An Area-Level Hierarchical Bayes Bivariate Threefold Linear Model for US State and County Indicators of Adult Skills in Literacy and Numeracy

Abstract

Significant enhancements have been made in small area estimation (SAE) methodology because there has been an increased demand for reliable estimates through SAE over the past decades. This article describes the advanced statistical methodology used to produce state and county model-based estimates of average scores and various proficiency levels of adults for all states and counties, using data from the first cycle of the US Program for the International Assessment of Adult Competencies and the American Community Survey. Challenges and issues are discussed especially in light of the small number of sample counties with survey data. Each major stage of the estimation process is discussed, including the approach for generating design-based survey estimates and modelled variances, identifying a set of predictor variables (available and measured consistently for all counties), the hierarchical Bayes linear threefold models, including bivariate models for proportions, and the diagnostics and evaluation.