Title: Adopting prior distributions for the variance-covariance matrices to fully specify an area-level bivariate hierarchical Bayes three-fold model for proportions of adult competency

Abstract:

The Program for the International Assessment of Adult Competencies (PIAAC) is a multicyle survey of adult skills and competencies sponsored by the Organization for Economic Cooperation and Development (OECD). For the U.S.PIAAC, survey data alone is not sufficient to produce reliable county-level estimates for all the counties, the county-level sample sizes being as small as zero. Westat developed small area estimation model-based techniques to combine sparse PIAAC survey data with data from auxiliary sources, to improve the precision of the estimates for counties with survey data, and to produce estimates for counties with no survey data.

For example, using the 2012/2014/2017 U.S. PIAAC survey data and data from auxiliary sources, a bivariate three-fold model was developed for two adult competency proportions (Level 1 and below, and Lever 3 and above), and specified as a hierarchical Bayes model, with priors adopted for the components of the variance-covariance matrices decomposed into a vector of standard deviations and a correlation matrix: half-Cauchy distribution adopted as prior for the standard deviations and LKJ (named for developers Lewandowski, Kurowicka, and Joe) distribution adopted as prior for the correlation matrix (LKJ-type priors). This presentation focuses on some of the internal model validation techniques that lead to the development of this model. Particularly, the performance of LKJ-type priors is compared to the performance of a traditional prior, the inverse-Wishart distribution. Statistical code is provided for the model specifications investigated, in R STAN.