利用折刀程序估計隨機效果px(i:h)設計的變異成分估計量與誤差變異數估計量的標準誤

Estimating Standard Errors of Variance Component Estimators and Error Variance Estimators in Random Effects px(i:h) Designs by Using Jackknife Procedure

概化理論中，G研究設計的變異成分估計量的標準誤估計是一個重要議題；因為有關受試者就學、就業的判定以及選擇一個最適當的D研究設計都與從G研究設計中所得到的變異成分估計量的準確性高度相關。本文提議一個用以估計隨機效果px（i:h）設計的變異成分估計量標準誤與誤差變異數估計量標準誤的折刀程序，並且將此程序應用於模擬的常態、二分與多分資料以檢查此折刀程序的可行性。研究結果顯示：不論資料型式為常態、二分或多分，本文所提折刀程序在估計px（i:h）設計的五個變異成分估計量的標準誤以及絕對與相對誤差變異數估計量的標準誤都相當準確。 Obtaining information about the variability of variance component estimates in G study designs is a very important issue in generalizability theory because the decisions to be made about examinees, or the choices of the most appropriate D study designs, are highly dependent on the accuracy of variance component estimates derived from G study designs. In this article, the jackknife procedure for estimating standard errors of variance component estimates and error variance estimates in random effects px(i:h) designs is proposed and applied to the simulated normal, dichotomous, and polytomous data with specified variance components. The simulation results show that the proposed jackknife procedure performs quite well for all three types of data under studied sample sizes.