Prior - Only know the sign (DCE newbie)

[mbarrowc]

Hello all,

My question is in regards to prior values. I have read previous posts and literature on this topic but still have a couple of questions. In my study, I only know the direction (sign) of my priors. Thus, I know I want to input the sign in to get a more efficient design but am unsure of the magnitude. Two questions I have can be summed up as:

(1) If I only know the sign of the priors do I just scale all priors so that each attribute is equal in effects? Or, if I believe that some attributes have a larger impact do I scale them accordingly? Under the first situation, it is my understanding that if you have for example 2 attributes (A&B) with 3 levels each and the attribute levels of A average 10 while the attribute levels of B average 5, than if I were to only know the sign and presumed that each had a similar impact, than I could input a prior of 0.01 for A and a prior of 0.02 for B, thus telling Ngene that both are positive and equally effect the decision.

(2) If I only know sign of the prior, not the actual level, am I able to look at nonlinear effects in ngene; i.e. dummy & effects coding?


I hope my questions were clear. Thank you for your help.
Michael

[admin]

If you only know the sign of the priors, but have no idea (not even a guess) about the actual value, you can either choose a small value very close to zero (e.g. 0.001 or -0.001) or use Bayesian priors (e.g. (u,-0.3,0) for a negative prior). The sign of the prior is important as it enables Ngene to eliminate dominant alternatives in an unlabelled experiment by putting a * behind the alternatives (e.g. ;alts = optionA*, optionB*). It will have an efficiency close to that of an orthogonal design (but in the case of Bayesian design, more robust) since you have not specified sufficiencly accurate levels of the priors. The more correct you are about the priors, the more efficient your design will be.

You are correct that 0.01 * 10 and 0.02 * 5 means that both attributes have an equal impact on utility, so you can indeed use such a rationale.

You are also able to look at nonlinear effects by adopting dummy or effects coding, you will need to set a prior for each of the levels. This means you would need to know the shape of the nonlinearity in order to know the signs of the dummy coded variables. If you do not know the shape, you may use zero priors, or for example a Bayesian prior like (n,0,0.1).

Note that when using inaccurate guesses for the priors (such as using small values for just entering the sign), the S-estimates will be very unreliable, as they are not based on accurate priors, so it is best to ignore them. You may pilot your design first with some colleagues, collect some data, and obtain better priors for generating the final design, and also get a better estimate for the sample size requirements.

[mbarrowc]

Thank you admin.

I do plan on piloting my design. However due to certain constraints will probably only be able to get 30 responses, maybe a little more for the pilot. The utility function I am basing my final design on will be nonlinear. With that being said, do you recommend piloting a design using linear or nonlinear effects? I understand what you said about ignoring the S-estimate when I am unsure of my priors yet I am not confident that I will get significant results from the pilot if I use a nonlinear utility function and receive 30 or so responses. Is it wise to use the pilot estimates if they are not significant as my priors for my final design?

Quick background: Right now my design contains 2 unlabeled alternatives that consists of 5 attributes each with 3 levels and a cost attribute with 4 levels along with a status quo option. I do know the signs (+,-) of each attribute along with a strong assumption about the relative magnitude of each attribute compared to the others. I followed your recommendation and use bayesian priors with a uniform distribution. I kept my priors small and scaled the priors accordingly to our assumptions regarding the magnitude of each attribute along with its level.

Thank you again for your help.
-Michael

[Michiel Bliemer]

(sorry I was logged in as admin last time)

Using 30 respondents should be enough for your pilot i think. Not all parameters will turn out significant, but that is not a problem, at least you get some indications for the parameter values and their uncertainty (the standard errors can be used for Bayesian priors).

You can optimise your design for estimation of nonlinear effects, and if in model estimation it turns out that they are not significant, you can always estimate linear effects. Even if you design your experiment assuming linear effects, you will likely be able to estimate nonlinear effects as well, so for the pilot it is not that important if you assume linear or nonlinear effects in your utility functions. However, if for some attribute you expect clearly nonlinear effects, then it is best to include them from the beginning in your design. Also for qualitative attributes you will have to use dummy or effects coding as well of course.