Prior information

[mires]

Hi dear listmembers

"If you already have some ideas about the priors (from literature study, or logically you know the sign of the parameter), it would be best to start with an efficient design"
How one can include prior parameters :
(i) knowing only the sign (ie.. price elasticity) but no idea about its range (random parameter) nor its value
(ii) knowing that attribute is ordinal (that coefficient must be lesser thant another one)

Is there any references, lecture, best pratice to read and integrate such information? and how incorporate such 'poor information' while building a DoE?

Best regards
Naji

[johnr]

Hi Naji

There is no literature on this that I am aware of, though I have both seen and used a number of different strategies over the past few years.

What many do is use an orthogonal design or an efficient design assuming zero priors for the pilot. What I typically do however is use Bayesian priors assuming a uniform distribution. This way you can control the sign, and account for ordinal nature of the priors. For example

b1[(u,-1,-0.5)]*X1[0,1,2] + b2[(u,-0.5,0)]*X2[0,1,2]

assumes that both priors are negative, and that b1 will be more so than b2.

The less information you have about the priors, the wider you can make the bounds of the distributions, though I would caution you about doing this too much. It can have some very undesirable effects. Firstly, the wider the bounds, the less efficient the design will tend to be, the greater the sample size. Secondly, I had one experience where I assumed priors that were not close to zero (see b1 above) with quite wide bounds and when I collected the data, due to a whole bunch of reasons (scale for example), the parameters when estimated were actually close to zero in magnitude (though significant). Hence, I would have been better off in that case using an orthogonal design generated under the null hypothesis.

I would be interested to hear other peoples experiences and how they handle this issue also.
John