The selection of priors for Bayesian efficient design

[Shan]

Dear Prof Bliemer,
I have several questions related to Bayesian efficient designs.

First, I have 16 parameters estimated in the pilot survey. However, only 7 of them are statistically significant, which can be used as Bayesian priors. I was wondering whether I can select another 3 estimations that are close to being significant (t-ratios are above 1.5) in the pilot survey as Bayesian priors? If I can, am I supposed to assign the estimated values and standard errors directly as priors, or I should adjust their values?

Second, what values should I assign to the insignificant parameters in the Bayesian efficient design? Assign a minimal value as fixed priors, such as -0.0001 or 0.0001, or I can use the estimations from the pilot survey as fixed priors even though they are insignificant?

Many thanks,
Shan

[Michiel Bliemer]

There are two things to consider:

1. You want to have a maximum of 10 to 12 Bayesian priors as otherwise the simulation requires an extremely large number of draws (which requires very long computation times) or otherwise would be unstable. Therefore, you need to set some priors as fixed. Generally, I choose priors of attributes that are least important (i.e. smallest contribution to utility, not the smallest parameter value) as fixed.

2. Parameter values do not need to be statistically significant to be included as a Bayesian prior, so please feel free to include parameters that are not statistically significant. They will just have a wide distribution, which may require more draws for simulation. It may be that these statistically not significant parameters belong to attributes that contribute least to utility, so then just set them as fixed priors.

3. If priors have an unexpected sign, then I would set them to 0.00001 or -0.00001 depending on the expected design.

Michiel

[Shan]

[quote="Michiel Bliemer"]

Hi Michiel,

Thank you for your detailed reply. I have one more question related to the least important attributes. The attributes I used in the utility functions are all linearly additive. For example,
V(car)=b_tt_car*ttime_car+b_parking*parking_car
V(bus)=asc_bus+b_freq_bus*bus_freq+b_tt_bus*ttime_bus+b_fare_bus*fare_bus
V(metro)=asc_metro+b_freq_metro*metro_freq+b_tt_metro*ttime_metro+b_fare_metro*fare_metro
In this case, the smallest estimated parameters mean the smallest contribution to the utility, right?

Thanks,
Shan

P.S. Merry Christmas!

[Michiel Bliemer]

No, as the size of the parameters depends on the units chosen for your attributes.

utility functions are defined as U = b1 * X1 + b2 * X2 + ..., and a contribution to utility of attribute X1 is b1 * X1, you need to multiply the parameter with the average attribute level. For dummy coded parameters you only need to look at the parameter value.

Michiel

[Shan]

[quote="Michiel Bliemer"]

I see. Thanks!