Interactions and experimental design

[kimsauha]

Dear Ngene Team,

Thank you for the Ngene software and for developing this helpful user forum. I have a few questions about using interaction terms in Bayesian design. The above discussion topic is much more advanced than my questions, so I hope it is appropriate to post my questions under this thread. I tried my best to make sure my questions weren't already answered, but I may have overlooked some items, so please bare with me if there are any repeats.

My experimental design is unlabeled, characterized by two product alternatives and a no-buy alternative. I have completed my pre-test and am at the stage of generating my Bayesian design, using the following syntax:

design
;alts = Alt1*, Alt2*, Alt3
;rows = 16
;eff = (mnl,d, mean)
;block = 2
;bdraws = gauss(3)
;model:
U(Alt1) = b1.effects[[(n,0,0.13)|(n,0,0.16)]*loc[2,1,0]
+ b2.effects[(n,0.25,0.19)|(n,0,0.18)|(n,0,0.17)]*hops[3,2,1,0]
+ b3.effects[(n,0.17,0.09)]*org[1,0]
+ b4[(n,-0.12,0.03)]*price[6.99,9.99,10.99,12.99,16.99]
+ i4*loc.effects[2]*hops.effects[2]
+ i6*loc.effects[2]*hops.effects[3]/
U(Alt2) = b1.effects*loc
+ b2.effects*hops
+ b3.effects*org
+ b4*price
+ i4*loc.effects[2]*hops.effects[2]
+ i6*loc.effects[2]*hops.effects[3]/
U(Alt3) = b0[(n,-1.63,0.36)]$

My questions are as follows:

1) We did not design the pre-test CE with interaction terms. While I understand it would be ideal to have included the interaction terms in the pre-test design, is it okay to include them at this stage in the Bayesian design?
2) As you can see from the code, we included interaction terms for only certain levels of certain attributes, as those are the interactions that we feel pertain to our research question. Is this acceptable or is it necessary to include interaction terms for all levels of the desired attributes?
3) Depending on how many interaction terms we end up including, we may need to increase the number of rows and blocks to account for the increase in expected parameters. In the pre-test we had 16 rows across 2 blocks, but we may need to increase this for the Bayesian design if we significantly increase the number of interactions. Is that acceptable?

I hope the information provided and my questions are clear. Thank you in advance for your response.

Kim

[Michiel Bliemer]

Dear Kim,

I believe it is important to realise that as long as you collect a sufficiently large sample, and as long as there is enough variation in your design, then you should be able to estimate most models. Only if an attribute and an interaction are confounded perfectly you cannot estimate it, and this does not happen often. Including interaction effects in the design ensures that you will be able to estimate these parameters, but you will in most cases also be able to estimate many other interaction effects, especially if you design is sufficiently large.

You have 3 alternatives with 16 choice tasks, you that means you have 32 degrees of freedom, i.e. you will be able to estimate 32 parameters with the design. So far you are estimating far less parameters.

So answering your questions:

1) Yes that is fine

2) What you are doing is fine, you can only include a subset of interactions that you think are most important and optimise the design for those. That does not mean you cannot estimate other interaction effects (the design just does not optimise for that)

3) Yes that is fine, although I note above that I think you have a sufficient number of choice tasks, but increasing it does not hurt. Especially if you want to estimate mixed logit models (in which you estimate besides the mean also a standard deviation) you will need more degrees of freedom.

Michiel

[kimsauha]

Thank you for your quick response!