Dominance of alternatives in Bayesian D-efficient design

[Carla_Barlagne]

Dear all,

I have been reading through the posts related to redundant choice cards and dominant alternatives and the manual and found that one way to deal with them is to write the alternatives with an *. I have run a pilot and am trying to generate a Bayesian D-efficient design but I still come across quite a high number of dominant alternatives sometimes more than one in a block. So I would like to check that my design is OK as well as to double-check what a dominant alternative is.

My design comprises:

2 origins: imported vs local which we ranked before the pilot as: imported < local
3 modes of production: conventional, integrated, organic which we ranked before the pilot as: conventional < integrated < organic. Priors obtained from the pilot indicated another order as follow: conventional < organic < integrated
4 prices: 8.5, 11, 13.5, 16

Priors have been obtained from a pilot (10% of the final sample size) and estimated by an MNL model

The design is as follow:

Design? Bayesian D-efficient

;alts = alt1*, alt2*, NONE
;rows = 12
;block = 2
;eff = (mnl,d,mean)

;model:

U(alt1) = b0[1.83]
+ b1.dummy[(n,1.16,0.20)]*ORI[2,1]
+ b2.dummy[(n,0.92,0.25)|(n,0.25,0.27)]*PROMOD[2,3,1]
+ b3[0.12]*PRIC[8.5,11,13.5,16]/

U(alt2) = b0
+ b1*ORI
+ b2*PROMOD
+ b3*PRIC
$

By default, Ngene implements Halton draws.

1/ Do we agree that in the following examples, according to the priors obtained from the pilot:

a/ alt 1 = local, integrated, 8.5 vs alt 2 = imported, conventional, 16, alt 1 is the dominant alternative and by far?
b/ alt 1 = local, organic, 13.5 vs alt2 : imported, conventional, 11, alt 1 is still the dominant alternative ?

2/ Is it normal to still obtain dominant alternatives? Is it possible to obtain a design with no dominant alternative at all? How to obtain one?

3/ Also, could you point me towards references to help decide what would be the best distribution for the parameters please?

Best wishes,

Carla

[Michiel Bliemer]

Your prior for price is positive, so a price of 16 is preferred over a price of 8. With this prior, in the two examples you gave there is NOT a dominant alternative:

alt 1: local, integrated, 8.5
alt 2: imported, conventional, 16

According to your priors, alt1 is better in ORI and PROMOD, but alt2 is better in PRICE.

So if PRICE is price paid, not price received, then change prior to -0.12.

If your priors were estimated from a pilot study, you would use normally distributed priors (n,MU,SIGMA) where MU is the parameter estimate and SIGMA is the standard error of the parameter estimate. If you did not estimate your priors, you may use uniform distributions to indicate a range, but when setting priors manually you should always be careful.

Michiel

[Carla_Barlagne]

Good afternoon,

My apologies for a delayed reply.

Thank you very much indeed for your indications. My design does not have dominant alternatives anymore.

Best wishes,

Carla