions:

-Why does estimates parameters of my attributes change when I add an interaction to the model, and how to interprete those parameters ?

Lizzie001
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  • Welcome to CV. This is too many questions for one post. The good news is that they are all answered elsewhere here: please search our site for threads about interactions and significance. – whuber Jan 17 '20 at 18:57
  • Questions already asked are focused on labelled alternative, I have modified the question to be more accurate @whuber – Lizzie001 Jan 17 '20 at 21:10

1 Answers1

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The main effects in a model that includes an interaction have a different meaning than in a model that does not include an interaction.

Without an interaction, a main effect can be interpreted as the association of a 1 unit change (or of the difference with respect to the reference level with a categorical variable) with the response/outcome variable, while the other variables remain unchanged.

When an interaction is present, the same logic applies, but it is impossible for the interaction to remain constant while one of the variables that is part of the interaction changes, unless the other variable that is part of the interaction is zero. Hence the main effect of one variable is the association of a 1 unit change in that variable with the response when the other main effect is zero (or at it's reference level in the case of a categorical variable. This often does not make sense (for example if one of the variables is height, it makes no sense to interpret other variables when height is zero since a person't height can never be zero. Therefore it is common for variables to be centered around their main if it is going to be part of an interaction.

Robert Long
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  • Thank you very much ,now it makes sense, It is possible to use a nested logit model instead ? with a nest for the opt-out and a another for the other alternatives ? @Robert Long – Lizzie001 Jan 28 '20 at 09:17