Effects of skewness of the third variable on estimation of the mediation effect in the moderating mediator model

두 변인의 인과관계에서 제3변인이 매개효과를 갖는지, 조절효과를 갖는지, 혹은 두 효과를 모두 갖는지 확인하기 위한 목적으로 제3변인이 매개효과와 조절효과를 동시에 갖는 모형(조절매개변인 모형)을 사용할 수 있다. 이 모형은 조절모형에 기반하여 제3변인의 매개효과와 조절효과가 동시에 추정되기 때문에 제3변인과 상호작용항 사이의 비본질적 공선성이 매개효과 2차 경로의 표준오차를 증가시켜 조절효과에 비해 매개효과의 통계적 유의성을 과소평가할 수 있다. 예측변인과 제3변인의 평균중심화를 통해 이 공선성을 감소시킬 수 있지만, 공선성의 감소 정도는 두 설명변인의 분포가 이변량 정규성을 따르는 정도에 따라 달라진다. 본 연구는 조절매개변인 모형에서 제3변인의 왜도를 조작함으로써, 설명변인들의 분포가 이변량 정규성에서 벗어나는 정도에 따라 평균중심화된 제3변인과 상호작용항의 공선성과 매개효과의 2차 경로 회귀계수의 표준오차가 얼마나 증가하는지를 가상실험(simulation) 절차를 통해 확인하였다. 평균중심화에도 불구하고 제3변인의 왜도가 크면 우려할 만한 수준의 비본질적 공선성이 유발됨이 확인되었고 동시에 조절매개변인 모형의 매개효과 추정에 부정적 영향을 미침이 확인되었다. 또한 표본크기를 크게 하는 것이 이 부정적 영향을 줄인다는 것도 확인되었다. 이러한 결과는 조절매개변인 모형을 적용하여 동일한 제3변인의 매개효과와 조절효과를 평가하고자 할 때 제3변인의 왜도가 클 것으로 예상되는 경우 충분한 크기의 표본을 사용하는 것이 필요함을 시사한다.

keywords: moderating mediator model, mean centering, collinearity, skewness, moderation model, 조절매개변인 모형, 평균중심화, 공선성, 왜도, 조절모형

Abstract

A model with a third variable that has both mediation and moderation effects, i.e., the moderating mediator model, can be used to determine whether the third variable has mediation effect, moderation effect, or both in a causal relationship between two variables. Because this model is analyzed base on a moderation model, nonessential collinearity between the third variable and the interaction term may increase the standard error of estimation for the second path of the mediation effect and the increased standard error generates underestimation of statistical significance of mediation effect over and beyond the moderation effect of the third variable. Although researchers may use mean-centering on the predictor and the third variable to decrease the collinearity, degree of the decrease depends on the bivariate normality of the explanatory variables. The current study investigated how much nonessential collinearity and standard error of the estimation for the second path of the mediation effect increased as the amount of deviation from bivariate normality of the explanatory variables increased by manipulating skewness of the third variable. We found that high skewness of the third variable produced substantial amount of nonessential collinearity even with mean-centered variables, which negatively influenced on the estimation of the mediation effect in the moderating mediator model. We also found that increase in sample size attenuated the negative effects. The results suggest that a large number of samples are required in applications of the moderating mediator model with a highly skewed third variable.

keywords: moderating mediator model, mean centering, collinearity, skewness, moderation model, 조절매개변인 모형, 평균중심화, 공선성, 왜도, 조절모형

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논문 상세

Vol.33 No.2

제3변인이 매개효과와 조절효과를 동시에 갖는 모형에서 제3변인의 왜도가 매개효과의 표준오차 추정에 미치는 영향

Effects of skewness of the third variable on estimation of the mediation effect in the moderating mediator model

초록

Abstract

참고문헌

한국심리학회지: 일반