Asymptotic Efficiency of REML Error Components as a Function of Unbalancedness

• Activity Number: 409 - Small-Area Estimation and Use of Unit-Level Models
• Type: Contributed
• Date/Time: Tuesday, August 1, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Jyothsna Sainath*
• Companies: University of Utah
• Keywords: Mixed Models ; Unbalanced Data ; Small Area Estimation ; Variance Component Estimation ; Residual Maximum Likelihood Estimation

Abstract

Residual maximum likelihood estimation (REML) is a likelihood-based method of estimating error components of a linear mixed model (LMM) that yields consistent and asymptotically normal estimators even with unbalanced datasets. It is also known that the asymptotic variance of the error components is larger in the case of a unbalanced dataset under comparable conditions for the fixed effects. Ahrens and Pincus (1981) derived a measure of unbalancedness that is bounded between 0 and 1. We express the asymptotic variance covariance matrix of a one-way error component model (which has been variously derived by Jiang (1998), Searle (1970) and others) as a function of the Ahrens-Pincus measure to demonstrate the growth of the asymptotic variance of the error component as the degree of unbalancedness grows. These results are further demonstrated through a simulation exercise.