Overlapping and Partial profile

[Andrew]

Hi,

I have a couple of questions regarding different issues. Appreciate any answer.

We have a design with 8 attributes -> 3^3 and 6^5.

1. Is it possible to create a partial profile design with Ngene? That is, we would like to systematically show only 6 out of 8 attributes in any choice set.

2. How does Ngene handle overlaps?

3. Hope next question is not too weird. Concerning the following code, the design output shows that only 1st and 3rd levels of three-level-attributes are compared and the 2nd level is constantly overlapped. In terms of attributes with six levels, first levels are only compared with latter ones, e.g. 1 with 5, 1 with 4, 0 with 4, 2 with 3. What is the systematic behind this? Does Ngene assume a linearity because we did not specify any priors, not even signs? Especially concerning attributes with 3 levels, Ngene seems to imply there is no reason to estimate middle levels.

Code: Select all

Design
;alts = alt1, alt2
;rows = 120
;block =10
;eff = (mnl,d)
;model:
U(alt1) =  b2 * A[15,20,25]     
         + b3 * B[0,1,2]         
         + b4 * C[0,1,2]   
         + b5 * D[0,1,2,3,4,5]   
         + b6 * E[0,1,2,3,4,5] 
         + b7 * F[0,1,2,3,4,5] 
         + b8 * G[0,1,2,3,4,5]  /
U(alt2) =  b2 * A
         + b3 * B
         + b4 * C
         + b5 * D
         + b6 * E
         + b7 * F
         + b8 * G$


4. Why do we get different results (efficiency and design output) when using "real" values, e.g. 15, 20, 25 which is percentage in this case, instead of 0,1,2?

Thanks.

Andrew

[Michiel Bliemer]

All excellent questions.

1. Not in the current release version of Ngene. We have implemented this functionality in our research version of Ngene, to be released as version 2.0 (which is not eminent yet). We presented this capability at the International Choice Modelling Conference in Sydney last year. This involves actually the optimisation of two designs, namely the 'master' design which selects 6 out of 8 attributes (for example a BIBD design) and the actual design with attribute levels.

2. This is another functionality that can be taken into account by using a 'master' design. Kessels et al. have recently published some papers on this. Ngene cannot do this, this is again a version 2.0 feature.

3. Not a weird question at all. With linear effects (as you have specified in your utility functions, this has nothing to do with the fact that you have implicitly assumed zero priors, but due to the fact that you have not used dummy or effects coded coefficients). With linear effects, the most optimal design will be to use big differences between attribute levels. So with three levels, 0-2 = -2, 1-1=0, 2-0=2, will yield the largest trade-offs, as it contains two large trade-offs and 1 non-trade-off. This is more efficient than for example 0-1=-1, 1-2=-1, 2-0=2, which only contains 1 large trade-off and two smaller ones. This has to do with the formula of the Fisher information matrix. Since attribute level balance is assumed by default in Ngene, it will be forced to use the inner levels, however it would be more efficient to only use the two extreme levels when linear effects are considered. If you would include dummy or effects coded coefficients, then clearly this is an entirely different story, and there will be trade-offs between all levels, as otherwise the coefficient for the inner level cannot be estimated. So Ngene provides you with the most efficient design for the utility function that you specify. If you do not require attribute level balance, you can include ;alg = mfederov, which will find an even better design but relaxes the attribute level balance assumption (and will therefore not use the inner levels much).

4. The Fisher information matrix depends not only on the prior parameter values (which you have implicitly assumed all equal to 0), but also depends on the attribute levels, see for example Huber and Zwerina (1996). The wider you choose the levels, the statistically more efficient your design, as level range has a positive effect on the Fisher information (since trade-offs are larger). So in a D-efficient design you ALWAYS have to specify the 'real' attribute levels that you present to respondents and that you use to estimate your model. Only in case of dummy or effects coding these attribute levels are irrelevant. In case of orthogonal designs, attribute levels are again irrelevant.

[Andrew]

Michiel,

many thanks. This makes perfect sense and was of great help to understand Ngene better.
For our study with overlaps we are with Kessels etal right now. Looking forward to Ngene 2.0.

Best
Andrew

[rich_imr]

Greetings,

With regard to Andrew's first question, how would one estimate a choice model from the "partial" attribute profile design? When setting up the design in, say, NLOGIT would one code attributes that are out of the choice set as -888? Essentially coding it as a "missing attribute" and constraining the beta to 0 or is there a different method?

Any help is greatly appreciated!

Regards,

Richard

[Michiel Bliemer]

Attributes that do not vary within partial profiles are actually irrelevant (as long as you do not have interactions in your model and as long as your parameters are generic across alternatives; these are strict requirements for partial profile designs). Attributes that do not appear are assumed to be equal across alternatives and hence can be set to anything as they drop out. So you can set them all to zero, or to one, or to any value. The easiest would be to set attributes that do not appear in the choice task to zero.

I have no knowledge on Nlogit so I cannot comment there, but as above, setting to zero will work.

Michiel