Attribute levels of efficient design

[mgj2]

In our model below when we run it, the Attribute 'Seedlings' does not give choice of '10 or 20' in any scenario. There are '0 and 10' and '10 and 10' and '0 and 20' etc but no 10 and 20. We have tried with a number of designs with different priors etc and the same. Can you explain why?

Design
;alts = alt1*, alt2*, OptOut
;rows = 36
;block = 3
;eff = (mnl,d)
;alg = swap(stop=noimprov(120 secs))

;model:
U(alt1) =
b1[-0.001] * Seedlings[0,10,20]
+ b2.effects[-0.01] * Labor[1,2]
+ b3.effects[0.01|0] * Maturation[3,4,6]
+ b4.effects[-0.01|0] * Yield[15,25,40]
+ b5[0.001] * Price[3,5,10,15,20,40]

/

U(alt2) =
b1 * Seedlings + b2 * Labor + b3 * Maturation + b4 * Yield + b5 * Price

/

U(OptOut) = None[-0.001]
$

[johnr]

Hi

I just ran your design and got several - e.g. choice sets 1, 2, 6, 10, 17, 21, 30 and 35. I have ran several times with same result. Bad luck is my best guess.

Choice situation alt1.seedlings alt1.labor alt1.maturation alt1.yield alt1.price alt2.seedlings alt2.labor alt2.maturation alt2.yield alt2.price Block
1 10 1 6 40 5 20 1 4 25 20 3
2 10 2 6 25 15 20 1 4 40 10 2
3 20 2 4 40 10 0 1 3 25 3 2
4 0 1 6 40 40 20 1 3 25 3 3
5 0 2 4 15 10 10 2 6 25 15 3
6 10 1 3 40 15 20 2 4 15 5 1
7 20 1 6 40 3 0 1 4 25 40 1
8 0 2 3 40 20 20 2 6 25 15 2
9 10 2 3 15 40 10 2 4 40 5 2
10 20 1 3 15 3 10 2 4 40 40 3
11 10 1 3 40 5 0 2 6 15 20 3
12 10 2 3 25 20 10 1 6 15 3 2
13 20 1 3 25 15 0 1 4 15 10 1
14 0 2 4 15 20 0 1 6 40 3 1
15 10 2 6 25 10 10 1 3 15 15 1
16 10 1 4 15 15 0 2 3 25 10 2
17 20 2 6 40 10 10 1 3 25 5 3
18 0 2 6 40 10 0 1 3 40 3 1
19 10 1 4 25 5 20 1 6 25 5 3
20 0 1 6 15 3 10 2 3 40 40 2
21 10 2 3 25 5 20 1 4 15 15 3
22 20 1 6 15 20 0 2 4 40 20 3
23 0 1 3 40 40 0 1 4 15 3 3
24 20 2 3 15 15 20 1 4 40 5 1
25 20 1 6 25 20 10 2 4 15 20 1
26 20 2 3 25 10 0 1 6 15 15 2
27 0 2 6 25 40 20 2 3 40 5 1
28 20 1 4 40 40 0 2 3 15 10 2
29 0 1 4 40 15 10 2 6 25 20 1
30 10 2 6 15 3 20 2 3 25 40 3
31 10 2 4 15 40 0 2 6 40 10 3
32 20 1 4 25 5 20 2 6 40 40 1
33 0 2 3 15 3 10 1 6 25 15 2
34 0 1 4 25 3 10 2 3 15 40 2
35 20 2 4 15 20 10 2 3 40 10 2
36 0 1 4 25 5 20 1 6 15 20 1

John

[mgj2]

Luck or strange? no explanation otherwise? just want to be sure there is no explanation.

[johnr]

It is odd. I only ran the design for a minute. The only theoretical explanation I can think of is that efficiency in some cases is achieved when you maximise the differences between the attribute levels (it is more complex than this in reality, as it is related to the specific priors used, the efficiency measure you employ, etc.). That is, it is is likely to result in end points or extreme combinations than those in the middle. It is possible that in your case, the combination of the priors you have assumed alongside the attribute levels themselves is causing this when you are running the design for longer.

This is purely a conjecture, however if you look at your priors, the average impact on utility for each attribute is tiny (for seedlings for example, the average level is 10, and your prior is -0.001 hence the average impact on utility is -0.01, for price it is 0.015). These values are near zero, so the only way the design can achieve efficiency is by maximising the differences between the attribute levels, and again, we have found empirically (i.e., without proof) that this often results in combination of levels in the middle not being chosen. To test if this is the case, try increasing the magnitudes of your priors one decimal point and see if the problem persists.

John