第八讲 中介效应及其检验MSci2019

1、第八讲 中介效应及其检验,吴建祖 教授 兰州大学管理学院,中介变量,中介变量（mediator）是自变量对因变量发生影响的中介。 中介效应的研究主要是为了打开两个变量之间关系的黑盒子，解释变量之间关系的内部机理。 McKinnon DP. 2008. Introduction to statistical mediation analysis. Taylor and Francis Group: New York.,2,吴建祖 博士,论文样例,3,吴建祖 博士,中介效应路径模型和回归方程,4,吴建祖 博士,检验中介效应的回归方程,5,吴建祖 博士,中介效应,Total effect = Dir

2、ect effect + Indirect effect Total effect, c Direct effect, c Indirect effect (Mediated effect), a*b 总效应=直接效应+间接效应（中介效应） 总效应, c 直接效应, c 间接效应（中介效应）, a*b,6,吴建祖 博士,证明：总效应=直接效应+间接效应（中介效应）,7,吴建祖 博士,完全中介 vs. 部分中介,8,吴建祖 博士,8,X,M,Y,X,M,Y,完全中介(Complete mediation),部分中介(partial mediation),中介效应的检验方法,Barron & Ke

3、nny模型 Sobel检验 Bootstrapping,9,吴建祖 博士,Barron & Kenny模型,中介效果的检验,11,吴建祖 博士,主管的 不当对待领导,下属的 公平知觉,下属的 工作满意度,三部曲 (1)以X去预测Y (2)以X去预测M (3)同时以X与M去预测Y,(X, 自变量),(M,中介变量),(Y, 因变量),Based on Baron Also see Shaver(2005),Barron and Kenny, 1986,12,吴建祖 博士,Step 1: Relation of X to Y,13,吴建祖 博士,MEDIATOR,M,INDEPENDENT VAR

4、IABLE,X,Y,DEPENDENT VARIABLE,c,The independent variable is related to the dependent variable: Y = i1 + cX + e1,Step 2: Relation of X to M,14,吴建祖 博士,MEDIATOR,M,INDEPENDENT VARIABLE,X,Y,DEPENDENT VARIABLE,2. The independent variable is related to the potential mediator: M = i2 + aX + e2,a,Step 3: Rela

5、tion of X and M to Y,15,吴建祖 博士,MEDIATOR,M,INDEPENDENT VARIABLE,X,Y,DEPENDENT VARIABLE,a,3. The mediator is related to the dependent variable controlling for exposure to the independent variable: Y = i3+ cX + bM + e3,b,c,Sobel Test,Sobel Test,17,吴建祖 博士,A Example of Sobel Test,18,吴建祖 博士,http:/quantpsy

6、.org/sobel/sobel.htm,Sobel Test,The Sobel test works well only in large samples. We recommend using this test only if the user has no access to raw data. If you have the raw data, bootstrapping offers a much better alternative that imposes no distributional assumptions. Preacher K, Hayes A. 2004. SP

7、SS and SAS procedures for estimating indirect effects in simple mediation models. Behavior Research Methods, Instruments, & Computers 36(4): 717-731.,19,吴建祖 博士,Bootstrapping,Distribution of the Product,The mediated effect is the product of two coefficients a and b. The distribution of the product ha

8、s a normal distribution only in special cases. At low values of a and b, the distribution has excess kurtosis and skewness, e.g. when a and b are both zero, kurtosis is 6. It is not surprising that the confidence limits are inaccurate if the distribution is assumed to be normal. One solution is to u

9、se the distribution of the product in statistical tests and confidence limits.,21,吴建祖 博士,Bootstrapping,22,吴建祖 博士,Critical Values for Distribution of the Product,Because the distribution of the product is not normal, there are different critical values for the distribution for each value of a/sa and

10、b/sb. The critical values are -1.96 and +1.96 for the 95% confidence interval from the normal distribution. There are different upper and lower critical values for the distribution of the product. Confidence limits and significance tests are more accurate using the critical values from the distribut

