When beta coefficient is more than 1 and dummy coded

[Tiziana]

Hi, in the results of pilot study, a coefficient was more than 1 (1.48). Hence , could you put 1 instead 1.48 in the bayesian design? Is it correct? I think that 1.47 is too high. Moreover, if i forget to identify that the attributes with only two leves are dummy coded, what are the implications in my subsequent bayesian design?
Thanks in advance

[johnr]

Hi Tiziana

A design is optimised for the specification you assume, hence if you treat an attribute as linear but later estimate the model as if it is non-linear, you will loose efficiency. Loss of efficiency implies larger standard errors and larger sample sizes than what you thought you would obtain/need when you generated the design. You can use model averaging to optimise for both.

The question is why do you think 1.48 is too large? do you not trust your pilot? In using a Bayesian design approach, you are assuming a distribution of prior parameter estimates, so you could potentially treat 1.48 as the upper bound in a uniform distribution. As I said above, if you change the prior, the design will be optimised under that assumption. If you are wrong, it simply means you will loose efficiency. So if you did make it 1, and it is truly 1.48, then you will loose efficiency. If you are right however, and it really is 1 in the population, then your design will be more efficient than if you assumed the prior to be 1.48.

John