An IERI – International Educational Research Institute Journal
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 |