Priors and scale

[davidj]

Hi All,

I have a following question in relation to using priors for the initial development of a Bayesian efficient design.

The only prior information I have is the sign, so will be initially using a uniform design, with priors very close to zero ( as I do not now the magnitude). Please see the syntax below.

However, I am concerned about the units of my attributes and the associated impact on scale. For example, price is around 10K, but costs is in cents. Ie a relationship)

So would I do the following:

- Make all priors with a rating of 0.01 ( it is close to zero, but the scale impact would be out)
- Scale the priors – for example attribute A will be using .001 ( as it is 1000 times the value of attribute b) and attribute 0.01.

Any help or guidance, would be very much appreciated.

Thanks for all your help.

Cheers

James

Syntax:

Design
;alts = cv, ev1*, ev2*
;rows = 9

;eff = (mnl,d, mean)
;bdraws = halton(200)
;model:

U(cv) = b2[(U, -0.00001,0)] * A.ref[30000] + b3[(U, -0.01,0)] * B.ref[20] + b4[(U,0,0.001)] * C.ref[850] + b5[(U, -0.001,0)] * D.ref[180] + b6[(U, 0,0.01)] * E.ref[10] /
U(ev1) = b7 + b2 * A.piv[10000,20000,30000] + b3 * B.piv[-20%,-40%,-60%] + b4 * C.piv[-85%,-70%,-55%] + b5 * D.piv[-100%,-90%,-80%] + b6 * E.piv[0%,10%,20%]/
U(ev2) = b8 + b2 * A.piv[10000,20000,30000] + b3 * B.piv[-20%,-40%,-60%] + b4 * C.piv[-85%,-70%,-55%] + b5 * D.piv[-100%,-90%,-80%] + b6 * E.piv[0%,10%,20%]$

[Michiel Bliemer]

Your approach will be fine either way if you are using the D-error as efficiency measure. A design that minimises the D-error for one set of units will also minimise it for another set of units. But they do have to make sense (as they influence the probabilities), so I think you have used a good approach by ensuring that the contribution to utility (beta * attribute) is not too large and similar for all attributes.