Incorporate contextual variables into orthogonal design

[rich_imr]

Greetings,

Is there a possible possible work-around to incorporate contextual (socio-economic) variables into fractional factorial designs?

I know this is possible with efficient designs, but I need to run fractional factorial designs because I either need no correlations within or across attributes depending on the intent of the design (I believe this is the same as an efficient design with 0 as priors, but I need designs with no correlations. Whenever I run these designs there ends up being correlations.)

In this particular design case, attributes A-E are unlabeled and F-L are the contextual (socio-economic) variables that need to force to have identical levels within choice sets.

I ran the below syntax and received this error: Error: An attribute that mimics another attribute's levels (i.e. scenarios) was specified and is not compatible with orthogonal designs.

Code: Select all

Design
? This will generate a fractional factorial orthogonal design
;alts = alt1, alt2
;rows = 48
;orth = seq
;block=12
;model:
U(alt1) = b0 +b1*A[1,2,3]+b2*B[1,2,3]+b3*C[1,2,3,4]+b4*D[1,2]+b5*E[1,2,3,4]+b6*F[1,2,3] +b7*G[1,2,3,4] +b8*H[1,2,3,4] +b9*I[1,2,3,4] +b10*J[1,2,3] +b11*K[1,2,3,4] +b12*L[1,2,3,4]/
U(alt2) =     b1*A       +b2*B       +b3*C         +b4*D     +b5*E         +b6*F[F] +b7*G[G] +b8*H[H] +b9*I[I] +b10*J[J] +b11*K[K] +b12*L[L]       
$

Thanks for any help!

[Michiel Bliemer]

Hi,

Note that efficient designs are also fractional factorial designs. All designs that only present a subset of the full factorial are called fractional factorial. So I assume you mean orthogonal designs.

Orthogonal designs unfortunately have no flexibility, NO CONSTRAINTS can be imposed on orthogonal designs, as any constraint makes them non-orthogonal. This also means that it is not possible to impose scenario constraints. However, you can introduce socio-demographics in Ngene, I refer to Section 8.4 of the manual.

It is important to note that the utility functions that you have provided CANNOT BE ESTIMATED. Clearly, socio-demographics are constant across alternatives and therefore coefficients b6 to b12 cannot be estimated. If your alternatives are labelled, you have to leave the socio-demographics out of one of the alternatives. If your alternatives are unlabelled (generic), then you need to use interaction effects (e.g., b6*F*A). It is important to correctly specify these utility functions, as otherwise you will not be able to estimate your model.

Michiel

[rich_imr]

Greetings Michiel,

Perhaps what I am trying to achieve is a little unorthodox.

1. I am trying to create a fractional factorial orthogonal design for unlabeled alternatives with contextual attributes.

2. In my studies, the respondent makes a choice of an alternative conditional on the contextual attribute levels present in the choice set.

2.1 For the sake of example, one study could be surveying parents on what car they would choose (the unlabeled alternatives) conditional on a hypothetical teenager (the contextual attributes in the choice set). The contextual attributes could be age, employment status, and/or performance in school for the teenager.

3. From the standpoint of actually implementing the design in a survey, the respondent will need to see the two unlabeled alternatives and one set of contextual attribute levels from which they make their appropriate choice per choice set.

4. It is my understanding that, a design as described above would need no correlation between alternative one and the contextual attributes, as well as no correlation between alternative one and the contextual attributes, but there can be correlation between the alternatives.

5. As you mentioned, strictly speaking, a model from such a design would be unestimable. But, if one interacts the context attributes with alternative specific constants and estimates them for J-1 alternatives, one can estimate a model.

6. My work around is to create a labeled alternative design using

Code: Select all

;orth=sim

, where the context variables only enter one alternative (to achieve one set of context variables per choice set). For example:

Code: Select all

Design
;alts = alt1, alt2
;rows = ##
;orth = sim
;model:
U(alt1) = b0+b1*A[1,2]+b2*B[1,2,3]+b3*C[1,2,3,4]+b4*D[1,2,3]     +b5*E[1,2,3]+b6*F[1,2,3,4] +b7*G[1,2] +b8*S[1,2]+b9*H[1,2,3,4] +b10*I[1,2]/
U(alt2) = b14+b1*A    +b2*B       +b3*C         +b4*D            +b5*E       +b6*F          +b7*G       
$

6.1 Attributes after "G" are contextual. The problem here is that, since the alternatives are specified as labeled, some choice sets have identical alternative levels when used for unlabeled alternative studies. My solution has simply been to switch the alternate levels from choice sets in which this occurs to other choice sets, which induces some correlation in the design.

Finally, my question: is there a better workaround to the one described above?

I am not comfortable with efficient designs yet (from my understanding page 174 of the manual, creating such a design for the issues described above is possible when creating an efficient design). So, unless creating an efficient design using

Code: Select all

 ;eff = (mnl,d)

will give me a design with almost no correlation, then I’d rather not attempt it.

Thank you very much for your time.

Regards,

R

[Michiel Bliemer]

Your model is still not estimable; you need to include interactions with attributes that vary levels, not the constants (since then the values are still constant across alternatives). You need to specify the model exactly as how you would estimate it, and the model you formulate cannot be evaluated by Ngene since attribute levels are identical across alternatives.

What you are trying to do is a SCENARIO, which is described in the Ngene manual. It is fine using an unlabelled experiment, as long as you use interactions with attributes.

Orthogonal designs are not really used anymore since we know that correlations are not relevant for choice models. Hence, it is fine using an efficient design. Simply use zero priors. This is the best way to create your design, orthogonal designs are just not suitable and cannot be used with scenarios. I do not think there is any work around, either theoretically or in Ngene. The only way in my opinion is formulating the utility functions of the model you are actually estimating (including interactions), specifying scenarios (which you have done without interactions), and let Ngene find a design with which you can estimate the model.

Unfortunately the literature from the 1980s has made many people scared of correlations and let them think they need an orthogonal design. You only need orthogonal designs in linear regression model in order to avoid multicollinearity. Such problem does not exist in discrete choice models (since they are nonlinear).

Michiel