Optout with no attributes' levels

[Anat Tchetchik]

Hi All,
We have a design in which each respondents received two type of labelled choice tasks:
1. Buying washing machine: 3 menus in which respondents had to choose which washing machine to buy (brand new, 2nd hand, or  recycled)
2. Leasing washing machine: 3 menus in which respondents had to choose which washing machine to lease (brand new, second hand, recycled)- or optout   i.e. not interesting in leasing.
The other attributes are the same for both tasks (buying/leasing); e.g. payment, warranty period, and recyclability at end of life..

When estimating the leasing data (via mixed logit) the optout has no attributes levels (only the ASC), thus, estimation of the model with the optout is impossible. 
How should this fact be addressed? 

Best,
Anat   

[Michiel Bliemer]

I am not sure why estimation is impossible?

Utility functions:

U(buying) = asc1 + b1 * ...
U(leasing) = asc2 + b1 *
U(optout) = 0

You can have 2 constants with three labelled alternatives. The above model parameters should all be identifiable.

Michiel

[Anat Tchetchik]

Thanks Michiel,
I wasn't clear enough, sorry, there were two consequent choice tasks
the first choice task (buying only) present no problem, has no optout
U(buying_new) = asc1 + b1 *
U(buying_2nd_hand) = asc2 + b1 *
U(buying_recyclable) = b1*

The second choice task (leasing only+optout) is the one that bothers me, assuming that these are the utility functions:
For the optout alternative, x1 and x2 are empty observations, since they are not really zeros.. (optout here, means choosing to buy and rather than lease)
in that case Stata treats them as missing observations..

U(leasing_new) = asc1 + b1* x1+b2*x2
U(leasing_2nd_hand) = asc2 + b1 *x1+b2*x2
U(leasing_recyclable) = asc3+ b1* x1*b2*x2
U(optout)= 0 +b1* x1*b2*x2

[Michiel Bliemer]

If an optout has levels then it is not an optout alternative but rather a status quo alternative.

A status quo alternative has fixed attribute levels, which you can set within the syntax directly for continuous attributes or via constraints for dummy/effects coded attributes. If the status quo is choosing to buy, then it must have a price level etc, not?

Michiel

[Anat Tchetchik]

I now realize that the design was bad. We ask respondents which machine out of 3 they would buy - (new, made of recyclable materials or 2nd hand) and then we told them to assume that they can lease instead of buying and gave them 3 leasing options plus a 'not-interested in leasing' which is an opt-out.. but in fact that could be interpreted as a preference to buy. yet no levels where attached to this option.. seems like an unsolvable problem..

[Michiel Bliemer]

Yes I have seen this more often where the optout alternative is unclear.

The best way to deal with this at this stage is to assume only a constant for this alternative and make this constant random (essentially an error component mixed logit model), i.e. in estimation you assume a normally distributed constant where you estimate the mean and stdev.

Michiel

[Anat Tchetchik]

that's a good idea, Thank you so much Michiel!