11、ion of the product (MacKinnon et al. 2004).,23,吴建祖 博士,Resampling Methods,Another good option for data that do not have a normal distribution is resampling methods (MacKinnon et al. 2004). Bootstrap method for mediated effects was described by Bollen & Stine (1991), Lockwood & MacKinnon (1998), MacKi

12、nnon et al., (2004) and Shrout & Bolger (2002) Purpose is to use the data itself to form a distribution of a statistic (Manly, 1997). Does not make as many assumptions and can handle non-normal distributions. The value of a statistic in the observed sample is compared to the distribution of the stat

13、istic formed by resampling from the data a large number of times.,24,吴建祖 博士,Bootstrapping,Bootstrapping uses computer intensive resampling to make inferences rather than making assumptions about the population. In other words, bootstrapping treats a given sample as the population.,25,吴建祖 博士,Bootstra

14、pping,Bootstrap the sampling distribution of ab and derive a confidence interval with the empirically derived bootstrapped sampling distribution. The bootstrapping is accomplished by taking a large number of samples of size n (where n is the original sample size) from the data, sampling with replace

15、ment, and computing the indirect effect, ab, in each sample.,26,吴建祖 博士,Bootstraping,27,吴建祖 博士,Bootstrapping,Assume for illustration that 1,000 bootstrap samples have been taken. The point estimate of ab is simply the mean ab computed over the 1,000 samples. The sd of the 1000 values is the SE. To de

16、rive the 1- confidence interval: SORT the elements of the vector of 1,000 estimates of ab from low to high. The lower limit of the confidence interval is the (/2)1000 value, and the upper limit is the (1-/2)1000 th value in the sorted sample.,28,吴建祖 博士,Bootstrapping,The confidence interval can and o

17、ften is asymmetric ( in accordance with the skewness of the sampling distribution of ab ) If 0 is outside the CI , the null hypothesis of no mediation is rejected at the level of significance.,29,吴建祖 博士,The steps of a bootstrap procedure,30,吴建祖 博士,The steps of a bootstrap procedure,31,吴建祖 博士,Bootstr

18、ap Test for Mediation,Estimate the mediated effect in the sample. Make a new data set by sampling N subjects data with replacement and estimating the mediated effect in each of a large number (e.g. 2000) of bootstrap samples. Determine significance level by locating the mediated effect for the obser

19、ved sample in the distribution of the bootstrap sample. Find 2.5% and 97.5% values for confidence interval. Bias-corrected bootstrap makes a correction for the difference between the observed and average bootstrapped mediated effect.,32,吴建祖 博士,Advantages of Bootstrapping,The advantage of bootstrappi

20、ng over analytical methods is its great simplicity. It is straightforward to apply the bootstrap to derive estimates of standard errors and confidence intervals for complex estimators of complex parameters. Bootstrapping is becoming the most popular method of testing mediation because it does not re

21、quire the normality assumption to be met, and because it can be effectively utilized with smaller sample sizes .,33,吴建祖 博士,Minor Drawbacks of Bootstrap,More time consuming for the computer Bootstrap yields slightly different CIs each time you apply this method to the same data.,34,吴建祖 博士,Statistical

22、 Mediation Tests Summary,Tests differ substantially in Type I error and statistical power. Requirement for significant total effect, c, and requirement that c is non-significant reduces accuracy of causal steps methods. Assumption that the mediated effect divided by its standard error has a normal d

23、istribution is incorrect for some values. Best tests are based on the distribution of the product and resampling methods.,35,吴建祖 博士,Wood et al., 2008,For all approaches, the assumption of causality is implicit in the definition of mediation. A mediator is defined as an explanatory mechanism through

24、which one variable affects another. However, including a mediator in a study does not guarantee that the commonly accepted conditions for inferring causality are met. Wood RE, Goodman JS, Beckmann N, Cook A. 2008. Mediation Testing in Management Research: A Review and Proposals. Organizational Research Methods 11(2): 270-295.,36,吴建祖 博士,小结,Baron &