Unlabelled efficient design always present the same levels

[paul]

Hello everyone,

I've used Ngene to generate a few unlabelled factorial plans presenting two alternatives, using efficient design.
I noticed that there was a perfect correlation between the attributes' levels chosen by Ngene.
e.g. For an attribute of time with levels [1,2,3,4], the questions will always include level 1 Vs 4 or level 2 vs 3, and never 1 Vs 3 or 4 Vs 4 or any other combination.

Is this a normal properties for efficient design ? I would have expected some question to present the same level for an attribute X, in order to be able to analyse the other attributes Ys without interference of X.

Best,
Paul

[Michiel Bliemer]

If you used zero priors and numerical attributes, then yes this is expected since 1 vs 4 and 2 vs 3 will generate more information (and hence more efficiency) than other comparisons. Fisher information is maximised if trade-offs are large, hence an design will prioritise comparing extreme levels (1 vs 4) and for attribute level balance it will also include the other levels (2 vs 3). If you let go of attribute level balance, for example when using the modified Federov algorithm, then it would mainly show 1 vs 4 and not use 2 vs 3 at all.

If you use categorical attributes that are dummy or effects coded, then you would see more variation in the level comparisons.

If you use non-zero priors, then you will likely also see more variation in the attribute level combinations since efficiency is optimised at specified choice probabilities.

If there is a dominant attribute, for example price with a large negative parameter, then Ngene WILL also include attribute level comparisons such as 1 vs 1 and 2 vs 2 to allow trade-offs across other attributes.

In summary, the actual attribute level comparisons depend heavily on the coding (dummy/effects or not) and the priors you use. If you want all combinations to appear equally across your choice tasks, you will need to use an orthogonal design (but this comes at the cost of a lower efficiency and cannot avoid dominant alternatives).

Michiel

[paul]

Thanks a lot for the explanation, I will read some more on Fisher informations and the different algorithms but your answer already made it a lot more clear.

Best,
Paul