Advances in Business Statistics, Methods and Data Collection

31Variance Estimation Under Nearest Neighbor Ratio Hot Deck Imputation for Multinomial Data: Two Approaches Applied to the Service Annual Survey (SAS)

Rebecca Andridge¹, Jae Kwang Kim², and Katherine J. Thompson³

¹Division of Biostatistics, The Ohio State University, Columbus, OH, USA

²Department of Statistics, Iowa State University, Ames, IA, USA

³Associate Directorate of Economic Programs, U.S. Census Bureau, Washington, DC, USA

31.1 Introduction

Sample surveys are often designed to estimate totals (e.g. revenue, earnings). In addition, many surveys request sets of compositional variables (details) that sum to a total, such as a breakdown of total expenditures by type of expenditure or a breakdown of total income by source. The detail proportions can vary greatly by sample unit, and their multinomial distributions may be related to a different set of predictors than those associated with the total. All survey participants are asked to provide values for the total items (hereafter referred to as “totals”), whereas the type of requested details can vary. This creates two separate but related missing data challenges: (i) to develop viable imputation models for the total; and (ii) to develop viable imputation models for the set of associated detail items.

For business – or many establishment – surveys, the primary missing data challenge is the treatment of the details. With totals, reliable auxiliary data from the same unit are often available for direct substitution (e.g. administrative ...