Confidence intervals for posterior intercepts, with application to the PIAAC literacy survey.

Abstract

For variance component models, it is often the posterior estimate of the random effect (‘posterior intercept’) rather than the estimate of the fixed effect parameters, which is of main interest. This is the case, for instance, when ranking region–wise mortality rates (where the crude, regional rates are unreliable due to small observed counts) or for the construction of educational league tables from complex sample surveys. However, in order to be able to decide whether two cluster–level units can actually be distinguished, it is clear that one needs a measure of variability of these posterior intercepts. We present an exploration of methods to address this issue which appears to be still undeveloped in the context of the model class considered.