Are priors obtained in pilot valid if an att. is dropped?

[Anat Tchetchik]

Dear all,

We have conducted a pilot of 100 respondents (6 menus each) to obtain priors to be used in a D-error Bayesian efficient design (below is the pilot's syntax)
Respondents' comments on the pilot indicated that the attribute "clean air" was dominant and many of them basically ignored the other attributes when choosing.
MNL analysis of the pilot data revealed that the coefficient of the "clean air" att. is high compare to the other atts' coefficients (i.e. over 2 compare to 0.5-0.9)
We consider removing this att. from the final design. The question is can we still use the priors obtained from the pilot for the remaining atts? or do we need to run a new pilot that lacks the "clean air" att? (if relevant to my question: the signs the other coefficients were as expected and significant in the MNL results)

Anat

Code: Select all

Design
;alts = alt1*,alt2*,optout
;rows=24
;block=4
;eff=(mnl,d)
;model:
U(alt1)=c1+b1[0.00001]*greening[1,2,3]+b2.dummy[0|0]*agri_crop[1,2,3]+b3[0.00001]*cleanair[1,2,3]+b4[-0.00001]*cost[0,100,150,200]/
U(alt2)=c2+b1*greening+b2*agri_crop+b4*cleanair+b5*cost$


[Michiel Bliemer]

Dropping an alternative from the utility function may affect the values of the other parameters since in a logit model the parameters cannot be estimated independently (even with an orthogonal design). However, priors do not need to be exact, there can be a degree of uncertainty around them by using Bayesian priors.

If one of the attributes is considered to be dominant, then you may want to think about the following.
You can keep this attribute fixed across both alt1 and alt2, ie if alt1.cleanair is 1 then also alt2.cleanair is 1, etc. It therefore becomes some kind of scenario variable. You can achieve this as follows in Ngene:

U(alt2)=c2+b1*greening+b2*agri_crop+b4*cleanair[cleanair]+b5*cost$

This way, people will always trade-off on the other attributes between alt1 and alt2, and since you have an optout alternative, you can still estimate this model.

You can also choose to vary cleanair for a few choice sets of you like. If the prior for cleanair is very large (i.e. dominant), then efficient designs will often lead to choice tasks in which the level is kept the same across both alternatives in order to be able to estimate the parameters of the other attributes.

Michiel

[Anat Tchetchik]

Thank you very Michiel!

I understand the first option (keep this attribute fixed across both alt1 and alt2) which I use frequently.
Not sure I understand the second one (vary cleanair for a few choice sets) do you mean integrating (some how) between two designs? one which includes this att. and one which doesn't?
Anat

[Michiel Bliemer]

You could either manually change some of the cleanair attributes to make them different across choice tasks, or you can impose a high prior in which overlap of cleanair across alternatives occurs naturally but there will still be many choice tasks in which these levels are not overlapping. It depends on whether you think cleanair is a dominant attribute for all respondents or only for some.

Michiel

[Anat Tchetchik]

Thank you very much Michiel.

I took your advice and imposed high priors on the 'cleanair" att. (see the Bayesian design below).
One last thing that remains unclear; Previously (in the pilot) the opt-out alt. had no atts. . Now, I want to assign to it one att. with fixed level (i.e: cleanair, level ==1 which indicates a polluted air)
I'm not sure how to handle this. My best idea is to add a constant with negative prior to the last utility eq. (this raw did not exist at all in the pilot)
Does it make any sense?

Code: Select all

Design                           
;alts = alt1*, alt2*, optout                           
;rows = 36                           
;block=9                           
;eff = (mnl,d)                           
;rep=1000                           
;bdraws=gauss(3)            
;model:                                          
U(alt1)=b1.dummy[(n,1.15,0.16)|(n,0.84,0.18)]*green[3,2,1]+b2.dummy[(n,0.95,0.20)|(n, 0.59,0.22)]*agri_crop[3,2,1]+b3.dummy[(n,0.55,0.17)|(n,0.42,0.21)]*beach[3,2,1]+b4.dummy[(n,3.03, 0.37) | (n,2.56, 0.32)]*cleanair[3,2,1]+b5[(n,-0.007, 0.0029)]*cost[50,100,150]/    
U(alt2)=b1*green+b2*agri_crop+b3*beach+b4*cleanair+b5*cost/
U(optout)= c1[-0.0001]$

[Michiel Bliemer]

I believe you are looking for this:

Design
;alts = alt1*, alt2*, optout
;rows = 36
;block=9
;eff = (mnl,d)
;alg = mfederov
;rep=1000
;bdraws=gauss(3)
;require:
optout.cleanair = 1
;model:
U(alt1)=b1.dummy[(n,1.15,0.16)|(n,0.84,0.18)]*green[3,2,1]+b2.dummy[(n,0.95,0.20)|(n, 0.59,0.22)]*agri_crop[3,2,1]+b3.dummy[(n,0.55,0.17)|(n,0.42,0.21)]*beach[3,2,1]+b4.dummy[(n,3.03, 0.37) | (n,2.56, 0.32)]*cleanair[3,2,1]+b5[(n,-0.007, 0.0029)]*cost[50,100,150]/
U(alt2)=b1*green+b2*agri_crop+b3*beach+b4*cleanair+b5*cost/
U(optout)= b4*cleanair$

I have added a ;require command and added cleanair to optout. Note that ;require only works with the Modified Federov algorithm (;alg = mfederov), which lets go of attribute level balance. This is generally not a problem, but if you require some degree of balance, you may want to impose attribute level restrictions such as:

b5*cost[50,100,150](8-16,8-16,8-16)

which means that each level (50,100,150) appears between 8 and 16 times across the design.

Michiel

[Anat Tchetchik]

That's perfect! thank you very much Michiel!