Bayesian Post-Stratification Models Using Multilevel Penalized Spline Regression

• Activity Number: 138
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Survey Research Methods Section
• Author(s): Qixuan Chen*+ and Yajuan Si and Andrew Gelman
• Companies: Columbia University and Columbia University and Columbia University
• Keywords: Bayesian multilevel modeling ; poststratification ; penalized spline regression

Abstract

Poststratification is a standard approach to account for differences between survey samples and its target population by incorporating population distribution of variables into survey estimates. However, classical poststratification estimators can have unacceptably high variance because of sparse or empty poststratification cells. Instead, we proposed a multilevel penalized-spline poststratification model (MPPM), in which in the first level of model a distinct mean and variance are assumed in each poststratum, and in the second level of model the cell mean is further assumed to follow some distribution with mean as a spline function of inclusion probability. This multilevel modeling not only facilitates the estimation of cell mean in sparse or empty cells but also gains efficiency in the survey estimates by modeling the association between survey outcomes and the inclusion probabilities for cases in different poststratification cells. We compared the MPPM to the classical method using simulation studies and showed its application in a survey studying the mental health problems of Reserve and National Guard Service members returning from the conflicts in Iraq and Afghanistan.