ApolloChoiceModelling forum

Dear Stephane and David,

I would like to ask you about alternative specific constants in unlabelled forms.

I saw some articles (e.g. Möser et al., 2019 in Journal of Choice Modeling) where the researcher estimated alternative specific constant value for two alternatives (they had 3 alternatives (A, B and opt-out), and they fixed the A alternative to zero and estimated the alternative speicific constant for B and opt-out).

However, I saw some articles and read that in unlabelled forms it is worth to estimate alternative specific constant values for only the choose (which contain A, B, C and other possibilities) and opt out options, one of which is kept at a fixed value (e.g. the choose option).

Which one is the best partice?

Thanks for your help!

Regards,
Peter

Peter

only differences in utility matter. If the ASCs are not random, then it makes no difference which ASC you normalise. The differences between them will remain the same

Stephane

I understand that, it doesn't matter which asc I keep fixed.

So, among the following two forms, just the first is the correct?

form 1:

asc_alt1
asc_alt2
asc_optout

fixed (asc_alt1)

U1= asc_alt1 +....
U2= asc_alt2 +....
Uoptout= asc_optout


form 2:

asc
asc_optout

fixed (asc)

U1= asc +....
U2= asc +....
Uoptout= asc_optout


So we cannot gather (alternatives-1) asc-s into one asc in unlabelled form? Do we have to estimate (alternatives-1) asc-s in each case?

Peter

whether the second is correct depends on what happens in your data. In theory, and this is a point that is misunderstood by many, you should always have a full set of ASCs. This is where the distinction that people make between "labelled" and "unlabelled" is not helpful. Random utility models are based on the assumption that the mean of the error terms is equal. This implies that any differences except for random noise between the alternatives are captured in the systematic part of utility. As it is almost never possible to do this, we estimate ASCs that capture the differences across alternatives in any factors that we have not captured through the systematic parts of utility, i.e. the explanatory variables. Of course, this is especially salient in so called "labelled" settings, but especially in stated choice (as opposed to real choice data), there are often effects of people reading from left to right or the design not being completely balanced, etc, etc.

So basically, my opinion is that analysts should always estimate a model with a full set of ASCs (of course with an appropriate normalisation). Then you can easily test whether there are differences in the ASCs. So in your case, specification 2 should only be used if in specification 1, there is no difference between the ASCs for the first two alternatives, i.e. if asc_alt2=0, given the constraint you have put in.

Hope this helps

Stephane

Thank you Stephane!

You helped a lot!

Regards,
Peter