Size of priors for bayesian D-efficient design

[hae-young.kim]

Dear Dr Bilemer,

This is my first time using the Ngene to design a DCE design, and I would really appreciate your thoughts and help on finalizing the design. Based on the information from a previous study conducted in a similar setting, I set the priors then conducted a pre-test study among 12 participants, in which each respondent received 9 choice sets. I used the following syntax to generate the design:

;alts= alt1*, alt2*
;rows=18
;eff = (mnl, d)
;block = 2
;model:
U(alt1) = b1.dummy[0.2|0]*Location[1,2,3] + b2.dummy[-0.2|-0.2]*Frequency[1,2,3] + b3[-0.1]*Time[0.5,1,2] + b4.dummy[-0.2|0]*Other_needs[1,2,3] + b5.dummy[-0.2|0]*Adherence[1,2,3] + b6[-0.2]*Confidential[1,2] /
U(alt2) = b1.dummy*Location + b2.dummy*Frequency + b3*Time + b4.dummy*Other_needs + b5.dummy*Adherence + b6*Confidential
$

I got the following beta (and SE of beta) by fitting a multinomial/conditional logit.

Location 1: beta= 0.756, SE = 0.24
Location 2: beta= 0.05, SE = 0.24
Frequency 1: beta= -0.05, SE=0.24
Frequency 2: beta= 0.006, SE=0.23
Time: beta=0.344, SE=0.27 (continuous variable)
Other_needs 1: beta= -0.205, SE=0.22,
Other_needs 2: beta=-0.766, SE=0.22
Adherence 1: beta= -0.20, SE=0.22,
Adherence 2: beta= -0.013, SE=0.24
Confidential: beta= -0.528, SE=0.17

In addition, I'd like to increase the number of rows to 48 with 4 blocks (thus each block has 12 questions, not 9 questions) and change it to bayesian D-efficient design to fit a mixed logit for the final analysis.

My questions are:
1) From the readings, I think the size of the prior matters but I am not sure whether I need to use the exact estimated betas from the pre-test study (for example, 0.756 for Location 1, instead of 0.2); or shall I use a smaller value like 0.10 or 0.20?

2) For the final analysis, I’d like to run a mixed logit model. Therefore, I would like use bayesian D-efficient design with some priors for both fixed and random parameters. Since I have run only a small pre-test study (n=12, 9 choice sets per respondent), I cannot fit a mixed logit (i.e., a mixed logit does not converge). What would you recommend to use as prior information for “random parameters”?

Thank you so much for your help and time.

[Michiel Bliemer]

1)
I think that you can use the parameters from your pilot study directly as Bayesian priors. The seem reasonable, not too large. So I think that you can use for example (n,0.756,0.24) as Bayesian prior. You could scale them down slightly if you think that your original design contained some weakly dominant alternatives.

You may want to check the signs of the betas for frequency 1 and 2 to make sure that the preference order is as expected, as currently these coefficients are not statistically significant and you could make small manual adjustments if you like.

2)
I would strongly recommend to optimise your design for the MNL model. It is computationally not really possible to optimise designs for the (panel) mixed logit model, even if you could obtain prior values. A design that is optimised for the MNL model will typically also work well for estimating mixed logit models.

Michiel