PriorConcentration in Bayesian Contigency Tables
Hi all,
I am testing a directional H1 for a 2x2 contingency table. I am looking at it in R as well as in JASP in order to understand. I set the sample to "joint multinomial" (I analyse the data in both frequentist and bayesian way. Thus I had a fixed N given from a power analysis).
My question is now whether prior concentration should remain at the default value of 1 or whether I should adjust it. I have looked at Jamil et al. 2017 (Default “Gunel and Dickey” Bayes factors for contingency tables).
The following lines seem relevant to me, without nearly understanding the whole math behind:
For the matrix of prior parameters a∗∗ (i.e., the gamma shape parameters of the Poisson rates for the cell counts, see below), a default value is obtained when each arc=a=1 – in the multinomial case, this indicates that every combination of parameter values is equally likely a priori. Higher values of a bring the predictions of ℋ1 closer to those of ℋ0;
--> In my mind, this is now related to how big the effect I expect under H1 is. Is that correct?
And if yes, what Prior Concentration should be chosen in case I expected an effect of "medium" size (Cramers V = 0.3). The actual effect size I found for these data was V = 0.13.
Any thoughts on this or a link to a practice oriented paper will be highly appreciated! Many thanks in advance.
Best wishes
Christoph
Comments
Hi Christoph,
If you are testing the difference between two proportions, I would recommend the AB-test instead (see for instance https://osf.io/preprints/psyarxiv/z64th) You can find many papers on this test on my website (https://www.ejwagenmakers.com/papers.html).
The a parameter represents, roughly, the number of hypothetical prior counts in the different cells.
Cheers,
E.J.