Imputation of Ordinal Data in the Agricultural Resource Management Survey Using Bayesian Methods

• Activity Number: 615 - Bayesian Methods for Complex Survey Designs and Data
• Type: Topic Contributed
• Date/Time: Thursday, August 3, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Christopher Burns* and Sujit K Ghosh and Daniel Prager and Li Zhang
• Companies: USDA-Economic Research Service and North Carolina State University and USDA-Economic Research Service and George Mason University
• Keywords: Latent distribution ; Bernstein Polynomials ; Missing Data ; Iterative Sequential Regression ; Survey Data

Abstract

Missing data in complex surveys is a well-known and persistent problem.The problems of missing data can be further compounded when the data are ordinal instead of continuous (e.g. economic surveys often ask respondents to report their financial information in value codes). Ordinal data often represent a discrete realization of an unobserved (latent) continuous distribution, where the upper and lower limits of each interval can be viewed as cut points in the latent density. In complex high-dimensional surveys like the Agricultural Resource Management Survey there is a need to have a flexible model for estimating the latent density. We propose a method of adapting an existing imputation method known as Iterative Sequential Regression (ISR) to impute for missing ordinal data. We first estimate the latent density of the ordinal data using a non-parametric method that builds a sequence of mixtures of (scaled) Beta densities. The transformed densities are then used to build a sequence of conditional linear models for imputation. In a cross-validation study, we test ISR against two competing imputation methods, a MICE ordered probit model and conditional mean.