Model-Assisted and Model-Calibrated Estimation for Class Frequencies with Ordinal Outcomes

Abstract

This paper considers new techniques for complex surveys in the case of estimation of proportions when the variable of interest has ordinal outcomes. Ordinal modelassisted and ordinal model-calibrated estimators are introduced for class frequencies in a population, taking two different approaches. Theoretical properties and numerical methods are investigated. Simulation studies using data from a real macro survey are considered to evaluate the performance of the proposed estimators. The empirical coverage and the length of confidence intervals are computed using several techniques in variance estimation. We also use data from an opinion survey to show the behavior of the proposed estimators in real applications.

Keywords

• complex surveys
• model calibration
• ordinal data
• weighted least squares
• weighted maximum likelihood