Orthogonal design with interactions

[claudiab]

Hello,

I am trying to generate an orthogonal design with interactions. When I include the command "block" in the syntax, the program crashes.

Here is the code I would like to run:

Design
;alts = alt1, alt2, alt3
;orth = seq
;rows = 24
;block = 2
;model:
U(alt1) = b1*PR[1.75,2.75,3.75,4.75] + b2*CL[0,1] + b3*CF[0,1] + b4*AN[0,1] + b5*CL*CF + b6*CL*AN/
U(alt2) = b1*PR + b2*CL + b3*CF + b4*AN + b5*CL*CF + b6*CL*AN$

I am wondering if I can ask for some help to fix the problem.
Thanks in advance.
Claudia

[Michiel Bliemer]

I am not sure why Ngene crashes. Which version of Ngene are you using?

I ran the syntax on version 1.1.2 and I obtain the following design:

Code: Select all

Choice situation   alt1.pr   alt1.cl   alt1.cf   alt1.an   alt2.pr   alt2.cl   alt2.cf   alt2.an   Block   alt1.cl*alt1.cf   alt1.cl*alt1.an   alt2.cl*alt2.cf   alt2.cl*alt2.an
1   3.75   0   1   1   1.75   0   1   0   2   0   0   0   0
2   2.75   1   0   1   1.75   1   1   1   1   0   1   1   1
3   4.75   1   1   0   2.75   1   0   0   1   1   0   0   0
4   3.75   0   0   1   1.75   1   1   1   2   0   0   1   1
5   1.75   1   0   0   3.75   0   0   1   2   0   0   0   0
6   2.75   0   1   0   4.75   0   0   0   1   0   0   0   0
7   1.75   0   1   0   3.75   1   0   0   1   0   0   0   0
8   3.75   1   0   0   2.75   0   1   1   1   0   0   0   0
9   2.75   0   0   1   1.75   1   0   0   2   0   0   0   0
10   1.75   1   1   1   2.75   0   0   1   1   1   1   0   0
11   4.75   0   0   0   1.75   0   0   1   2   0   0   0   0
12   4.75   1   1   1   3.75   0   1   0   1   1   1   0   0
13   1.75   0   0   0   2.75   0   1   0   1   0   0   0   0
14   1.75   1   1   1   4.75   0   1   1   2   1   1   0   0
15   4.75   0   0   0   2.75   1   1   0   1   0   0   1   0
16   3.75   1   1   0   4.75   0   0   0   2   1   0   0   0
17   2.75   0   1   1   3.75   1   1   0   2   0   0   1   0
18   4.75   1   0   1   4.75   1   1   0   2   0   1   1   0
19   3.75   1   0   1   2.75   1   0   1   1   0   1   0   1
20   4.75   0   1   1   3.75   0   1   1   1   0   0   0   0
21   2.75   1   1   0   4.75   1   1   1   2   1   0   1   1
22   1.75   0   0   1   4.75   1   0   1   1   0   0   0   1
23   3.75   0   1   0   3.75   1   0   1   2   0   0   0   1
24   2.75   1   0   0   1.75   0   0   0   2   0   0   0   0


[Michiel Bliemer]

Alternatively, you can create a foldover design, which ensures that there is no correlation between main effects and interaction effects:

Design
;alts = alt1, alt2, alt3
;orth = seq
;rows = 12
;foldover
;model:
U(alt1) = b1*PR[1.75,2.75,3.75,4.75] + b2*CL[0,1] + b3*CF[0,1] + b4*AN[0,1]/
U(alt2) = b1*PR + b2*CL + b3*CF + b4*AN$

With ;foldover ther will automatically be two blocks.

[claudiab]

Dear Michiel,
Thank you very much for your kind reply. I am sorry if I reply just now. I have been traveling in the last weeks and have not checked the Ngene post. A colleague of mine was able to get a newer version of Ngene and we finally got our design. Thanks again for your availability.

I hope you do not mind if I take advantage of this post to ask for some suggestions.

I am working on a CE where we are going to use different treatments. The treatments will differ in terms of how we describe one of the CE attributes. To illustrate, we are using beef as product in question and one of the CE attributes is irradiated beef. Specifically, in one treatment we will specify this attribute as “irradiated”. In the other one as “bacteria free”.
I would like to use a Bayesian D-efficient design for this experiment, but I am wondering how I should specify the prior of the “irradiated beef” attribute. This is because the attribute might be evaluated differently by respondents belonging to the two treatments. Any suggestion would be extremely appreciated.

Finally, I have one more question. In another CE study we used a Bayesian D-efficient design without including interaction effects between the attributes. For curiosity, I ran a RPL model including interaction effects and I got interesting results. In the design, I used a number of choice tasks that is higher than the degrees of freedom I have when I also consider the interaction effects. Given the “good” number of choice tasks, I was wondering whether it would be ok to estimate a model accounting for interaction effects, although the interactions were not specified in the utility function of the design.

