Using dummy-coded vs effects-coded estimates as priors in Ngene

[sara38]

Hello everyone,

I am relatively new to DCE design and would appreciate some advice regarding priors and coding schemes in Ngene. For context, I first designed a pilot experiment using zero priors because I had no prior information available. I then collected data from 12 respondents and estimated an MNL model in Apollo. My intention is now to use the estimated coefficients and robust standard errors from this first pilot as Bayesian priors for a second pilot design in Ngene. My categorical attributes were specified using effects coding in Ngene. During analysis in Apollo, however, I estimated equivalent models using both dummy coding and effects coding, as I understand that these are simply alternative parameterisations of the same model and should lead to identical model fit and predictions, differing only in coefficient interpretation and scale.

What I am unsure about is which estimates should be used as priors in Ngene. For example, consider the attribute "Health" with three levels: Do nothing, Take probiotics and Take natural supplements

The estimated coefficients were:
Dummy coding:
Do nothing (base) = 0
Probiotics = 0.91 (rob s.e. = 0.22)
Natural supplements = 0.30 (rob s.e. = 0.26)

Effect coding:
Probiotics = 0.51 (rob s.e. = 0.12)
Natural supplements = -0.10 (rob s.e. = 0.14)
Do nothing = -0.4015

My understanding is that I should use (in Ngene) either:
dummy coding estimates with dummy coding: hlth.dummy[(n,0.91,0.22)|(n,0.30,0.26)] * SUPPLEMENT[0,1,2]
or
effect coding estimates with effect coding: hlth.effects[(n,0.51,0.12)|(n,-0.10,0.14)] * SUPPLEMENT[0,1,2]

However, someone from my department suggested that I could instead use the dummy-coded estimates together with an effects-coded specification in Ngene, i.e.: hlth.effects[(n,0.91,0.22)|(n,0.30,0.26)] * SUPPLEMENT[0,1,2], which sounds incorrect to me.

I have not been able to find any documentation or forum discussions that explicitly address this point.

Is it correct that the priors should be expressed in the same coding scheme as the Ngene specification, or is there a reason why dummy-coded estimates could be used directly within an effects-coded Ngene design?

The resulting designs are quite different, so I would be very grateful for any guidance.

Thank you!
Sara

[Michiel Bliemer]

Hi Sara,

You can use either dummy or effects coding. Coefficients in dummy coding are evaluated relative to the base level, whereas for effects coding this is relative to the mean utility. Given these differences, statistical significance of the coefficients have different meanings, where for effects coding they refer to differences to the base while for effects coding it is differences to the mean. In most cases, dummy coding has a more meaningful interpretation that is also easier to understand, but you can choose either type of coding. It is not a problem if you used effects coding in the design of the experiment and dummy coding during model estimation.

Another important thing to understand is that the LAST level in Ngene is the base level.

You do not mention the coding you adopted, so I assume the following:
0 = probiotics
1 = natural supplements
2 = do nothing

Then these are correct (so you understood correctly):
hlth.dummy[(n,0.91,0.22)|(n,0.30,0.26)] * SUPPLEMENT[0,1,2]
hlth.effects[(n,0.51,0.12)|(n,-0.10,0.14)] * SUPPLEMENT[0,1,2]

However, if 0 = do nothing, 1 = probiotics and 2 = natural supplements, then you need to use SUPPLEMENT[1,2,0].

You should not use estimates for dummy coefficients if you are using effects coding. When adopting priors from Apollo, you should use the same coding in Ngene.

Michiel

[sara38]

Hi Michiel,

Thank you so much for the quick reply and for confirming that I should use estimates for effects coefficients if I use effect coding in ngene.

Many thanks,
Sara