Keeping base design but additonal level for an attribute?

[TimB]

We have inherited a experimental design. Now we are undertaking a new replication study, and we want to match the original study as closely as possible, ideally offering respondents the same choice sets. However, one attribute requires an additional level.

(The original was a 2^1 * 3^1 * 4^3 experiment, but now one of the 4-level attributes has become 5 levels. The original was a 16 alternative main effects design.)

I fully expect we need to create a new experimental design with similar design characteristics (OMEP).

However, I thought I would check if through NGENE or other tool it would be possible to calculate how many extra choice sets would be required to expand the experimental design with the additional level to one attribute. (i.e., not changing the existing design but adding new choices)

Any advise on the issue or on the use of NGENE for such tasks would be appreciated!

Thank you,
Tim

[johnr]

Hi Tim

Unfortunately, there is very little known about orthogonal arrays involving attributes with 5 levels. Most research has focused on OMEP designs for 2 or 3 levels. Using these designs as a base, it is then sometimes possible to then generate OMEP designs for attribute levels that are products of combinations of 2 or 3 levels (e.g., you might get a 4 level attribute made up from two 2 level attribtues - likewise, a 6 level attribute might be constructed from a 2 and 3 level attribute). In this case, Ngene and most other software will not be able to locate an OMEP design for 5 levels.

There is a trick you might try, but I cannot guarantee that it will provide a perfect OMEP design. Give the following a try:

Step 1: determine the number of choice tasks you will need at a minimum. This should be a number divisible without remainder by all attribute levels (in this case, 2, 3, 4 and 5). The smallest number I know of is 60 in this instance.

Step 2: Generate a sequential orthogonal design for a single alternative for the attributes that you want to keep from the original design. In this case, it will be 2^1 * 3^1 * 4^2 but in 60 rows. When you generate this design, create a blocking column with ;block = # of levels you want for the new attribute (in this case 5). See below:

Design
;alts = Alt1, Alt2
;rows=60
;eff= (mnl,d)
;orth=seq
;block=5
;model:
U(alt1) = b1[0]*x1[1,2] + b2[0]*x2[1,2,3]
+ b3[0]*x3[1,2,3,4] + b4[0]*x4[1,2,3,4] $

This will generate a design that will be near orthogonal for the block (it will try and minimise the correlation between the design and blocking column). You can then use this blocking column as your 5 level attribute.

Note that the program will randomly try different combinations for the blocking column and has a relatively short number of iterations, before it gives you the result. You can increase the time it takes to search (so it will search more combinations) say by changing the ;block = command to ;block=5,total(2 mins). This is explained on P196 of the manual.

John