Constraint on the number of attribute levels for OOD design?

[Yuanyuan Gu]

Dear Michiel, John and others

First of all many thanks for making Ngene available to us. I found it very handy to use.

I recently used Ngne for an OOD design. The syntax is given below:


design
;alts = alt1, alt2
;rows = 16
;orth = ood
;model:
U(alt1) = b0 + b1*A[0,1,2,3,4,5,6,7] + b2*B[0,1,2,3] + b3*C[0,1,2,3]/
U(alt2) = b1*A + b2*B + b3 *C$


An OOD design was created but the 'D optimality' was shown as 'Undefined'.

I reduced the number of levels for A from 8 to 4 and ran it again:


design
;alts = alt1, alt2
;rows = 16
;orth = ood
;model:
U(alt1) = b0 + b1*A[0,1,2,3] + b2*B[0,1,2,3] + b3*C[0,1,2,3]/
U(alt2) = b1*A + b2*B + b3 *C$


This time 'D optimality' was shown as 94.494079%.

Base on this I suspect there is a constraint on the number of attribute levels for OOD design in Ngene. However, I could not find any text related to this constraint in the manual.

So here are my quesions:

(1) Is there such a constraint and if yes what is the constraint?

(2) Is a OOD design still valid when the 'D optimality' is 'Undefined'?

I look forward to your reply.

Many thanks,
Yuanyuan

[Michiel Bliemer]

No there is no constraint, but an orthogonal array for the levels of each alternative needs to exist. In this case, such an orthogonal array exists (you can check by looking at the correlations in the design (in the design window, see Design / Correlations / Pearson Product Moment for example, where you can see that there are no correlations between attribute levels within an alternative, only across alternatives).

Further, you can see that the D-error exists (0.0649).

The design is fine, it is just that the D-optimality criterion proposed by Street and Burgess cannot be calculated (maybe because they assume orthonormal contrast coding). I do not think there is any problem in using this design. The best check is always to do a little pilot study (just give to a few colleagues) and see if the questions make sense. If not, change attribute levels or possibly the design type.