​Stata：8大中介效应检验命令大比拼

方程1 ：Y=cX+e1；

方程2 ：M=aX+e2；

方程3 ：Y= c′X+bM+e3。其中，c是X对Y的总效应，a、b是经过中介变量M的中介效应，c′是直接效应。当只有一个中介变量时，效应之间有c=c′+ab，中介效应的大小用c-c′=ab来衡量。中介效应检验过程

中介效应是间接效应，无论变量是否涉及潜变量，都可以用结构方程模型分析中介效应。步骤为：

第一步检验系统c，如果c不显著，Y与X相关不显著，停止中介效应分析，如果显著进行第二步；

第二步依次检验a，b，如果都显著，那么检验c′，c′显著，为部分中间效应模型，c′不显著，为完全中介效应模型；

如果a，b至少 有一个不显著，做Sobel检验，检验的统计量是Z = ^a^b / Sab，显著则中介效应显著，不显著则中介效应不显著。

第一步检验系统c，如果c不显著，Y与X相关不显著，停止中介效应分析，如果显著进行第二步；

第二步依次检验a，b，如果都显著，那么检验c′，c′显著，为部分中间效应模型，c′不显著，为完全中介效应模型；

如果a，b至少 有一个不显著，做Sobel检验，检验的统计量是Z = ^a^b / Sab，显著则中介效应显著，不显著则中介效应不显著。

本例使用hsbdemo数据集，其中science作为DV, math作为IV, read作为中介变量。也就是说，模型说数学影响阅读，而阅读反过来又影响科学。这个模型可能有也可能没有太大的实际意义，但是它将允许我们演示运行一个中介效应测试的过程。我们将使用sgmediation command来完成这个任务，您可以使用findit sgmediation来下载这个命令。

该数据包括200个学生的选择的项目类型(prog， 三种类型 categorical variable), 他们的社会地位（ses 三种地位 categorical variable），写作分数（write， a continuous variable）。导入数据，然后进行查看数据

方法1、逐步检验回归系数方法

逐步检验回归系数方法分为三步：

逐步检验回归系数方法分为三步：

reg readmath //分析 x 和 m 之间的关系

reg science readmath // 加入 m，看 x 和 y 之间的关系

操作结果为：

方法2、两步回归法 (two-step regression)

Zhao, Lynch et al. (2010)对传统的逐步检验回归系数方法提出再次思考，但其具体的步骤方法与逐步检验回归系数方法接近，只是取消了第一步中的检验自变量 x 和因变量 y 之间的关系， 代码为：

reg readmath //分析 x 和 m 之间的关系

reg science readmath // 加入 m，看 x 和 y 之间的关系

方法3、sobel检验--中介效应检验程序Sobel-Goodman mediation tests

语法格式为：

sgmediation depvar [ifexp] [inrange] , mv:(mediatorvar) iv(indvar) [ cv(covarlist) quietly ]

选项含义为：

depvar表示因变量

mv:(mediatorvar) 表示用于指定中介变量

iv(indvar) 表示用于指定自变量

cv(covarlist)表示用于指定控制变量

depvar表示因变量

mv:(mediatorvar) 表示用于指定中介变量

iv(indvar) 表示用于指定自变量

cv(covarlist)表示用于指定控制变量

查看数据

edit

desc

数据如下：

. helpsgmediation

. use "C:\Users\Metrics\Desktop\hsbdemo.dta", clear

(highschool and beyond (200 cases))

. desc

Contains data from C:\Users\Metrics\Desktop\hsbdemo.dta

obs: 200 highschool and beyond (200 cases)

vars: 13 30 Oct 2009 14:13

size: 10,000

--------------------------------------------------------------------------------------

storage display value

variable name typeformat label variable label

--------------------------------------------------------------------------------------

id float%9.0g

female float%9.0g fl

ses float%9.0g sl

schtyp float%9.0g scl typeof school

prog float%9.0g sel typeof program

readfloat%9.0g reading score

write float%9.0g writing score

math float%9.0g math score

science float%9.0g science score

socst float%9.0g social studies score

honors float%19.0g honlab honors english

awards float%9.0g

cid int %8.0g

--------------------------------------------------------------------------------------

Sorted by:

. setmore off

进行操作为：

sgmediation science, mv(read) iv(math)

结果为：

. sgmediation science, mv(read) iv(math)

# 表示mv(read)为中介变量，iv(math)为自变量

Model with dv regressed on iv (path c)

Source | SS df MS Number of obs = 200

-------------+---------------------------------- F(1, 198) = 130.81

Model | 7760.55791 1 7760.55791 Prob > F = 0.0000

Residual | 11746.9421 198 59.3279904 R-squared = 0.3978

-------------+---------------------------------- Adj R-squared = 0.3948

Total | 19507.5 199 98.0276382 Root MSE = 7.7025

------------------------------------------------------------------------------

science | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

math | .66658 .0582822 11.44 0.000 .5516466 .7815135

_cons | 16.75789 3.116229 5.38 0.000 10.61264 22.90315

------------------------------------------------------------------------------

Model with mediator regressed on iv (path a)

