ISSN 1671-3710
CN 11-4766/R

心理科学进展 ›› 2022, Vol. 30 ›› Issue (5): 1183-1190.doi: 10.3724/SP.J.1042.2022.01183

• 研究方法 • 上一篇    


方杰1, 温忠麟2()   

  1. 1广东财经大学广东经济与社会发展研究院/应用心理学系, 广州 510320
    2华南师范大学心理学院/心理应用研究中心, 广州 510631
  • 收稿日期:2021-07-29 出版日期:2022-05-15 发布日期:2022-03-24
  • 通讯作者: 温忠麟
  • 基金资助:

Moderation analysis and its effect size based on a two-level regression model

FANG Jie1, WEN Zhonglin2()   

  1. 1Institute of Guangdong Economy and Social Development & Department of Applied Psychology, Guangdong University of Finance & Economics, Guangzhou 510320, China
    2Center for Studies of Psychological Application & School of Psychology, South China Normal University, Guangzhou 510631, China
  • Received:2021-07-29 Online:2022-05-15 Published:2022-03-24
  • Contact: WEN Zhonglin


使用多元回归法进行调节效应分析在社科领域已常有应用。简述了目前多元回归法的调节效应分析存在的不足, 包括人为变换检验模型、自变量和调节变量区分不足、误差方差齐性的假设难以满足、调节效应量指标ΔR2没有直接测量调节变量对自变量与因变量关系的调节程度。比较好的方法是用两水平回归模型进行调节效应分析并使用相应的效应量指标。在介绍新方法和新效应量后, 总结出一套调节效应的分析流程, 通过一个例子来演示如何用Mplus软件进行两水平回归模型的调节效应及其效应量分析。最后讨论了两水平回归模型的调节效应分析的发展, 包括稳健的调节效应分析、潜变量的调节效应分析、有调节的中介效应分析和有中介的调节效应分析等。

关键词: 调节效应, 两水平回归模型, 多元回归法, 效应量


In recent years, multiple regression has been widely used in social sciences to analyze the moderating effect. However, this practice was found to have at least four weaknesses. First, the concept of moderation is artificially treated as interaction. Second, the role of the predictor X is confounded with that of the moderator Z. That is, the roles of the predictor and the moderator are statistically indistinguishable, or the moderation effect of Z equals that of X. Third, the assumption of homoscedasticity of error variances across different values of X and Z is often violated by data in social and behavioral sciences. Violating this assumption often results in an inflated Type Ⅱ error rate and a low power. Fourth, △R2 does not directly measure the effect of moderation as conceptually defined. That is, a measure that reflects the impact of Z on the relationship between X and Y (i.e., X→Y) should be used to quantify the moderating effect.
Compared to multiple regression, the two-level regression model has many advantages in the analysis of moderating effect. First, the two-level regression model does not require the homoscedasticity assumption in moderation analysis. Second, the two-level regression model allows the regression coefficients of a dependent variable Y on predictor X (i.e., X→Y) are further regressed on moderator variables Z. Therefore, the two-level regression model permits estimating the percentage of variance of each regression coefficient that is due to moderator variables (i.e., the moderation effect size). The two-level regression model directly shows us to what extent a moderator explains the variance of the regression coefficient between the dependent variable and the predictor.
At the present study, we propose a procedure to analyze the moderating effect based on the two-level regression model. The first step is to determine the moderating effect using the two-level regression model. If the variance of the error εi1 of the level 2 slope equation is statistically significant, the result of the two-level regression model and the corresponding effect size should be reported. Otherwise, go to the second step. In the second step, multiple regression was used to work out the moderating effect. If the Bayesian information criterion of the two-level regression model is smaller than that of the multiple regression, the result of the two-level regression model and the corresponding effect size should be reported. Otherwise, the result of the multiple regression and the corresponding effect size △R2 should be reported.
We exemplify how to conduct the proposed procedure by using Mplus. It is noteworthy that, with this software, a two-level regression model could be built via a “trick” for 2-level model with single level data. The Mplus syntax is offered to facilitate the implementation of two-level regression model in analyzing moderated mediation effects. The program can be managed easily by empirical researchers.
Directions for future study on two-level regression model are discussed at the end of the paper. First, if data contains outliers or heavy tails, robust methods of two-Level regression model should be adapted. Second, if the measurement error of the variables needs to be taken into account, two-level moderated latent variable model should be adapted. Third, two-level regression model could be used to analyze the mediated moderation model and moderated mediation model.

Key words: moderating effect, two-level regression model, multiple regression, effect size