I have questions about the usage of draws from a MCMC. I estimate a hierarchical bayesian Multinomial Logit model (using bayesm in R). I am interested in the ratio of two coefficients 1 and 2, say b1/b2. 1. Is it better to calculate the mean of draws for each coefficient separately and then the ratio (mean(b1)/mean(b2)) or to calculate the ratio b1/b2 for each draw and then the mean of the ratios (mean(b1/b2 in draw 1; b1/b2 in draw 2 ...))? I assume, that the second idea is better? 2. An equivalent of "significance test" can be obtained for a coefficient by calculating mean and sd of the draws and then (mean(b1-Draws)/sd(b1-Draws). What can I do to test, if the ratio b1/b2 > 0? Can I simply calculate the ratio for each draw and take a look at the relative number larger than 0 (e.g. 97% of the ratios b1/b2 of my draws are >0 is equivalent to a p-value of 0,03)? 3. I also have to compare the ratio of the coefficients in two different experimental groups A and B. The Hypotheses is, that b1A/b2A > b1B/b2B. One idea is to estimate only one model and use group membership as a concomitant variable in the model. However, can I also estimate separate models for both groups and compare the draws (Calculate b1A/b2A for each draw in group 1; calculate b1B/b2B for each draw in group 2; look for each draw, if b1A/b2A > b2A/b2B)?
Thank you for any help! Stefan