Unexpected priors

[ASAL2433]

Hi,

I’m working on an experimental design and have completed a pilot study with 100 participants to obtain priors for a D-efficient design. For one of the attributes, the coefficient was unexpectedly negative. This coefficient was also not significant, at a p-value of 0.005.

For the final design, instead of using the pilot coefficient for this attribute, I assigned a small positive value (0.001). However, the s-estimate for this attribute is now over 3,000, while for all other attributes, it is under 200.

Should I assign a coefficient value of 0.001 for this attribute, and is it normal for the s-estimate to be this large?

Thanks,
Amber

[Michiel Bliemer]

If the sign is unexpected then I would indeed set the prior manually to the expected sign but keep it sufficiently close to zero. You can use a Bayesian uniform prior if you believe you have a good feeling about an appropriate upper bound, while the lower bound is 0.

For priors manually set close to zero you need to ignore sample size estimates because they are not meaningful as they will go to infinity as the prior is close to zero. Only sufficiently reliable non-zero priors provide meaningful sample size estimates.

Michiel