Stata：中介效应之sgmediation操作
中介效应是指变量间的影响关系（X→Y）不是直接的因果链关系，而是通过一个或一个以上变量(M)的间接影响产生的，此时我们称M为中介变量，而X通过M对Y产生的的间接影响称为中介效应。
中介效应是间接效应的一种，模型中在只有一个中介变量的情况下，中介效应等于间接效应；当中介变量不止一个的情况下，中介效应不等于间接效应，此时间接效应可以是部分中介效应和（或）所有中介效应的总和。
自变量X对因变量Y的影响，如果X变量通过影响M变量来影响Y变量，则M为中介变量。
通常将变量经过中心化转化后，得方程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。
Sobel检验免费的在线计算器：
“http://www.danielsoper.com/statcalc/calc31.aspx”，只要把这a、b、SEa、SEb四个数输入，就可以直接得到Z值及其单侧与双侧概率。
中介效应检验程序Sobel-Goodman mediation tests
语法格式为：
sgmediation depvar [if exp] [in range] , 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
案例应用
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
edit
desc
数据如下：
. help sgmediation
. 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 type format label variable label
--------------------------------------------------------------------------------------
id float %9.0g
female float %9.0g fl
ses float %9.0g sl
schtyp float %9.0g scl type of school
prog float %9.0g sel type of program
read float %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:
. set more 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
.
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)
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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
References
Aroian, L.A. (1944). The probability function of the product of two normally distributed variables. Annals of Mathematical Statistics, 18, 265-271.
Baron, R.M. & Kenny, D.A. (1986), Moderator-Mediator Variables Distinction in Social Psychological Research: Conceptual, Strategic, and Statistical Considerations. Journal of Personality and Social Psychology, 51 (6), 1173–82.
Goodman, L.A. (1960) On the exact variance of products. Journal of the American Statistical Association, 55, 708-713.
MacKinnon, D. P. & Dwyer, J. H. (1993). Estimating mediated effects in prevention studies. Evaluation Review, 17, 144-158.
MacKinnon, D. P., Warsi, G., & Dwyer, J. H. (1995). A simulation study of mediated effect measures. Multivariate Behavioral Research, 30(1), 41-62.
Preacher, K. J. & Hayes, A. F. (2004). SPSS and SAS procedures for estimating indirect effects in simple mediation models. Behavior Research Methods, Instruments, & Computers, 36(4), 717-731.
Sobel, M.E. (1982) Asymptotic confidence intervals for indirect effects in structural equation models. Sociological Methodology, 13, 290-312.
Sobel, M.E. (1986) Some new results on indirect effects and their standard errors in covariance structure models. Sociological Methodology, 16, 159-186.