Thanks a lot for all your support and apologies again for my late notice.

Claudia

[Michiel Bliemer]

To answer your two additional questions:

1. Perhaps you could treat the description of the beef as an additional attribute that to interact with beef. Something like:
U(alt1) = ... b1*beef[1,2,3] + b2.dummy*beefdescr[1,2] * beef + ...
If you would rewrite this, the model you are estimating is (b1 + b2*beefdescr) * beef. In other words, b2 would capture the effect that the description of beef will have on the preference of beef, i.e. the adjustment of b1.

2. You will typically be fine including interactions. The only time where it can go wrong is if the interaction effect is perfectly correlated with one of the other attributes. This is unlikely to occur, especially if you have a sufficiently large number of choice tasks as you indicate. Note that orthogonal designs result in zero correlations, but zero correlations is not necessary for model estimation, even high correlations are fine, as long as they are not perfectly correlated.

Michiel

[claudiab]

Michiel,
Thank you very much for the suggestion.

1) Regarding my question related to the beef experiment, I do not know if I understood correctly your suggestion. The design is an unlabeled design with two beef product options and a no-buy option. “Irradiated” is one of the four experimental attributes (sorry.. I should have mentioned this before)
Here is what I understood:
I would generate a design like this:

Design
;alts = alt1, alt2, alt3
;rows = 24
;block = 2
;eff = (mnl,d)
;model:
U(alt1) = b1*PR[4.50,8.50,12.50,16.50] + b2.dummy*IR[1,0] + b3.dummy*IRdescrb[1,0] + b4.dummy[(n,0.41,0.12)]*CF[1,0] + b5.dummy[(n,0.63,0.14)]*AN[1,0]/
U(alt2) = b1*PR + b2*IR + b3* IRdescrb + b4*CF + b5*AN$

In preparing my choice tasks to present to the respondents, when the attribute related to the use of irradiation process is present (IR=1), will be described as “irradiated” if IRdescrb=0, while it will be described as “bacteria free” if IRdescrb=1. Then, I will estimate the model using (b2+ b3.dummy*IRdescrb). The information regarding the (b2+ b3.dummy*IRdescrb) coefficient will be used as a prior of IR in the Bayesian design . Is it correct?

Actually, we have already collected data from a pilot just using only the term “irradiated” to describe the use of irradiation process on beef. So in case there is not the possibility to run a second pilot, I was thinking that one possibility would be to define the prior of the irradiated beef as a uniform distribution as follows: (u,-0.5,0.5), while the other attributes priors with a normal distribution and means and standard errors from the pilot, e.g (n, -0.21, 0.02). Do you think it could work?

2)About the interaction effects, I think there are no problems. I checked the correlation matrix of the interactions in the Ngene output and I had a maximum value of 0.5. Just a curiosity.. in the case of interactions of the same attributes between the two alternatives, e.g. alt1AN*alt2AN, I observed that there is an exclamation mark (!). What does it mean?

Thank you so much again for all your help and sorry for all these long posts.

Claudia

[Michiel Bliemer]

It is difficult for me to exactly understand what your experiment is about, as my previous suggestion to use an interaction term may actually not be necessary and the syntax formulation you propose may be fine.

Just to be clear, if you say that the description of beef varies across treatments, does this mean that the description is the same for both alternatives in each choice task? So it cannot happen that alt1 is bacteria-free beef and in alt2 it is irradiated beef? And does one respondent only see one description while another respondent sees the other, or is it varied across choice tasks in which respondents see both descriptions? Could you perhaps give a few examples of what the choice tasks actually look like? Once i better understand what you are doing I will do my best to provide an answer.

I am not sure I can answer the question about the exclamation marks. I would assume it is a value that Ngene cannot compute (like division by zero), but i would have to be able to reproduce it on my own computer to understand what is exactly happening.

Michiel

[claudiab]

Michiel,
Thank you very much for your interest and sorry for being vague in the description of the experiment.
Yes, the description of the attribute will be the same in both alternative 1 and alternative 2. It is a between subjects treatments approach: one respondent will see only “irradiated” and another respondent will only see “bacteria free”.

In treatment 1 respondents will see 12 choice tasks like the following (in alt1 and alt2 the product is a beef steak):

Alt1 Alt2 Alt3
Irradiated Irradiated
Carbon foot print label Neither
Antibiotics free
$4.50 $16.50

In treatment 2 the respondents will see 12 choice tasks like the following:

Alt1 Alt2 Alt3
Bacteria Free Bacteria Free
Carbon foot print label Neither
Antibiotics free
$4.50 $16.50

