efficient design with interaction effects

[izakro]

Hi all,

I obtained pilot results for a labeled design aimed at choosing either a circular washing machine (i.e. recovered or secondhand) or brand new. Only two atts. are included.
I suspect there might be an interaction between the ASC of (for example) the recovered machine and its durability (or recyclability) levels.
How do I introduce an interaction effects between an ASC and an att.? is this even possible?
This is the final design:
Design
;alts = New, recovered ,secondhand
;rows=15
;block=5
;eff=(mnl,d)
;bdraws = halton(200)
;model:
U(New)=b1[0.0001]+b2[(n, -0.009,0.001)]*cost[1600,1900,2200]+b3[(n, 0.313, 0.050)]*durability[4,8,12]+b4[(n, 0.130, 0.06)]*recyclability[1,2,3,4,5]/
U(recovered)=b2*costR[900,1100,1300]+b3*durability+b4*recyclability/
U(secondhand)=c1[-0.001]+b2*costSH[1300,1600,1900]+b3*durability+b4*recyclability$

Thanks!
R.

[Michiel Bliemer]

An interaction between an attribute and an ASC simply becomes a main effect. You already included durability and recyclability as main effects, adding it again does not make sense. You can interact durability with recyclability but not with the ASC.

I am a bit worried about your priors. Value -0.009 for b2 is too large for such large cost levels, it would make cost a completely dominant attribute. Also 0.313 is quite large with respect to the durability levels. Further, if you use informative priors for b2, b3, and b4, you should also use informative priors for ASCs b1 and c1, but both are near-zero. How did you determine these priors? They should preferably come from a model that was estimated in a pilot study. If no prior information is available, consider using zero priors. Manually setting too large priors may result in INefficient designs.

Michiel

[izakro]

As always, your answers are so helpful and prompt Michiel.
I understand your answer regarding interaction with the ACS.
Regarding the high cost prior, it is great that you noticed that! The pilot was taken in Germany and the price levels were in Euros!. We ran it now in Israel and Israeli shekels 3.5 times lower.
The ACS are mistakes (should be ~3 for the new machines and ~(-1 ) for the new machine made of recovered materials.

If I would be interested in adding interaction effects between, say, durability and recyclability, would it look like this? (assuming the interactions may differently affect the probability to choose each machine)
Design
;alts = New, recovered ,secondhand
;rows=15
;block=5
;eff=(mnl,d)
;bdraws = halton(200)
;model:
U(New)=b1[(n, 3.1, 1.2)]+b2[(n, -0.009,0.001)]*cost[460,542,629]+b3[(n, 0.313, 0.050)]*durability[4,8,12]+b4[(n, 0.130, 0.06)]*recyclability[1,2,3,4,5]+i1*durability*recyclability/
U(recovered)=b2*costR[257,314,371]+b3*durability+b4*recyclability+i2*durability*recyclability/
U(secondhand)=c1[(n,-1.5,0.4)]+b2*costSH[371,460,542]+b3*durability+b4*recyclability+i3*durability*recyclability$

Best
Anat

[Michiel Bliemer]

Yes that is how you could add interaction effects for numerical attributes (for categorical attributes using dummy/effects coding it would be somewhat different).

Michiel