Interaction Terms and Logit Models I have read the previous discussions on interaction effects and main effects, and I have a question on the subject.
I am running a destination choice model (multinomial logit), and I have one continuous variable (distance in meters) and several dummy variables accounting for given behavior (main activity at destination) which I am hypothesizing as having an interaction effect. 
In this particular model, the effect of Distance is as expected significant by itself, and also are significant the interactions between Distance and the dummy variables, 
however, when I try to include the dummy variables alone to get their main effects, the model cannot be estimated even after including only one dummy variable. I illustrate this below:


*

*Distance+Distance*Dummy2+Distance*Dummy3 = Significant main and interaction effects (s.e. of interaction not estimated)  

*Distance*Dummy2+Distance*Dummy3 = Significant interaction effects  

*Distance+Dummy1+Dummy2 = Model cant be estimated  

*Distance+Dummy1+Dummy2+Distance*Dummy2+Distance*Dummy3 = Model cant be estimated  


So my question would be:
 1. if it is possible to account only for the interaction terms without the main effects given what I explained before? 
 A: In any discrete choice model, there are two types of variables: those that vary across the alternatives, and those that are constant for each decision maker. The first become generic coefficients, and the second are alternative-specific. There is one generic $\beta$ that is the same for all alternatives, but each alternative has its own alternative-specific $\beta$. So for $J$ alternatives, each alternative-specific variable creates $J-1$ parameters.
In a typical discrete choice model, this isn't a problem. But a residential location choice model usually has $J$ somewhere near 1000. It is impractical to consider 999 different parameters for a single variable. This is why variables that do not vary across alternatives (like a person's income) are usually interacted with variables that do (like the average cost of a home in each zone). In standard econometrics, we typically include the non-interacted components to separate correlation between income and home price as much as possible. But in your problem, you don't really have a choice.
