Designs with subsets of attributes for a pooled model

[msrbpdr]

Hello

I will run an unlabelled experiment with 3 treatments, 9 set per person:
1: attribute C and price
2: attribute H and price
3: attributes C and H and price

C and H are 3 level categorical variables (low, med , high)
People are randomly assigned to 1 treatment at random
It is a consequential lab experiment (not hypothetical) so samples will be small - c.80 per reatment

I want to see how the the value of C and H are affected when they appear alone versus with the other non-price attribute.

So I plan to estimate a pooled model, with treatment interactions.
I ran pilots with orthogonal designs so I have priors.

I would appreciate wisdom on the design(s) for the main study given the intention to pool the data and test for treatment effects.

eg should I:
A--Generate 3 different designs using priors from the 3 pilots
B--Generate a single design ( orthogonal / D eff zero priors) and remove the C and H attributes in the relevant treatments
C--Generate an efficient design from treatment 3 pilot and remove the C and H attributes in the relevant treatments
D-- other...

A has the advantage of efficient design (with a small sample) but risks any treatment effects being affected by the differences in design
B seems likely to avoid any design effect, at the cost of efficiency.
C is a hybrid!

One note - the priors for C and H are very similar - see below for the syntax used to generate an efficient design for T3

thanks
Dan

Code: Select all

Design
;alts = Alt1, Alt2, Alt3, None
;rows = 144
;block = 18
;eff = (mnl,s, mean)
;model:
U(Alt1) = h.dummy[ (n,1.2,0.6) | (n,0.6,0.3)]*h[0,1,2] + c.dummy [(n,1.8,0.6) | (n,0.8,0.3)]*c[0,1,2]+ pr[(n,-1.5,0.6) ]*p[2:6:0.5]   /
U(Alt2) = h.dummy*h[0,1,2] + c.dummy*c[0,1,2] + pr*p[2:6:0.5]   /
U(Alt3) = h.dummy*h[0,1,2] + c.dummy*c[0,1,2] + pr*p[2:6:0.5]   /
u(None) = n[n,(n,-3,0.3),(u,0.1,0.5)]*none[1]
$



[Michiel Bliemer]

I think you will have issues with each approach (A,B,C) if you are using 3 generic alternatives because one of the alternatives will be dominant, understanding that all attribute levels are decreasing in utility. So I think that you can only consider 2 generic alternatives.

Approach A would work, but as you say it loses statistical power when comparing treatments.

Approach B would work if you manually impose dominance constraints, see script below. There exist only 648 choice tasks without dominant alternatives after removing C or H.

Approach C could possibly make sense although after removing C or H the choice probabilities change and the design may no longer be efficient.

Code: Select all

Design
;alts = Alt1*, Alt2*, None
;rows = 144
;block = 18
;eff = (mnl,d)
;alg = mfederov(candidates = 648)
;reject:
Alt1.h <= Alt2.h and Alt1.p <= Alt2.p,
Alt1.h >= Alt2.h and Alt1.p >= Alt2.p,
Alt1.c <= Alt2.c and Alt1.p <= Alt2.p,
Alt1.c >= Alt2.c and Alt1.p >= Alt2.p
;model:
U(Alt1) = h.dummy[0.02|0.01]                                * h[0,1,2]
        + c.dummy[0.02|0.01]                                * c[0,1,2]
        + pr.dummy[0.08|0.07|0.06|0.05|0.04|0.03|0.02|0.01] * p[2,2.5,3,3.5,4,4.5,5,5.5,6]
        /
U(Alt2) = h                                                 * h
        + c                                                 * c
        + pr                                                * p
        /
U(None) = n[0]
$


When using uniformative near-zero priors, I generally consider dummy coded variables for all attributes as this provides a design with more variation, which is also beneficial when interested in interaction effects. Later in model estimation you can of course use a linear numerical effect for price.

Michiel

[msrbpdr]

Thanks for this Michiel
You are right, there is/was a problem with dominated options using 3 generic Alts, esp with only one non-price attribute.
2 Alts makes much more sense

Thanks also for the suggestion re dummy coding all attributes when using uniformative near-zero priors.

Just be sure....is your syntax using that approach relating to my option B:

"Generate a single design ( orthogonal / D eff zero priors) and remove the C and H attributes in the relevant treatment"

thanks
Dan

[Michiel Bliemer]

Yes my script reflects your option B, where you simply omit one of the attributes, which does not affect efficiency when using uninformative priors.

[msrbpdr]

Great, thank you

Dan