problem with design with continuous attribute levels

[Anat Tchetchik]

Dear Ngene users,

In my previous post, I was referring to the same design (6 labeled alt. one attribute only- Receipt). I was thinking to conduct a blocked full factorial design, but having read more I start thinking that design with continuous attribute levels, will suit better (?)

I ran this two stages design:
(1)
Design
;alts = Resyclcomp, Ebay, returnCellComp, giveaway, donate, throw
;rows = 27
;orth=ood
;model:
U(Resyclcomp) = a1[-0.0] + b2[0.0] *priceL[1,2,3] /
U(Ebay) = b[-0.0]1+ b2 *priceH[7,8,9] /
U(returnCellComp)=c1[-0.0] +b2*priceM[4,5,6]/
U (giveaway)= d1[0.0] /
U(donate)= e1[0.0] $

(2)
Stage 2
Design
;alts = Resyclcomp, Ebay, returnCellComp, giveaway, donate, throw
;rows = 27
;eff = (mnl, d)
;alg = neldermead(nointerim=0, stop=total(20000 iterations))
;start = initial OOD.ngd
;model:
U(Resyclcomp) = a1[-0.0] + b2[0.0] *priceL[1:3] /
U(Ebay) = b1[-0.0] + b2[0.0] *priceH[7:9] /
U(returnCellComp)=c1[-0.0] +b2[0.0]*priceM[4:6]/
U (giveaway)= d1[0.0] /
U(donate)= e1[0.0] $

However I receive a design whose levels are very badly distributed between the levels' limits, any ideas what went wrong?
Choiceresyclcomp ebay returncellcomp
1 2.999694 8.998687 4.002517
2 2.999795 8.993539 4.002856
3 2.993433 7.000189 4.000493
4 2.997612 7.000779 5.995126
5 2.996142 7.004456 5.996723
6 1.001732 8.989932 4.001474
7 1.00268 7.00236 4.024977
8 1.003889 8.995652 5.994996
9 2.999824 8.997146 4.000834
10 1.000366 8.997462 5.996709
11 2.990816 7.001599 4.010932
12 1.005177 7.00085 5.99839
13 1.005343 7.009948 4.000195
14 2.995379 8.998593 4.002726
15 2.995879 7.008172 5.997839
16 2.99802 8.996511 4.002232
17 2.999614 7.000728 5.998861
18 2.986174 8.997317 6
19 1.000172 8.999026 4.002775
20 2.999264 7.003268 5.98518
21 2.993463 8.990139 4.009737
22 1.006579 8.999564 4.01499
23 1.007325 8.99977 5.999307
24 2.997931 7.00919 4.000772
25 1.001455 8.998704 5.9989
26 1.007227 8.998082 5.99934
27 1.00942 7.011195 5.997541

[Michiel Bliemer]

The output is correct. End point designs are most optimal. When using only the outer two limits, a maximum trade-off is achieved. There is no need to put levels in the middle for efficiency, only if you are interested in estimating nonlinear effects (using dummy or effects coding). This holds for any attribute in which you only estimate a single parameter/coefficient.

By the way, the neldermead optimisation will work, but it is not very useful without specifying priors. Keeping them all zero is not informative, so you can greatly improve upon your design by putting in realistic priors.

[Anat Tchetchik]

Thank you very much (again) Michiel,
Just one quick clarification; you mean that the neldermead will work better if I provide priors in the second stage, rather than providing only the signs (as we did in the example)
Best,
Anat

[Michiel Bliemer]

Yes in a second stage it would be useful to put in realistic priors and optimise the design more. Without much information on priors, there is not much to optimise on.

[johnr]

Hi Anat

Putting a sign in with a zero prior does not represent placing a sign as a prior as you suggest. -0 is still zero, as +0 is 0. If you want to place a sign on the prior, you will need to use a Bayesian prior. We typically use uniforms for this. e.g., a1[(u,-0.5,0)].

John

[Anat Tchetchik]

Thank you John, I'll employ your advice.
Anat