Mean-centering and opt-out option

[greenvanilla]

Dear all,

this is rather an analysis question than a choice design question, but as it is quite choice experiment-specific, maybe you could help me nevertheless?

I would like to use effects coding for my variables as I would like to avoid confounding with the opt-out option which I specified as effects-coded dummy variable.
So the product attribute levels are all zero for the opt-out option.
But I have a Price variable and I was thinking about using mean-centering/normalization for this one.
Now I am a bit confused because I am not sure whether to exclude the opt-out option (with zero price) from mean-centering or not.
This decision influences the Price opt-out variable's coefficient. If I include the zero value of the opt-out option, the opt-out coefficient does not change, but now the normalized Price is not zero anymore for the opt-out option. If I exclude the zero value of the opt-out option, the opt-out coefficient changes.
The Price coefficient remains the same in all three cases.

This question might be trivial but I'm currently really confused about which is the correct way.
Is mean-centering necessary/recommended at all in this case? It's some time ago that I read it somewhere, but I'm not really sure about it and I could not find anything related to mean-centering of the Price variable in DCEs.

Could anybody provide an idea on that?

Thanks a lot!

[Edit: I thought about it again and found that mean-centering without considering the opt-out option does not make sense, as then a new zero center is created with the effect that a low price is now a negative price and therefore better then the still zero-price opt-out option.]

[Michiel Bliemer]

I have not used mean-centering or normalization in discrete choice model estimation myself, I think that it is generally not necessary, the resulting behavioural model will be the same, the difference is in the interpretation of the coefficients. The same holds for dummy and effects coding, they both explain the same behaviour and lead to the same behavioural model, only the interpretation is different (in effects coding, all coefficients are relative to the mean, while in dummy coding all coefficients are relative to a specific base level). It has been shown that there it does not matter whether you use dummy or effects coding (I can provide a reference if you like).

I do not understand what you mean with the statement that you specified the opt-out option as an effects-coded dummy variable. An opt-out is an alternative and not an attribute, so I am not sure what you mean that you effects-coded it. The opt-out typically can be set to zero (i.e., it has no coefficients) and all other utilities are relative to the opt-out.

U(option 1) = a1 + b2 * X + b3 * Y ...
U(option 2) = a2 + b2 * X + b4 * Z + ...
U(opt-out) = 0

Michiel

[greenvanilla]

Dear Michiel,

Thanks a lot for clarification!

With respect to the opt-out option, I meant that I created a variable as an alternative-specific constant for the opt-out option instead of using alternative-specific constants for the product options. Meaning that this effects-coded opt-out variable is now 1 in the rows that reflect the opt-out alternative, and -1 otherwise.

In some other post you already provided me with the article by Daly et al. (2016) on the equivalence of dummy-coding and effects-coding, but I thought that in the case I have a variable indicating the opt-out option it might make sense to rather use effects-coding to make the coefficient of this opt-out variable better interpretable.

[Michiel Bliemer]

Yes it is true that depending on your study, certain types of coding make coefficients easier to interpret, so that could well be the case when using effects coding in which coefficients are interpreted as deviations from the mean.

Michiel