I conducted an ACBC study and estimated the utilities with HB. Lighthouse Studio conveniently reports the part-worths (raw and zero-centered) and relative attribute importances which stem from the averages of every single respondent.

Now I would like to report the following:

1. 95% confidence interval for attribute levels.

Following the Bayesian approach, I take the alpha file and sort the utilities (after convergence) of every attribute level from low to high and note the 2.5th and 97.5th percentile for the interval. That part is easy.

However the confidence interval is based on the raw values reported in the alpha file. I would like to report part-worths using ZCD because I will anyhow report the zero-centered utilities as the main findings. Means, the confidence interval should also be on the same scale (ZCD, not raw).

How do I transform the (raw) utilities from the alpha file into the same ZCD scale that Lighthouse is using for the summary sheets. How do I proceed here?

PS: When I cumulate the average part-worths within an attribute (across all draws after convergence), I get 0 (well almost 0, it's a figure with lots of decimal values). --> Saw the raw figures somehow sum up to zero... So aren't they actually zero-centered? This is confusing...

2. Standard deviations:

In Bayesian statistics, is it common to report standard deviations? If yes, I would also need the zero-centered ones? (this ties to question 1 above)

3. Significance of attributes and attribute levels

If I wanted to follow the Bayesian approach, I have to think a bit differently and count the percentage of alpha utilities (for every level) with the same sign. Is that correct?

So I would not declare an attribute level based on the Frequentist 95% convention, but just report as it is: e.g. if 92% of alpha draws have negative sign, I can say that with a confidence of 92% the level is "significant". Is that right?

In terms of attribute significance. I read in another thread that it does not make sense to calculate this, not just because it takes some effort but because in the end it's all relative and highly dependent on the level ranges and so on.