Studies on the estimation of the slope parameter in the simple linear regression model with one-fold nested error structure
Titel:
Studies on the estimation of the slope parameter in the simple linear regression model with one-fold nested error structure
Auteur:
Tong, Lee-Ing Cornelius, P.L.
Verschenen in:
Communications in statistics
Paginering:
Jaargang 18 (1989) nr. 1 pagina's 201-225
Jaar:
1989
Inhoud:
Four estimators of the slope, β1, in the simple linear regression model with one-fold nested error structure were compared with respect, to their mean squared error in a Monte Cario 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 [image omitted] is large, GLS is better than ML, but the reverse is true when [image omitted] is small. Some approximate formulas for [image omitted] and [image omitted] derived by regression methods are given. Kackar-Harville approximations for [image omitted] and [image omitted] are satisfactory if a≥11 and may be “good enough” if a≥7.
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