A Bivariate Dirichlet-Multinomial Small Area Share Model with Application to Joint Estimation of School District Population and Poverty

• Activity Number: 310 - Modern Approaches to Small Area Estimation with Spatial Modeling and Machine Learning
• Type: Topic Contributed
• Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Survey Research Methods Section
• Author(s): Jerry Maples*
• Companies: U.S. Census Bureau
• Keywords: Small Area Estimation; Dirichlet Multinomial ; Poverty; School Districts; SAIPE

Abstract

The Small Area Income and Poverty Estimates (SAIPE) program produces estimates of the number of children, total and in poverty, for each school district across the United States. Currently, the estimation methodology for school district child population is based on the most recent decennial census school district to county shares that do not change between censuses. The methodology for school district poverty estimates is based on shares determined by the most recent ACS 5-year and Federal Tax data (see Maples 2007). Neither method is built on a statistical model framework. Maples (2019) proposed a set of independent Dirichlet-Multinomial share models to estimate the in-poverty and not-in-poverty school district to county shares. We extend the work from Maples (2019) to allow for dependencies between the two Dirichlet distributions for the in-poverty and not-in-poverty shares. With the prediction of shares from the model and the given county estimates of school-aged child population and poverty, estimates of the number of school-aged children in school district (both total and in-poverty) are derived along with their measure of uncertainty.