Marginal Effects of interaction when main effect insignificant

[Ellen Sterk]

Dear all,

I conducted an unlabelled discrete choice experiment and use a mixed logit model (using the command cmxtmixlogit) to analyze it. Now I added an interaction term between an alternative-specific attribute and an individual characteristic. Doing that turns the main affect of the alternative-specific attribute insignificant. My question is whether it still makes sense to calculate the effect of that individual characteristic on the probability of choosing, since I use the coefficient of the (insignificant) main effect of the alternative-specific attribute in that calculation.

I hope I managed to explain my issue clearly enough. Thank you in advance for any help!

[Hong Il Yoo]

Ellen Sterk I don't see anything wrong with including the insignificant main effect coefficient. Not directly relevant to your question but another two cents: You may want to pay closer attention to the implications of the way you have coded your "individual characteristic" before saying something about the insignificant main effect. If the individual characteristic is a dummy variable (e.g., 1 for women vs 0 for men), an insignificant main effect suggests something potentially interesting (e.g., men's utilities do not respond to variation in that attribute). If the individual characteristic is something like the person's age in years (e.g., 45 for 45 year olds), however, whether the main effect is significant or not is much less interesting because the main effect measures how the 0-year old's utility function responds to variation in that attribute (I assume that your study is not about the newborn's behavior).

[Ellen Sterk]

Hong Il Yoo Again, thanks a lot for your response!
Your addition is in fact very useful, since some of my characteristics are indeed dummy variables (and the continuous ones also are interpretable with a value of 0). That's a great addition to my interpretation of results. Thank you!