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# Table 6 Coverage rates of low variances simulated data

From: Sampling weights in multilevel modelling: an investigation using PISA sampling structures

Software | Weighting approach | CR \(\widehat{{\beta }_{0}}\) | CR \(\widehat{{\beta }_{1}}\) | CR \(\widehat{{\beta }_{2}}\) | CR \(\widehat{{\sigma }_{\varepsilon }^{2}}\) | CR \(\widehat{{\sigma }_{\tau }^{2}}\) |
---|---|---|---|---|---|---|

A: Coverage rates—low variances simulated data—Model 1 | ||||||

SAS | No weights | 0.94 | 0.94 | 0.87 | ||

Unscaled weights | 0.93 | 0.62 | 0.74 | |||

Only school weights | 0.94 | 0.94 | 0.87 | |||

Only student weights | 0.91 | 0.43 | 0.70 | |||

Withincluster weights | 0.94 | 0.77 | 0.94 | |||

Scaled weights: cluster | 0.94 | 0.94 | 0.87 | |||

Scaled weights: ECluster | 0.94 | 0.94 | 0.87 | |||

Clustersum | 0.94 | 0.95 | 0.87 | |||

House weights | 0.94 | 0.95 | 0.90 | |||

Mplus | No weights | 0.94 | 0.94 | 0.92 | ||

Unscaled weights | 0.95 | 0.94 | 0.90 | |||

Only school weights | 0.94 | 0.94 | 0.90 | |||

Only student weights | 0.94 | 0.94 | 0.91 | |||

Withincluster weights | 0.94 | 0.94 | 0.91 | |||

Scaled weights: cluster | 0.95 | 0.94 | 0.90 | |||

Scaled weights: ECluster | 0.95 | 0.94 | 0.90 | |||

Clustersum | 0.94 | 0.94 | 0.92 | |||

House weights | 0.94 | 0.94 | 0.91 | |||

B: Coverage rates—low variances simulated data—Model 2 | ||||||

SAS | No weights | 0.89 | 0.90 | 0.94 | 0.91 | |

Unscaled weights | 0.91 | 0.92 | 0.62 | 0.06 | ||

Only school weights | 0.91 | 0.91 | 0.96 | 0.91 | ||

Only student weights | 0.87 | 0.91 | 0.41 | 0.72 | ||

Withincluster weights | 0.91 | 0.93 | 0.78 | 0.52 | ||

Scaled weights: cluster | 0.91 | 0.92 | 0.96 | 0.91 | ||

Scaled weights: ECluster | 0.91 | 0.92 | 0.96 | 0.91 | ||

Clustersum | 0.89 | 0.91 | 0.95 | 0.92 | ||

House weights | 0.90 | 0.91 | 0.95 | 0.93 | ||

Mplus | No weights | 0.89 | 0.90 | 0.95 | 0.92 | |

Unscaled weights | 0.91 | 0.92 | 0.95 | 0.92 | ||

Only school weights | 0.91 | 0.92 | 0.95 | 0.92 | ||

Only student weights | 0.89 | 0.90 | 0.95 | 0.93 | ||

Withincluster weights | 0.91 | 0.92 | 0.95 | 0.92 | ||

Scaled weights: cluster | 0.91 | 0.92 | 0.95 | 0.92 | ||

Scaled weights: ECluster | 0.91 | 0.92 | 0.95 | 0.92 | ||

Clustersum | 0.89 | 0.91 | 0.95 | 0.92 | ||

House weights | 0.89 | 0.90 | 0.95 | 0.93 | ||

C: Coverage rates—low variances simulated data—Model 3 | ||||||

SAS | No weights | 0.87 | 0.93 | 0.95 | 0.95 | 0.91 |

Unscaled weights | 0.91 | 0.93 | 0.93 | 0.62 | 0.03 | |

Only school weights | 0.90 | 0.94 | 0.95 | 0.96 | 0.90 | |

Only student weights | 0.86 | 0.93 | 0.94 | 0.40 | 0.52 | |

Withincluster weights | 0.90 | 0.93 | 0.95 | 0.74 | 0.43 | |

Scaled weights: cluster | 0.90 | 0.94 | 0.95 | 0.96 | 0.91 | |

Scaled weights: ECluster | 0.90 | 0.94 | 0.95 | 0.96 | 0.90 | |

Clustersum | 0.87 | 0.93 | 0.94 | 0.95 | 0.91 | |

House weights | 0.88 | 0.93 | 0.95 | 0.95 | 0.92 | |

Mplus | No weights | 0.87 | 0.93 | 0.95 | 0.95 | 0.93 |

Unscaled weights | 0.90 | 0.94 | 0.95 | 0.95 | 0.92 | |

Only school weights | 0.90 | 0.94 | 0.95 | 0.95 | 0.91 | |

Only student weights | 0.87 | 0.93 | 0.95 | 0.95 | 0.93 | |

Withincluster weights | 0.90 | 0.94 | 0.95 | 0.95 | 0.92 | |

Scaled weights: Cluster | 0.90 | 0.94 | 0.95 | 0.95 | 0.92 | |

Scaled weights: ECluster | 0.90 | 0.94 | 0.95 | 0.95 | 0.92 | |

Clustersum | 0.87 | 0.93 | 0.94 | 0.95 | 0.93 | |

House weights | 0.87 | 0.93 | 0.95 | 0.95 | 0.93 |