推論力係數估算法之模擬研究

A Simulation Study on Estimators for G-Coefficient of Generaliziability Theory

本研究採電腦模擬探討不同估算法在應用推論力理論估算變通性評量之信度時，對推論力係數之影響。在實驗設計上，先產生三因子變異數分析模擬資料，再比較ANOVA、MLE、REML及MINQUE等估算法，在不同的實驗情況下，估算變異成分及G係數的精準度。結果發現不論是平衡、不平衡或巢隔設計，在小樣本時，以MLE表現最佳，REML次之，而ANOVA與MINQUE表現較差；但估算G係數時，REML則較佳，而MLE稍有低估。若各變異成分相差甚大時，ANOVA及MINQUE甚至會有負值之G係數出現。當樣本數夠大時，則各估算法表現相當接近；但當資料為不平衡設計或大變異量時，各估算法之精準度均會降低。

In this study， we compare ANOVA， MLE， REML， and MINQUE in estimating variance components and G-coefficients of generaliziability theory for evaluating reliability of alternative assessments. The three-way ANOVA design was used to simulate aritifial datasets for the comparisions of estimators under various experimental conditions. When sample sizes are small， MLE perform the best and is followed by REML while ANOVA and MINQUE have the worst accuracy rates; no matter the designs are balanced， unbalanced， or nested. MLE has lower accuracy rates than REML does in estimating G coefficients. When differences between variance components increase， the differences in accurately estimating G-coefficients increase too; in particular， ANOVA and MINQUE methods may generate negative G coefficients. Performances of the four estimators become very similar when sample sizes are large enough. On the other hand， they can all perform poorly when it is unbalanced design with large variances.