Regarding interaction effects and the foldover technique

[peterbackstrom]

Dear Ngene users,

I'm fairly new to the software and to the choice experiment area in general, so my question might seem obvious to those who know more than me. So, I apologize in advance for my naivety.
Anyway, I have (tried) to design a quite straightforward orthogonal 2x2x2x4 choice experiment, with two unlabelled alternatives. Besides main effects, I am interested in all two-way interactions between attributes, which led me to implement the foldover-option.

Here is my experimental design:

Code: Select all

Design
;alts = SokandeA, SokandeB       ;rows = 8                        ;orth = seq                      ;foldover                        ;model:
U(SokandeA) = b0
            + b1 * KON[1,0]
            + b2 * ALDER[1,0]
            + b3 * LEDIG[1,2,3,0]                     
            + b4 * ENG[1,0]

                                                                                                            /
U(SokandeB) = b1 * KON + b2 * ALDER + b3 * LEDIG + b4 * ENG
$


My question relates to the interaction effects. After collecting some data, I tried to estimate the choice model (using Stata and the clogit command). I then found out that I cannot estimate all interaction effects. After returning to experimental design, I realized that this must (?) be a consequence of the design itself, rather than the statistical model or the number of observations.
Here is the experimental design I used for my experiment, as produced by the software (sorry for the formatting):

Choice situation sokandea.kon sokandea.alder sokandea.ledig sokandea.eng sokandeb.kon sokandeb.alder sokandeb.ledig sokandeb.eng Foldover block
1 1 1 1 1 1 1 0 0 1
2 0 1 3 1 0 0 1 0 1
3 1 0 2 1 1 0 3 0 1
4 0 0 0 1 1 0 2 0 1
5 1 1 0 0 0 0 0 1 1
6 0 1 2 0 0 1 3 0 1
7 1 0 3 0 0 1 2 1 1
8 0 0 1 0 1 1 0 1 1
9 0 0 0 0 0 0 1 1 2
10 1 0 2 0 0 1 3 1 2
11 0 1 3 0 1 1 1 0 2
12 1 1 1 0 1 0 3 1 2
13 0 0 1 1 1 0 2 1 2
14 1 0 3 1 1 1 1 1 2
15 0 1 2 1 0 1 2 0 2
16 1 1 0 1 0 0 0 0 2

For me, it is clear that, it is indeed impossible to estimate the interaction ALDER*LEDIG and the interaction KON*LEDIG at the same time; for cases in which attribute LEDIG=3, attributes KON and ALDER are always mirror images of each other (i.e. when KON=1, ALDER =0, and vice versa). Therefore their effects cannot be distinguished from each other, conditional on the specific value of the attribute LEDIG. At least not in the regression context I have in mind.

So, my question is: What am I missing? Why doesn’t the foldover work in the way I (naively) thought it would?

Kind regards,

Peter

[Michiel Bliemer]

A folder design of an orthogonal design ensures that each main effect is uncorrelated with each interaction effect. However, this does not mean that each interaction effect is uncorrelated with each other interaction effect. The only way to guarantee that is to specify all interaction effects into the utility functions and generate a design (for example a D-efficient design with zero priors) that explicitly accounts for all interaction effects. Another design that will guarantee that you can estimate all interaction effects with is a full factorial design. In your case, the full factorial has 32^2 rows.

Michiel

[peterbackstrom]

Thank you for reply, Michiel. And, thank you for pointing this out to me. Apparently, I need to think more closely about this, and settle for estimating the main effects only, at this stage.

Kind regards,

Peter

[Michiel Bliemer]

You will be able to estimate all main effects and SOME (but not all) interaction effects. So you can try with one, and progressively include more until you can no longer get estimates.

Michiel