choice-metrics.com

Dear Professors and moderators,

I have some questions regarding choice experiment designs and the subsequent interpretation of the results.

Q1. Dummy VS Effects coding and interpretation
I understand from other forum discussions that effects and dummy coding are essentially substitutes and it shouldn’t affect the results. However, I would love to understand a bit more about what sort of interpretation we can do if we were to use effects/dummy coding. In addition, I do not have any information about the priors.

To better illustrate, here is also an example of how my ngene code looks like:
Design
;alts = alt1*, alt2*, neither
;rows = 24
;block = 3
;eff = (mnl,d)
;model:
U(alt1) = b0[0] +
b1.effects[0|0|0] * type [0,1,2,3] +
b2.effects[0|0|0] * carb [2.5,7.5,10,5] +
b3.effects[0] * fa[4,26] +
b4.effects[0|0|0] * sod[20,85,215,150] +
b5.effects[0] * pro[0,30] +
b6[0] * price[5,15,25,35]/
U(alt2) = b0[0] +
b1 * type +
b2 * carb +
b3 * fa +
b4 * sod +
b5 * pro +
b6 * price
$

Is it true that we cannot determine which of the base levels of my attributes (e.g., between type(3) and fa(26)) have greater overall impact on utility if dummy coding was used?


Q2. Interpretation of the “I want neither alternative 1 or 2” option.
I would like to check if my specifications for the design above makes sense. Would the design above (Q1) allow me to estimate a constant for the ‘Neither’ option and one of the constants for the alternatives during the analysis stage on nlogit?


Q3. Designs and Analysis
In general, is it still possible for us to change to a different coding scheme from what was used during the design stage (switch from effects to dummy and vice versa) at the analysis stage?
In the same vein, is it possible to estimate ASCs for alt1 and alt 2 if I specified the design in this manner instead:

…
U(alt1) = b1.effects[0|0|0] * type [0,1,2,3] +
b2.effects[0|0|0] * carb [2.5,7.5,10,5] +
b3.effects[0] * fa[4,26] +
b4.effects[0|0|0] * sod[20,85,215,150] +
b5.effects[0] * pro[0,30] +
b6[0] * price[5,15,25,35]/
U(alt2) = b1 * type +
b2 * carb +
b3 * fa +
b4 * sod +
b5 * pro +
b6 * price /
U(neither) = b0[0]
$

Thank you for this support channel and for your time taken to clarify my doubts!

Best,
Chloe

Q1
Dummy and effects coding only differ with respect to what you compare the estimated utilities to. With dummy coding you compare to the selected base level, whereas with effects coding you compare with respect to the average utility across all levels. You can always convert coefficients of dummy coded coefficients into coefficients for effects coded coefficients and vice versa, only the interpretation of the coefficients differs. If you want to do hypothesis testing where you compare an effect to the base level, then dummy coding is most useful. If you want to do hypothesis testing where you compare an effect to the average utility across all levels, then effects coding is useful. Interpreting dummy coding is easier and it is also easier to implement in model estimation in Biogeme and Apollo within the utility function, so most people will use dummy coding. For model estimation in Nlogit, I believe you need to do the coding outside Nlogit and then dummy and effects coding is the same effort.

For more information I refer to this article:
https://www.sciencedirect.com/science/article/pii/S1755534516300781

Note that you can only compare estimated utilities WITHIN EACH ATTRIBUTE, for example the relative contribution of Blue versus Green, but you cannot compare utilities across attributes, which is like saying Blue is more preferred than Mild symptoms, which does not make sense. So neither with dummy coding nor with effects coding should you make comparisons across attributes. With dummy coding, the base level is confounded with the constant, while with effects coding the constant can be interpreted separately.

Q2
If your alternatives alt1 and alt2 are unlabelled, then you would have:
U(alt1) = b0 + ...
U(alt2) = b0 + ...
U(neither) = 0
or:
U(alt1) = ...
U(alt2) = ...
U(neither) = b0
Both are the same, you can choose. In model estimation, you can add one more constant, either for alt1 or alt2, to account for left-to-right reading bias in a choice experiment.

Q3
Yes you can change the coding scheme later. You can optimise for dummy coding and later use effects coding or the other way around. You can optimise for dummy coding and estimate a linear effect. The data will be optimised for the coding that you assumed when generating an efficient design, but you can certainly use different coding schemes later on. The only impact may be on efficiency, since the design was optimised for a specific coding type and you may lose a bit of efficiency if you change the coding. But I would not worry about it too much.

Michiel