## Abstract

Four estimators of the slope, β_{1}in 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 a^{2}
_{1}is small. Some approximate formulas for ^{T}/(β_{GLS}) and V(β_{ML}) derived by regression methods are given. Kackar-Harville approximations for V(β_{GLS}) and V(β_{ML}) are satisfactory if a >11 and may be “good enough” if a>7.

Original language | English |
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Pages (from-to) | 201-225 |

Number of pages | 25 |

Journal | Communications in Statistics - Simulation and Computation |

Volume | 18 |

Issue number | 1 |

DOIs | |

State | Published - 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