Abstract: Moderation indicates that the strength and/or direction of the relation between an independent variable and a dependent variable is affected by a third variable, which is called moderator. Moderation models are frequently used in the research of psychology and other social science disciplines, but some issues are still need to be clarified. The purpose of the present study is to clarify two issues in moderation effect analysis. One is the role of the mean-centering; the other is the advantages and disadvantages of two existing methods for testing simple slope. Firstly, the product term in moderated regression might be collinear with its constituent parts, making it difficult to detect interaction effects. Some researchers presumed that mean-centering could reduce colinearity and improve the precision of estimates from collinear data, but this is not true. After reviewing the role of mean-centering in moderated multiple regression, we emphasize that mean-centering does not change the coefficient of the product term (moderation term) of the regression, but changes the coefficients of the first-order terms (main effect terms) and improves the interpretability of results. Secondly, when an interaction is found, the interactive effect need to be further probed to fully explicate the relationship among the three variables. The most common method for probing interactions is to test simple slopes. We discuss the merits and demerits of two methods for testing simple slope: Pick-a-point method and Johnson-Neyman’s method. Pick-a-point method is to test simple slopes at several specific levels of the predictors and report whether they are significant, whereas Johnson-Neyman’s method is to test simple slopes in the whole range of the predictor and report the regions in which the simple effect is significant. We suggest that Johnson-Neyman’s method be adopted to analyze simple slope test when the moderator is a continuous variable, whereas the pick-a-point method be adopted to analyze simple slope test when the moderator is a categorical variable or researchers are interested in the test at some special points of the moderator. An example is given to illustrate how to conduct moderation effect analysis by multiple linear regressions and test simple slope by using Johnson-Neyman’s method. Directions for future study on moderation effect analyses are discussed at the end of the paper. In fact, in addition to mean-centering, standardization is an alternative to analyze moderation effects, and the effect tests with mean-centering and standardization are equivalent. Furthermore, two methods for testing simple slopes can expend to more complicated moderation models, such as multilevel moderation models and moderation models in which the dependent variable is a binary variable.

Key words: moderation effect, multiple linear regression, mean-centering, pick-a-point approach, Johnson-Neyman method

摘要： 在心理学和其他社科研究领域，大量实证研究建立调节模型，以分析自变量对因变量关系的影响机制，但在基于多元回归的调节效应分析实践中仍存在不足。我们回顾了均值中心化在基于多元回归的调节效应分析中的作用，均值中心化不影响乘积项(即调节效应)的检验，仅对一阶项(即主效应)的检验有影响。讨论了简单斜率的检验方法，建议在调节变量为连续变量时，使用Johnson-Neyman法进行简单斜率检验；在调节变量为类别变量或研究者对某个调节变量值感兴趣时，使用选点法。并用一个实际例子演示如何进行调节效应分析。随后展望了调节效应检验的拓展方向。

关键词: 调节效应, 多元线性回归, 均值中心化, 选点法, Johnson-Neyman法