No interaction term in design but like to do in analysis?

[Lily820]

Dear Ngene team,

I have done a D-efficient design using Ngene for my study and I am doing data analysis part.

One question: if I did not specify interaction terms in my utility function used for experimental design, can I still include the interaction terms in MNL models? Any mistake or possible problems by doing so? The interaction terms I mean here is the interaction terms between any two of the independent variables in utility function, but not the personal characteristics such as age, gender etc.

Thanks for your time and help.

Cheers
Lily

[Michiel Bliemer]

In most cases this will be possible yes, as long as there is enough variation in your data/design.

In some cases, the interaction term may be perfectly correlated with one of the other attributes, which would prevent estimating the parameter related to interaction effects. In that case the estimation software will give an error and state that some parameters are not identifiable. This is unlikely to be the case, so if your estimation software generates a result, you know it is fine.

You can test by looking at the correlations in your data. You can create an additional column in your data for the interaction effect and then ask Excel to calculate the correlations. If the interaction column is not perfectly correlated with another attribute/column (i.e., as long as the correlation is not +1 or -1), then all is fine.

Michiel

[johnr]

Hi Lily

As Michiel stated, generally this is not a problem. As pointed out, the main reason it may be a problem is due to near perfect correlations, however again, this generally will not be an issue in most cases. It can be an issue if you are dealing with interactions involving dummy codes. This is because you can end up with lots of zeros in your interaction, which in effect results in a sparse matrix, where for the interaction you have only a few 1s in the column. If you are not interacting dummy codes, this issue will not arise however so is not a concern.

John

[Michiel Bliemer]

You can also check in Ngene whether the interaction is an issue or not. You can use the ;eval command to evaluate your existing design, where you can add the interaction in the utility function(s). If Ngene provides a D-error then it is fine. If Ngene states that the D-error is undefined, then there are identification issues.

Michiel