運用S-B量尺卡方差異檢定於潛在變項交互作用檢定之研究

Evaluating Latent Interaction Effects by Model-Based Sattora-Bentler Scaled Chi-square Test and Path-Based Z-test

本研究目的主要提供潛在變項模式（latent variable model）於交互作用（interaction）檢定時，不同樣本數及交互作用效果（interaction effect）對於檢定結果正確性的影響，並說明潛在變項交互作用之檢定標準程序──SB量尺卡方差異檢定（Satorra-Bentler scaled chi-square difference test）。本研究以電腦數值模擬方式進行，修改吳宗祐與鄭伯壎（2006）的二步驟交互作用分析模式為單一步驟潛在變項交互作用模式，實驗中並探討包含樣本數、交互作用效果及潛在變項迴歸係數差異對於潛在交互作用的檢定影響。模式利用LMS（latent moderated structural equation）估算法估計，並進行潛在交互作用檢定篩選率（screening rate）計算。研究結果顯示，利用潛在變項模式進行交互作用檢定時，檢定篩選率除了會隨樣本數及潛在變項交互作用效果絕對值增加而提高之外，且存在交互作用的影響，因此，當進行相關研究時，本研究建議應採用S-B量尺卡方差異檢定法並同時考慮到多個因素對於檢測效果的影響。

The research is aimed to illustrate two statistical tests in evaluating latent interaction effects. The model-based Satorra-Bentler scaled chi-square difference test and path-based Z-test are the two statistical tests. By modifying Wu and Cheng's two-stage model (2006), the one-stage structural equation model with various latent interaction effects was created and simulated. Various sample sizes, interaction effects, and regression coefficients were designed in the numerical simulations to evaluate the two statistical tests. The latent moderated structural equations with robust standard errors estimation were used in estimating the simulated datasets. The results showed that increasing sample sizes or increasing the absolute values of interaction effects helped the performance of both tests. Effects of sample sizes and magnitudes of interaction effect were shown to interact with each other. The paper concludes that the model-based Satorra-Bentler scaled chi-square difference test should be used in testing latent interactions.