I am currently writing my master thesis on linear multilevel models. Could someone explain to me how I can manually extract a specific hypothesis for some residual standard deviation of my model? For example, let’s say that I want to make the hypothesis tests in order to find the posterior estimates for the two residual standard deviations of my 2 treatment groups in their actual scale. So, the hypothesis will contain a vector:
c(“exp(sigma_Intercept) = 0”, “exp(sigma_Intercept + sigma_treatment2) = 0”).
I have noticed that the results of the latter hypothesis are slightly different, compared to when I am trying to do it manually through the summary of my model, by setting the posterior estimated parameters and use them in order to compute: exp(sigma_Intercept) and exp(sigma_Intercept+sigma_treatment2). The whole problem comes from me trying to reduce the number of my experiment subjects from a dataset, create a subset of this dataset, sample with replacement n-times, fit the Bayesian linear model n-times and in the end, extract a hypothesis test for my parameters, based on the mean of all the n-hypothesis for my parameters. That is why I am asking if I can somehow do it manually, because the only thing I can certainly achieve is to obtain a vector with the mean of all the n - posterior estimated parameters that I want, but not hypothesis tests for them.