Bayesian Design

[Andrew]

Hi,

first many thanks for the great support and advices given in this forum. I still consider myself as (advanced) beginner and am always thankful for any help.
I have a couple of questions concerning a Bayesian design we want to use for an upcoming project. Priors are not completely known. We only have the probable order of preference. Based on prior studies based (literature research) and good thinking we defined 1st levels with presumed values and standard deviation of 0.1. For uncertain remaining levels we used a normal distribution with mean 0.01 and standard deviation 0.02. As we want to test for non-linearity we consider using effects-coding. It does not take Ngene long to generate a design. But we are not really convinced of the result in terms of overlaps. We are fine with overlaps. And as there are attributes with different number of levels there should be overlaps within first 3 attributes in any case to ensure variance balance. But overlaps Ngene creates have a systematic we do not understand. My questions:

1. Why are overlaps inconsistent over attributes with 3 levels? There seem to be more overlaps within first attribute (A) and non-uniform overlaps within the second (B) and third attribute (C).

2.Is our approach and use of priors appropriate or might we encounter any difficulties with our design strategy?

3. With fixed priors the last levels is the result of the inverted sum of first levels. What is the presumed value for the last level in a Baysesian design?

Code: Select all

Design
;alts = alt1, alt2
;rows = 36
;block = 3
;eff = (mnl,d,mean)
;model:
U(alt1) =
b1.effects[(n,0.9,0.1)|(n,0.01,0.02)]  * A[60,45,30]    +
b2.effects[(n,0.8,0.1)|(n,0.01,0.02)]  * B[10,20,30]    +
b3.effects[(n,0.7,0.1)|(n,0.01,0.02)]  * C[0,10,30]      +
b4.effects[(n,0.6,0.1)|(n,0.01,0.02)|(n,0.01,0.02)|(n,0.01,0.02)|(n,0.01,0.02)] * D[0,1,2,3,4,5]  +
b5.effects[(n,0.5,0.1)|(n,0.01,0.02)|(n,0.01,0.02)|(n,0.01,0.02)|(n,0.01,0.02)] * E[0,1,2,3,4,5]  +
b6.effects[(n,0.4,0.1)|(n,0.01,0.02)|(n,0.01,0.02)|(n,0.01,0.02)|(n,0.01,0.02)] * F[0,1,2,3,4,5]  +
b7.effects[(n,0.3,0.1)|(n,0.01,0.02)|(n,0.01,0.02)|(n,0.01,0.02)|(n,0.01,0.02)] * G[0,1,2,3,4,5]  +
b8.effects[(n,0.2,0.1)|(n,0.01,0.02)|(n,0.01,0.02)|(n,0.01,0.02)|(n,0.01,0.02)] * H[0,1,2,3,4,5]  /

U(alt2) = b1 * A  + b2 * B  + b3 * C  + b4 * D  + b5 * E  + b6 * F  + b7 * G  + b8 * H  $


Many thanks.

Best
Andrew

[Michiel Bliemer]

1. I am not sure I understand your question. I ran the syntax, and yes there are typically overlaps in efficient designs (which is good), but I do not clearly see more overlaps in attribute A and am not sure what you mean with non-uniform overlaps? Can you perhaps post the design you get and indicate what problems you see?

2. From what I understand, your first level is most preferred, while all other levels have lower preference (but no ordering within the other levels), correct? If this is the case, then the priors are fine. The Bayesian standard deviation of 0.02 is very small, however, which indicates quite certain values of 0.01. I am not sure this is what you want. If they are uncertain, why not using a standard deviation like 0.1 or larger?

3. In the Bayesian case it is the same, namely last coefficient = -(sum first coefficients). The first coefficients are drawn from Bayesian distributions, so the last coefficient is drawn from the resulting negative sum of distributions.