Collinearity in Labeled Choice Experiment

[mdanne]

Dear all,

please imagine the following labeled choice design for credits in developing countries:
- alternatives credit house bank, credit online bank
- attribute travelling distance:
--> for house bank the levels are: 5,10,15 kilometers
--> for online bank the levels are: 0.5 and 1 kilometer (because in developing countries the access point for internet is not per se in the household)

Is it possible to design such experiment where the levels for the same attribute are totally different between the alternatives? Or is there an issue about collinearity between the constants of the alternative and the attribute coefficient as for example 1 kilometer occurs only for alternative online bank and 10 km only for the house bank?

Thank you in advance, best regards,
Michael

[Michiel Bliemer]

Yes that is no problem, you can use different attribute levels for different alternatives and you can use a generic or alternative-specific coefficient for distance. Only when one of the labels would have a fixed distance (e.g., always 1km for online bank) then this attribute level would be confounded with the aternative-specifc constant.

Michiel

[mdanne]

Thank you Michiel,

can you justify this with statistical arguments? I have to answer a reviewer who says that this is not possible without causing collinarity.

Best regards,
Michael

[Michiel Bliemer]

It is a matter of parameter identifiability, there is no reason why there would be collinearity (unless you are using dummy or effects coding). If there exists collinearity, then you would not be able to estimate the constant and the D-error of the design would be infinite.
Using different attribute levels across alternatives is very common in labelled experiments, so I am not sure why the reviewer is of this opinion.

Below and example that shows that the D-error of this model is finite, therefore all parameters are identifiable and there is no collinearity (you can check in Ngene if you open a design and look at the covariance matrix; there are no perfectly correlated parameters.

Code: Select all

design
;alts = housebank, onlinebank
;rows = 12
;eff = (mnl,d)
;con
;model:
U(housebank)  = housebank
              + dist * DISTANCE_H[5,10,15]
              + fee  * FEE[1,2,3]
              /
U(onlinebank) = dist * DISTANCE_O[0.5,1]
              + fee  * FEE[1,2,3]
$

Michiel

[mdanne]

Thank you very much.

So after collecting data, how can I estimate the coefficient for travelling distance digital when it is not allowed to use dummy or effects coding?

[Michiel Bliemer]

Dummy of effects coding is typically only used for qualitative variable, not for quantative variables like distance. I would never use dummy / effects coding for quantitative variables as it increases the number of parameters, it does not allow you to use the model for forecasting with levels that differ from the ones assumed in the experiment, and it makes computing WTP and elasticities more difficult. Further, if you use dummy coding, the constant will be confounded with the base dummy level.

One would simply use beta * distance in the utility function, or if you want a nonlinear effect, something like beta * log(distance) or beta * distance^2.

Michiel