Fractional Factorial Design Syntax

[davidj]

Hi Michiel, John and Andrew,

I am now developing a fractional factorial design as per the following syntax, but have a few questions:

1.As I want to include a reference alternative, should I just include it in the alternatives above and not in the utility function? As i understand, a reference alternative will not affect choice option development in this case?
2.Attribute level dominance, I wanted to confirm whether the use of the asterix will still play any role in an orthogonal design development. I have reviewed the output and it does not seem to influence the scenarios.
3.Foldover effects - I have included the foldover condition to develop a design better suited for interactions. What has been you experience in using foldovers and do you see any value in its inclusion in a fractional factorial design?


Syntax is as follows:

Design
;alts = Base, Alt1*, Alt2*
;rows = 36
;orth = sim
;eff = (mnl,d)
;block = 8
;foldover
;model:

U(Alt1) = b1 * A[35,40,50,60] + b2 * B[16,12,8] + b3 * C[127.5,255,382.6] + b4 * D[0,18,36] + b5 * E[8,9,10]/
U(Alt2) = b6 + b1 * A[35,40,50,60] + b2 * B[16,12,8] + b3 * C[127.5,255,382.6] + b4 * D[0,18,36] + b5 * E[8,9,10]$

With the design appearing as follows:
Choice situation alt1.a alt1.b alt1.c alt1.d alt1.e alt2.a alt2.b alt2.c alt2.d alt2.e Block Foldover block
1 35 12 255 36 8 60 12 255 36 8 8 1
2 35 16 127.5 18 9 60 16 127.5 18 9 8 1
3 35 8 382.6 0 10 60 8 382.6 0 10 8 1
4 50 12 127.5 0 9 40 12 382.6 36 9 3 1
5 50 16 382.6 36 10 40 16 255 18 10 3 1
6 50 8 255 18 8 40 8 127.5 0 8 3 1
7 40 8 382.6 0 10 35 16 127.5 36 8 7 1
8 40 12 255 36 8 35 8 382.6 18 9 7 1
9 40 16 127.5 18 9 35 12 255 0 10 7 1
10 50 8 255 18 8 50 16 382.6 36 10 8 1
11 50 12 127.5 0 9 50 8 255 18 8 8 1
12 50 16 382.6 36 10 50 12 127.5 0 9 8 1
13 40 8 127.5 36 10 35 8 255 36 9 4 1
14 40 12 382.6 18 8 35 12 127.5 18 10 4 1
15 40 16 255 0 9 35 16 382.6 0 8 4 1
16 60 16 255 0 9 60 8 127.5 36 10 3 1
17 60 8 127.5 36 10 60 12 382.6 18 8 3 1
18 60 12 382.6 18 8 60 16 255 0 9 3 1
19 60 16 255 18 10 40 12 382.6 36 9 6 1
20 60 8 127.5 0 8 40 16 255 18 10 6 1
21 60 12 382.6 36 9 40 8 127.5 0 8 6 1
22 60 12 127.5 18 10 50 8 127.5 36 10 2 1
23 60 16 382.6 0 8 50 12 382.6 18 8 2 1
24 60 8 255 36 9 50 16 255 0 9 2 1
25 35 16 382.6 0 8 50 8 255 36 9 1 1
26 35 8 255 36 9 50 12 127.5 18 10 1 1
27 35 12 127.5 18 10 50 16 382.6 0 8 1 1
28 35 8 382.6 18 9 40 12 255 36 8 2 1
29 35 12 255 0 10 40 16 127.5 18 9 2 1
30 35 16 127.5 36 8 40 8 382.6 0 10 2 1
31 50 12 382.6 36 9 35 16 382.6 36 10 5 1
32 50 16 255 18 10 35 8 255 18 8 5 1
33 50 8 127.5 0 8 35 12 127.5 0 9 5 1
34 40 16 127.5 36 8 60 16 127.5 36 8 5 1
35 40 8 382.6 18 9 60 8 382.6 18 9 5 1
36 40 12 255 0 10 60 12 255 0 10 5 1
37 60 12 255 0 10 35 12 255 0 10 1 2
38 60 8 382.6 18 9 35 8 382.6 18 9 1 2
39 60 16 127.5 36 8 35 16 127.5 36 8 1 2
40 40 12 382.6 36 9 50 12 127.5 0 9 6 2
41 40 8 127.5 0 8 50 8 255 18 8 6 2
42 40 16 255 18 10 50 16 382.6 36 10 6 2
43 50 16 127.5 36 8 60 8 382.6 0 10 2 2
44 50 12 255 0 10 60 16 127.5 18 9 2 2
45 50 8 382.6 18 9 60 12 255 36 8 2 2
46 40 16 255 18 10 40 8 127.5 0 8 1 2
47 40 12 382.6 36 9 40 16 255 18 10 1 2
48 40 8 127.5 0 8 40 12 382.6 36 9 1 2
49 50 16 382.6 0 8 60 16 255 0 9 5 2
50 50 12 127.5 18 10 60 12 382.6 18 8 5 2
51 50 8 255 36 9 60 8 127.5 36 10 5 2
52 35 8 255 36 9 35 16 382.6 0 8 6 2
53 35 16 382.6 0 8 35 12 127.5 18 10 6 2
54 35 12 127.5 18 10 35 8 255 36 9 6 2
55 35 8 255 18 8 50 12 127.5 0 9 3 2
56 35 16 382.6 36 10 50 8 255 18 8 3 2
57 35 12 127.5 0 9 50 16 382.6 36 10 3 2
58 35 12 382.6 18 8 40 16 382.6 0 8 7 2
59 35 8 127.5 36 10 40 12 127.5 18 10 7 2
60 35 16 255 0 9 40 8 255 36 9 7 2
61 60 8 127.5 36 10 40 16 255 0 9 8 2
62 60 16 255 0 9 40 12 382.6 18 8 8 2
63 60 12 382.6 18 8 40 8 127.5 36 10 8 2
64 60 16 127.5 18 9 50 12 255 0 10 7 2
65 60 12 255 36 8 50 8 382.6 18 9 7 2
66 60 8 382.6 0 10 50 16 127.5 36 8 7 2
67 40 12 127.5 0 9 60 8 127.5 0 8 4 2
68 40 8 255 18 8 60 16 255 18 10 4 2
69 40 16 382.6 36 10 60 12 382.6 36 9 4 2
70 50 8 382.6 0 10 35 8 382.6 0 10 4 2
71 50 16 127.5 18 9 35 16 127.5 18 9 4 2
72 50 12 255 36 8 35 12 255 36 8 4 2

