Interactions between all levels of 2 dummies

[dsr]

I am generating a design for a 3 attribute, 2 alternative, experiment
I have a dummy (att1) with 4 levels [A,B,C,D]
I have a second dummy (att2) with 3 levels [X,Y,Z]

I want a design that will allow me to estimate the interactions between each level of these 2 attributes
A*X, A*Y, A*Z………..D*X, D*Y, D*Z
as well as the main effects.

I have priors for the marginal utilities of the levels of att1 & att2, but not for the interactions between them ( I hope to get them from the pilot)
There is a price attribute also.

Ignoring the price attribute for now, if I specify the utility function (of alternative 1) as

U(alt1) =
b1.dummy[0.18 | 0.34 | 0.439]*att1[0,1,2,3] +
b2.dummy[0.22 | 0.33] *att2[0,1,2] +
b3*att1*att2 /

is this specification sufficient to create a design which allows estimation of the impact on utility of the 12 interactions between each level of the 2 dummies (att1, att2)?

Or do I need to state this more explicitly, perhaps by having each dummy as a separate (0,1) attribute and all the interactions explicit:

U(alt1) =
b11[0]*A[0,1] + b12[0.18]*B[0,1] + b13[0.34]*C[0,1] + b14[0.439]*D[0,1]
b21[0]*X[0,1] + b22[0.22]*Y[0,1] + b23[0.33]*Z[0,1]
+ b31[0]*A*X + b32[0]*A*Y + b33[0]*A*Z
+ b41[0]*B*X + b42[0]*B*Y + b43[0]*B*Z
+ b51[0]*C*X + b52[0]*C*Y + b53[0]*C*Z
+ b61[0]*D*X + b62[0]*D*Y + b63[0]*D*Z /


If I need this latter specification then I presume I would need constraints such as:

;require:
alt1.A + alt1.B + alt1.C + alt1.D = 1,
alt2.A + alt2.B + alt2.C + alt2.D = 1

alt1.X + alt1.Y + alt1.Z = 1,
alt2.X + alt2.Y + alt2.Z = 1

_________
thanks,
d

[Michiel Bliemer]

The syntax

Code: Select all

...
U(alt1) = b1.dummy[0.18 | 0.34 | 0.439] * att1[0,1,2,3] + b2.dummy[0.22 | 0.33] * att2[0,1,2] + b3[0.1] * att1 * att2  /
...


will work, but assume that the interaction att1 * att2 has a single parameter only.

In your case, you want each interaction term to have a separate parameter, so b3 should contain 2x3 = 6 parameters in total. This is currently not supported in Ngene, as an error message in Ngene would come up:

Error: An interaction term is associated with a dummy or effects coded parameter. Interactions of dummy or effects coded attributes are not currently supported.

I think indeed the only way to make this currently happen is to put conditions in, as you suggest yourself. It will be something we will consider for the next version.

[dsr]

I would like to re-open this topic (after nearly 2 years!) as I have returned to this type of issue.

To recap on the issue:
I have att1 with 4 levels [A,B,C,D]
& att2 with 3 levels [X,Y,Z]

I want a 2 Alt design that will allow me to estimate the interactions between each level of these 2 attributes
A*X, A*Y, A*Z……… D*X, D*Y, D*Z
as well as the main effects.

In the absence of a quick way to do this I was entering the levels of the 2 attributes as separate [0,1] attributes.
Michael’s suggestion was that I use REQUIRE to ensure only 1 value of att1=1 in any option, and likewise for att2.

So I used:

Code: Select all

;require:
alt1.X + alt1.Y + alt1.Z = 1,
alt2.X + alt2.Y + alt2.Z = 1,
alt1.A + alt1.B + alt1.C + alt1.D = 1,
alt2.A + alt2.B + alt2.C + alt2.D = 1


When I try this the design constraints are not operating and I would be grateful for advice as to what I am doing wrong in this design:

Code: Select all

Design
;alts = alt1, alt2
;rows = 120
;block=10
;eff = (mnl,d)
;require:
alt1.X + alt1.Y + alt1.Z = 1,
alt2.X + alt2.Y + alt2.Z = 1,
alt1.A + alt1.B + alt1.C + alt1.D = 1,
alt2.A + alt2.B + alt2.C + alt2.D = 1
;model:

U(alt1) = b0[-0.2]*P[10,20,30,40,50,60,70,80,90,100]
        + b1[0.0]*A[0,1] + b2[0.17]*B[0,1] + b3[0.33]*C[0,1] + b4[0.43]*D[0,1]
        + b5[0.1]*X[0,1] + b6[0.21]*Y[0,1] + b7[0.43]*Z[0,1]
        + b15[0]*A*X + b16[0]*A*Y + b17[0]*A*Z
        + b25[0]*B*X + b26[0]*B*Y + b27[0]*B*Z
        + b35[0]*C*X + b36[0]*C*Y + b37[0]*C*Z
        + b45[0]*D*X + b46[0]*D*Y + b47[0]*D*Z /

U(alt2) = b0*P
        + b1 *A   + b2*B + b3*C + b4*D
        + b5 *X   + b6*Y + b7*Z
        + b15*A*X + b16*A*Y + b17*A*Z
        + b25*B*X + b26*B*Y + b27*B*Z
        + b35*C*X + b36*C*Y + b37*C*Z
        + b45*D*X + b46*D*Y + b47*D*Z $


This snippet of a resulting design indicates that my REQUIRE conditions are not being met.
ie, for Alt1:
A+B+C+D does not = 1 in SCE 1,2,3,5,6
X+Y+Z does not = 1 in SCE 1,3,5,6

Code: Select all

sce    alt1.p      alt1.A   alt1.B   alt1.C   alt1.D   alt1.X   alt1.Y   alt1.Z
1   70                  0      1      0             1      0      1      1
2   80                  1      0      0             1      0      1      0
3   60                  0      1      0             1      1      1      0
4   50                  1      0      0             0      1      0      0
5   90                  0      0      1             1      1      0      1
6   40                  0      0      0             0      0      0      0


Thanks
Dan