In both treatments, we are giving some information about the attributes before individuals answer the CE questions. The information will be the same in both treatments, so same information will be given for “Bacteria Free” and “Irradiated”. However, we are expecting that according to how we label this attribute, i.e. bacteria free or irradiated, individuals will evaluate this attribute differently. For now, we conducted a pilot using the claim “irradiated” for the attribute related to the use of irradiation. We would like to use the same experimental design for treatment 1 and treatment 2. However, my worrying is whether it would be appropriate to implement in treatment 2 (where the use of irradiation will be labeled as “bacteria free”) a Bayesian design using a prior for the irradiation attribute that has been obtained from a pilot where it was labeled differently. For this reason, I was thinking to specify the prior of the dummy variable “use of irradiation” with a uniform distribution from -0.5 to 0.5, while specify the priors of the other attributes with a normal distribution using mean and standard errors from the pilot estimates, but I am not sure if this can be ok.
Please see below codes I would like to use:
Design
;alts = alt1, alt2, alt3
;rows = 24
;block = 2
;eff = (mnl,d)
;con
;bdraws = gauss(3)
;model:
U(alt1) = b1[(n,-0.21,0.02)]*PR[4.50,8.50,12.50,16.50]
+ b2.dummy[(u,-0.50,0.50)]*IR[1,0]
+ b3.dummy[(n,0.38,0.17)]*CF[1,0]
+ b4.dummy[(n,0.51,0.19)]*AN[1,0]
+ i.1[0]*IR.dummy[1]*CF.dummy[1]
+ i.2[0]*IR.dummy[1]*AN.dummy[1]/
U(alt2) = b1*PR
+ b2*IR
+ b3*CF
+ b4*AN
+ i.1[0]*IR.dummy[1]*CF.dummy[1]
+ i.2[0]*IR.dummy[1]*AN.dummy[1]/
U(alt3) = b5[(n,-1.26,0.20)]$

I hope it is more clear.

Regarding the interactions, if you run the code above, the interaction in question with the exclamation mark is alt1.cf*alt2.cf. However, I think that you already gave me the answer and thanks a lot for this.
I do appreciate all your effort to help me in the development of the design of this experiment. I hope you find it interesting
Thank you!
Claudia

[claudiab]

Sorry..

the 12 choice tasks for treatment 1 will be as follows:

Alt1= Irradiated - Carbon foot print label - Antibiotics free - $4.50
Alt2= Irradiated - No info about Carbon foot print label - No info Antibiotics free - $16.50
Alt3= Neither

the 12 choice tasks for treatment 2 will be as follows:

Alt1= Bacteria Free - Carbon foot print label - Antibiotics free - $4.50
Alt2= Bacteria Free - No info about Carbon foot print label - No info Antibiotics free - $16.50
Alt3= Neither

[Michiel Bliemer]

Ok I understand now.

I would suggest the following syntax. I think you made a mistake in naming the interaction parameters, you cannot name them i.1 and i.2 since Ngene does not recognise the period in the middle, so Ngene did something different from what you would expect. I have renamed the variable names, and i have added a third one that captures the effect of the description on IR. This interaction variable will be able to estimate the impact the description has on the preference towards IR, this would be the appropriate model to estimate I think. I have used a normal Bayesian prior with a relatively small standard deviation since I think this effect should not overpower the other effects, so it is best to keep it conservative. IRdescr is a scenario variable because it is constant across alternatives, you will see that I have put IRdescr[IRdescr] in the syntax, which means it ensures the level is kept the same. Regarding your blocking in 2, Ngene cannot guarantee that you blocking column will be such that in 12 blocks you have one IR description, and in another 12 blocks you have the other IR description. If they are unevenly represented in the blocks, then just be pragmatic and change one of the IRdescr levels manually.

Finally, note that giving 2 different sets of questions to different set of people makes it difficult to test for the effect of the description, since differences that you find can merely be a result of differences in the sample. This is the reason why typically you need to give both treatments that you want to tests for to all respondents. But in your case I can understand it is a bit problematic as the respondents may be quite confused if you just change the name but not the description. So please be aware that testing for differences across different samples is often not very strong.

By the way, no exclamation marks appear in my correlations...

Design
;alts = alt1, alt2, alt3
;rows = 24
;block = 2
;eff = (mnl,d)
;con
;bdraws = gauss(3)
;model:
U(alt1) = b1[(n,-0.21,0.02)]*PR[4.50,8.50,12.50,16.50]
+ b2.dummy[(u,-0.50,0.50)]*IR[1,0]
+ b3.dummy[(n,0.38,0.17)]*CF[1,0]
+ b4.dummy[(n,0.51,0.19)]*AN[1,0]
+ i1[0]*IR.dummy[1]*CF.dummy[1]
+ i2[0]*IR.dummy[1]*AN.dummy[1]
+ i3[(n,0,0.3)]*IR.dummy[1]*IRdescr[0,1]/
U(alt2) = b1*PR
+ b2*IR
+ b3*CF
+ b4*AN
+ i1[0]*IR.dummy[1]*CF.dummy[1]
+ i2[0]*IR.dummy[1]*AN.dummy[1]
+ i3[(n,0,0.3)]*IR.dummy[1]*IRdescr[0,1]/
U(alt3) = b5[(n,-1.26,0.20)]$

Michiel