MNL covariance matrix:


Prior b1 b2 b3 b4 b5 b6
b1 0.000292 -0.000105 -2E-06 -8E-06 -0.001254 -0.000124
b2 -0.000105 0.002695 -5E-06 -1.7E-05 -0.00282 -0.000279
b3 -2E-06 -5E-06 3E-06 0 -5.9E-05 -6E-06
b4 -8E-06 -1.7E-05 0 0.000143 -0.000209 -2.1E-05
b5 -0.001254 -0.00282 -5.9E-05 -0.000209 0.013035 -0.003342
b6 -0.000124 -0.000279 -6E-06 -2.1E-05 -0.003342 0.083003


Thanks again for all your assistance. It is so valuable!

David

[Michiel Bliemer]

1. Orthogonal designs ignore reference alternatives; reference alternatives are only taken into account in efficient designs.
2. Dominance cannot be avoided with orthogonal designs; dominance can only be taken into account in efficient designs, and only if you have specified parameter priors (which you have not).
3. Foldover designs enable estimating two-way interaction effects. So if you suspect that you will be estimating one or more interaction effects, creating a foldover design is useful. You can block the foldover design in two.

[davidj]

Thank you Michiel for the response!

The only other question I have is:

- Are there any issues in including both two way interactions and the fold over condition in the design development. Example syntax would be:



Design
;alts = Base, Alt1*, Alt2*
;rows = 36
;orth = sim
;eff = (mnl,d)
;block = 9
;foldover
;model:

U(Alt1) = b1 * A[35,40,50,60] + b2 * B[16,12,8] + b3 * C[127.5,255,382.6] + b4 * D[0,18,36] + b5 * E[8,9,10] + b7*A*B + b8*C*D /

U(Alt2) = b6 + b1 * A + b2 * B + b3 * C + b4 * D + b5 * E + b7*A*B + b8*C*D $


My rational being that I want to incorporate specific two-way interactions, but also develop a design that is able to estimate non-specified interaction effects?

Thanks again for all the assistance.

David

[johnr]

hi David

The two are not necessarily mutually exclusive, so there is no harm in doing it.

John