Studies on the estimation of the slope parameter in the simple linear regression model with one-fold nested error structure

Lee-Ing Tong, P. L. Cornelius

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5 Scopus citations

Abstract

Four estimators of the slope, β1in the simple linear regression model with one-fold nested error structure were compared with respect to their mean squared error in a Monte Carlo simulation study. Estimators considered were ordinary least squares (OLS);maximum likelihood (ML), estimated generalized least squares (GLS) using analysis of variance estimates of variance components, and the “covariance” estimator (COV) which uses only within-first-stage-unit information. GLS and ML behave quite well if the number of first-stage sampling units a>5 with n>2 second-stage units per first-stage unit or if a =5 and n>2. When the first-stage variance component of is large, GLS is better than ML, but the reverse is true when a2 1is small. Some approximate formulas for T/(βGLS) and V(βML) derived by regression methods are given. Kackar-Harville approximations for V(βGLS) and V(βML) are satisfactory if a >11 and may be “good enough” if a>7.

Original languageEnglish
Pages (from-to)201-225
Number of pages25
JournalCommunications in Statistics - Simulation and Computation
Volume18
Issue number1
DOIs
StatePublished - 1 Jan 1989

Keywords

  • estimation
  • generalized least squares
  • hierarchical classification
  • maximum likelihood
  • mean squared error
  • mixed models
  • Monte Carlo simulation
  • simple linear regression
  • two-stage samples

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