Problem with bayesian efficient design + mfederov

[marianne.lefebvre]

Dear all,
I have read with interest the posts concerning bayesian efficient design and modified federov to add constraints, but I could not find any answer to the following question:
Why can Ngene not find a bayesian efficient design with the following structure ?
Priors are based on RPL estimation of pilot data (n=24). May be se are too large ?
I have tested with an efficient design based on CL estimation of pilot data and same constraints. This is working well.
Thanks a lot
Marianne

Design
;alts=GA*, GB*, SQ
;rows = 12
;block = 3
;rep=1000

;eff = (mnl,d,mean)
;alg=mfederov
;reject:
? If A/B offers better Indemnity and Expert while the other is Index (or both index or both experts) then not cheaper
GA.C>GB.C and GA.B<=GB.B and GA.D<GB.D,
GB.C>GA.C and GB.B<=GA.B and GB.D<GA.D

;model:
U(GA) = b1.dummy[(n,-1.258,1.418)]*A[1,0] + b2.dummy[(n,-0.880,3.284)]*B[1,0] +b3[(n,0.0597,0.0959)]*C[40,45,50,55,60,65] +b4[(n,-2.121,3.572)]*D[1,3,4,5,6,8] /
U(GB) = b1*A + b2*B + b3*C + b4*D /
U(SQ) = b0[(n,-2.011,3.905)]
$

[Michiel Bliemer]

Apologies for the late response, I was travelling for two weeks.

Your script shows an MNL model with Bayesian priors, but you mention a random parameter logit model with random parameters. These are two different things. Please use priors from the conditional logit estimation as Bayesian priors, I would not recommend using priors from a random parameter logit model.

In your script, none of the priors seem to be statistically significant, unless you are mixing up Bayesian priors with random parameters. For example, b4[(n,-2.121,3.572)]*D[1,3,4,5,6,8] means a Bayesian prior with mean -2.121 and standard deviation 3.572. Multiplying -2.121 with 1 to 8 results in an unrealistically large contribution to utility, and the standard deviation makes this even more extreme. In short, your priors do not make sense, they cannot be correct. Please look at the parameter estimates from your MNL model and use the beta parameters as mean and the standard errors as standard deviations. Make sure that you use exactly the same attribute coding on both model estimation and in Ngene.

Another comment: a status quo alternative should typically have attribute levels. Your SQ alternative only has a constant (like an opt-out alternative), whereas the SQ alternative usually has fixed levels for attributes.

Michiel

[marianne.lefebvre]

Dear Michiel
Thanks a lot for your answer. I now understood that bayesian efficient design can be generated based on pilot estimates from MNL.
I have another question
In the bayesian efficient design based on MNL model I have now generated, many of the price (D attribute) and indemnity (C attribute) levels are not in the choice cards. I guess this is due to the priors that show that respondants strongly prefered cheaper contracts with better indemnity. Six levels may therefore not be necessary. In the final paper, should I indicate the levels presented to the respondents in the final experiment, or the one envisaged by the researchers (and included in the pilot experiment) ?

;model:
U(GA) = b1.dummy[(n,-0.537,0.218)]*A[1,0] + b2.dummy[0]*B[1,0] +b3[(n,0.0354,0.0132)]*C[40,45,50,55,60,65] +b4[(n,-0.109,0.052)]*D[1,3,4,5,6,8] /
U(GB) = b1*A + b2*B + b3*C + b4*D /
U(OO) = b0[(n,1.13,0.71)]

Here is the design
Block Choicenumber C_Group1 C_Index1 C_Indem1 C_Price1 C_Group2 C_Index2 C_Indem2 C_Price2 C_Group3 C_Index3 C_Indem3 C_Price3
1 1 0 1 40 1 1 0 65 6 0 0 0 0
1 2 0 0 45 8 1 1 65 1 0 0 0 0
1 3 0 0 65 8 1 1 40 1 0 0 0 0
1 4 1 0 65 3 0 1 40 1 0 0 0 0
2 1 1 0 65 8 0 1 60 1 0 0 0 0
2 2 0 0 55 1 1 1 60 8 0 0 0 0
2 3 1 1 65 8 0 0 45 1 0 0 0 0
2 4 0 1 40 8 1 0 40 1 0 0 0 0
3 1 0 0 40 8 1 1 65 1 0 0 0 0
3 2 0 0 65 3 1 1 40 1 0 0 0 0
3 3 0 1 65 8 1 0 40 1 0 0 0 0
3 4 1 0 45 1 0 1 65 8 0 0 0 0

Thanks for your suggestions
best wishes !

[Michiel Bliemer]

When using the modified Federov algorithm, it is recommended to apply attribute level balance constraints to make sure that all levels are used. For example, D[1,3,4,5,6,8](1-3,1-3,1-3,1-3,1-3,1-3] to indicate that each level should appear between 1 and 3 times across the 12 choice tasks. You could also add +1*(imbalance) to the ;eff property to increase the likelihood of a more balanced design. Note that intermediate levels are not strictly necessary to estimate a linear effect, which is why they are omitted since it is more efficient to only use the extreme levels, but if you want to test for nonlinearities then they would be necessary.

Michiel