二層次結構方程式模型的應用：以教育心理學為例

Applying Two-Level Structural Equation Model to a Data Sample Drawn from Educational Psychology

本研究目的在介紹並應用多層次結構方程式模型方法學於實際的大樣本資料中。當資料的收集是來自多階段抽樣設計而具有巢套特性時，組內層級的樣本會因為組別脈絡效果而產生樣本獨立性假設違反的問題，此時應該使用多層次的統計分析技術來避免組內相關所產生的問題。樣本來自PISA2003 年資料庫中的加拿大948 個學校，包含26，884 位15 歲學生，並選擇其中五個構念共25 個題項或內容領域形成有意義的關係，以作為二層次結構方程式模型的分析範例。經由Mplus 統計軟體分析後，在模型與資料適配度良好的情況下，比較傳統結構方程式模型與二層次結構方程式模型的差異，並對二層次結構方程式模型的組內結構及組間結構進行解釋。研究結果提出許多新的發現及建議供未來研究參考。

The aim of this study is to introduce a two-level structural equation model and apply it to a large sample of empirical data. When data are collected from a multi-stage sampling design， they will have nested characteristics: in this case a within-level/within-group sample will violate the assumption of independence due to the between-level/between-group contextual effects. In such a case， multilevel statistical techniques should be applied to avoid problems due to intra-class correlations. The sample in this study was drawn from a PISA 2003 database: it included 948 schools and 26，884 15-year-old students. Five educational psychological constructs measured by 25 items were selected and formulated as an example for the analysis of a two-level structural equation model. After analysis via Mplus， which showed a good fit of model to data， the researchers compared the results using the conventional structural equation model with those using the two-level structural equation model， and furthermore explained the within-level and between-level structures of the two-level structural equation model. The many findings of this study are presented here， as well as suggestions for future studies based on these findings.