Careful: Order of operations, logit/ plogis, and psi/ p

[rBatt]

Need to be careful about transforming (draws from the) posteriors of JAGS models when they are represented as measures of central tendency: e.g., if something was lognormal, the distribution is parameterized as mean(log(x)), NOT as log(mean(x)). When using a measure of central tendency to condense the posterior output of the models, we are effectively doing the mean(x). Thus, it is incorrect to apply such transforms on the mean of the posterior and then compare to "true" values that have been correctly parameterized.

For an example of the effect:

vals <- replicate(1E2,{
                vals <- rnorm(1E3, sd=2);
                c("mean.first"=plogis(mean(vals)), "mean.second"=mean(plogis(vals)))
            })
            plot(t(vals)); abline(a=0, b=1)

All that being said, using the median as the measure of central tendency should help to greatly reduce this problem, because these transformations do not affect the rank/ order of the values (so nonparametric summary statistics should be more robust).