Estimating confidence intervals (CIs) for the correlation has been a challenge because the correlation sampling distribution changes depending on the correlation magnitude. The Fisher z-transformation was one of the first attempts at estimating correlation CIs but has historically shown to not have acceptable coverage probability if data were…

We consider Bayesian estimation of a hierarchical linear model (HLM) from small sample sizes. The continuous response Y and covariates C are partially observed and assumed missing at random. With C having linear effects, the HLM may be efficiently estimated by available methods. When C includes cluster-level covariates having interactive or other…