# 形成路劲a

Source | SS df MS Number of obs = 200

-------------+---------------------------------- F(1, 198) = 154.70

Model | 9175.57065 1 9175.57065 Prob > F = 0.0000

Residual | 11743.8493 198 59.3123704 R-squared = 0.4386

-------------+---------------------------------- Adj R-squared = 0.4358

Total | 20919.42 199 105.122714 Root MSE = 7.7015

------------------------------------------------------------------------------

read| Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

math | .724807 .0582745 12.44 0.000 .6098887 .8397253

_cons | 14.07254 3.115819 4.52 0.000 7.928087 20.21699

------------------------------------------------------------------------------

Model with dv regressed on mediator and iv (paths b and c')

Source | SS df MS Number of obs = 200

-------------+---------------------------------- F(2, 197) = 90.27

Model | 9328.73944 2 4664.36972 Prob > F = 0.0000

Residual | 10178.7606 197 51.6688353 R-squared = 0.4782

-------------+---------------------------------- Adj R-squared = 0.4729

Total | 19507.5 199 98.0276382 Root MSE = 7.1881

------------------------------------------------------------------------------

science | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

read | .3654205 .0663299 5.51 0.000 .2346128 .4962283

math | .4017207 .0725922 5.53 0.000 .2585632 .5448782

_cons | 11.6155 3.054262 3.80 0.000 5.592255 17.63875

------------------------------------------------------------------------------

Sobel-Goodman Mediation Tests

# 程序检验

Coef Std Err Z P>|Z|

Sobel .26485934 .05258136 5.037 4.726e-07

Goodman-1 (Aroian) .26485934 .05272324 5.024 5.072e-07

Goodman-2 .26485934 .05243909 5.051 4.400e-07

Coef Std Err Z P>|Z|

a coefficient = .724807 .058274 12.4378 0

b coefficient = .365421 .06633 5.50914 3.6e-08

Indirect effect = .264859 .052581 5.03713 4.7e-07

Direct effect = .401721 .072592 5.53394 3.1e-08

Total effect = .66658 .058282 11.4371 0

Proportion of total effect that is mediated: .39734065

Ratio of indirect to direct effect: .65931219

Ratio of total to direct effect: 1.6593122

In this example the mediation effect of read was statistically significant with approximately 40% of the total effect (of math onscience) being mediated.

在这个例子中，read的中介效果在统计上是显著的，通过这个可以得到（Proportion of total effect that is mediated: .39734065）大约40%的总效果(数学对科学)是被中介的。

操作案例2 如果需要加入协变量，则为如下命令

sgmediation science, mv(read) iv(math) cv(write)

结果为：

sgmediation science, mv(read) iv(math) cv(write)

Model with dv regressed on iv (path c)

Source | SS df MS Number of obs = 200

-------------+---------------------------------- F(2, 197) = 80.84

Model | 8793.36552 2 4396.68276 Prob > F = 0.0000

Residual | 10714.1345 197 54.3864694 R-squared = 0.4508

-------------+---------------------------------- Adj R-squared = 0.4452

Total | 19507.5 199 98.0276382 Root MSE = 7.3747

------------------------------------------------------------------------------

science | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

math | .4757015 .07094 6.71 0.000 .3358022 .6156009

write | .3055482 .0701157 4.36 0.000 .1672745 .443822

_cons | 10.68138 3.293391 3.24 0.001 4.186557 17.17621

------------------------------------------------------------------------------

Model with mediator regressed on iv (path a)

Source | SS df MS Number of obs = 200

-------------+---------------------------------- F(2, 197) = 96.80

Model | 10368.63 2 5184.31501 Prob > F = 0.0000

Residual | 10550.79 197 53.5573096 R-squared = 0.4956

-------------+---------------------------------- Adj R-squared = 0.4905

Total | 20919.42 199 105.122714 Root MSE = 7.3183

------------------------------------------------------------------------------

read| Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

math | .5196538 .0703972 7.38 0.000 .380825 .6584826

write | .3283984 .0695792 4.72 0.000 .1911828 .4656141

_cons | 7.541599 3.26819 2.31 0.022 1.096471 13.98673

------------------------------------------------------------------------------

Model with dv regressed on mediator and iv (paths b and c')

Source | SS df MS Number of obs = 200

-------------+---------------------------------- F(3, 196) = 65.32

Model | 9752.65806 3 3250.88602 Prob > F = 0.0000

Residual | 9754.84194 196 49.7696017 R-squared = 0.4999

-------------+---------------------------------- Adj R-squared = 0.4923

Total | 19507.5 199 98.0276382 Root MSE = 7.0548

------------------------------------------------------------------------------

science | Coef. Std. Err. t P>|t| [95% Conf. Interval]

