I was wondering if somebody could help me understand stan_(g)lmer better.
I have four questions, using as an example a simple hierarchical model where only the group-specific intercepts are modeled: stan_lmer(outcome ~ treatment + ( 1 | group),…).
- Just for clarification, does stan_(g)lmer model group-specific parameters as deviations from the global mean (e.g., from the global intercept)? I infer this from this rstanarm vignette and also from the output summary where the number of group-specific intercept parameters (excluding “(Intercept)”) estimated is equal to the number of groups (rather than the number of groups minus one, as it would be in the case of frequentist fixed-effect models).
- Also for clarification, does a prior for the covariance matrix (decov or lkj) control for the standard deviation, rather than the variance, of the normal distribution for group-specific parameters?
- This rstanarm vignette also says, “In the case where 𝚺 is 1 ×1, 𝜏 is the cross-group standard deviation in the parameters and its square is the variance (so the Gamma prior with its shape and scale directly applies to the cross-group standard deviation in the parameters).” In terms of actual code, if I set decov as, for example, decov(shape = 1, scale = 0.2), will it set the hyperprior on the standard deviation (and not the variance) parameter of the normal distribution for the group-specific parameter (say, group-specific deviations from the global intercept) as Gamma(shape = 1, scale = 0.2), or equivalently, Exponential(rate = 5)?
- Am I correct to understand that decov() does not have an autoscale argument and, therefore, I need to manually adjust a value for the scale argument, depending on my prior belief on the degree of the deviations of the group-specific parameter from the global mean?
I would appreciate your assistance!