-------------+----------------------------------------------------------------

read | .3015317 .0686815 4.39 0.000 .1660822 .4369813

math | .3190094 .0766753 4.16 0.000 .167795 .4702239

write | .2065257 .0707644 2.92 0.004 .0669683 .3460831

_cons | 8.407353 3.192799 2.63 0.009 2.110703 14.704

------------------------------------------------------------------------------

Sobel-Goodman Mediation Tests

Coef Std Err Z P>|Z|

Sobel .15669211 .04152593 3.773 .00016107

Goodman-1 (Aroian) .15669211 .04180646 3.748 .00017822

Goodman-2 .15669211 .0412435 3.799 .00014517

Coef Std Err Z P>|Z|

a coefficient = .519654 .070397 7.38174 1.6e-13

b coefficient = .301532 .068681 4.39029 .000011

Indirect effect = .156692 .041526 3.77336 .000161

Direct effect = .319009 .076675 4.16053 .000032

Total effect = .475702 .07094 6.70569 2.0e-11

Proportion of total effect that is mediated: .32939164

Ratio of indirect to direct effect: .49118333

Ratio of total to direct effect: 1.4911833

方法4：基于bootstrap的sobel检验方法

操作案例3 bootstrap with case resampling

bootstrap r(ind_eff) r(dir_eff), reps(1000): sgmediation science, mv(read) iv(math)

estat bootstrap, percentile bc

结果为：

bootstrap r(ind_eff) r(dir_eff), reps(1000): sgmediation science, mv(read) iv(math)

(running sgmediation on estimation sample)

Bootstrap replications (1000)

----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5

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Bootstrap results Number of obs = 200

Replications = 1,000

command: sgmediation science, mv(read) iv(math)

_bs_1: r(ind_eff)

_bs_2: r(dir_eff)

------------------------------------------------------------------------------

| Observed Bootstrap Normal-based

| Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+----------------------------------------------------------------

_bs_1 | .2648593 .0548346 4.83 0.000 .1573855 .3723332

_bs_2 | .4017207 .0819454 4.90 0.000 .2411106 .5623307

------------------------------------------------------------------------------

.

. estat bootstrap, percentile bc

Bootstrap results Number of obs = 200

Replications = 1000

command: sgmediation science, mv(read) iv(math)

_bs_1: r(ind_eff)

_bs_2: r(dir_eff)

------------------------------------------------------------------------------

| Observed Bootstrap

| Coef. Bias Std. Err. [95% Conf. Interval]

-------------+----------------------------------------------------------------

_bs_1 | .26485934 -.0057812 .05483462 .1520132 .3652509 (P)

| .1712486 .3799049 (BC)

_bs_2 | .40172068 .0059509 .08194541 .2422861 .563365 (P)

| .2336006 .5417721 (BC)

------------------------------------------------------------------------------

(P) percentile confidence interval

(BC) bias-corrected confidence interval

方法5 、结构方程中介效应检验

在使用结构方程模型(sem)估计完中介效应之后，我们可以使用medsem命令进一步检验中介效应。

medsem基于使用Stata的-sem命令估计的模型(包括观察到的变量或潜在变量，以及观察到的变量和潜在变量的组合)进行中介分析。有medsem使用两种方法作为其过程的基础。第一种方法是众所周知的Baron and Kenny方法，由Iacobucci等人(2007)调整用于结构方程模型。第二种方法是Zhao等人(2010)的方法。

首先下载安装该命令：

ssc install medsem，replace

命令medsem是专门用于sem命令之后计算中介效应的。

语法格式为:

medsem - Mediation analysis using structural equation modelling

medsem, indep(varname) med(varname) dep(varname) [mcreps(number) stand zlc rit rid]

选项含义为:

indep(varname)代表解释变量(X);

med(varname)代表中介变量(M);

dep(varname)代表被解释变量(Y)；

mereps(number)指定蒙特卡罗复制的数量，默认是样本的数量大小；

stand指定输出标准化的系数。当省略这一项时，默认输出非标准化系数；

zlc用于指定(Zhao et al..，2010)的中介效应估计方法，当省略这一选项时，默认是(Iacobucci et al. (2007))改进的BK方法。

选项rit用于指定输出中介效应与总效应之比，即rit, ratio of the indirect effect to the total effect

rid，即 rid用于指定输出中介效应与直接效应之比。

indep(varname)代表解释变量(X);

med(varname)代表中介变量(M);

dep(varname)代表被解释变量(Y)；

mereps(number)指定蒙特卡罗复制的数量，默认是样本的数量大小；

stand指定输出标准化的系数。当省略这一项时，默认输出非标准化系数；

zlc用于指定(Zhao et al..，2010)的中介效应估计方法，当省略这一选项时，默认是(Iacobucci et al. (2007))改进的BK方法。

选项rit用于指定输出中介效应与总效应之比，即rit, ratio of the indirect effect to the total effect

rid，即 rid用于指定输出中介效应与直接效应之比。

. qui sem (readanomia71 pwless71)(SES->educ66 occstat66)(Alien67anomia66 pwless66)(F3->anomia67 pwless67)(F4->anomia71 pwless71)(F2 F3anomia66 pwless66)(F3->anomia67 pwless67)(F2