Mplus model86 模型讲解

来自图书《MPlus中介调节模型》

Mplus 高级教程：串联中介与调节模型

• 理论模型：深入理解两个中介变量和一个调节变量的复杂作用机制。
• 数学模型：详细呈现模型中的各个路径及其相互作用的数学表达式。
• 数学推导：解释模型参数如何通过数学方式进行估计，以及如何进行假设检验。
• 代码解读：逐行分析 Mplus 代码，掌握如何定义变量、构建模型、计算效应和绘制交互图。

大家好，欢迎来到本次Mplus高级教程。今天我们将学习如何构建和分析包含两个串联中介变量和一个调节变量的复杂模型。本次教程分为四个部分。首先，我们将从理论层面探讨这个复杂模型的运行机制，明确各个变量之间的相互作用关系。其次，我们会将这些理论关系转换为数学模型，详细列出模型的各个路径及其对应的数学表达式。然后，我们将进一步解释如何通过数学推导得到模型的参数估计值，以及如何利用这些参数进行假设检验。最后，我们将深入剖析Mplus代码，逐行解释如何定义模型变量、构建模型结构、计算条件效应，以及绘制交互作用图。通过本教程，您将掌握使用Mplus分析复杂中介调节模型的核心技能。

理论模型

我们来看，这个图展示了一个复杂的关系模型。这里有五个变量，分别是W、X、M1、M2和Y，它们都用方框表示。箭头表示变量之间的影响方向。X可以直接影响Y，同时X还会影响M1。M1会影响M2，而M1和M2都会影响Y。此外，W会影响M1和Y。最后，W和X的交互作用也会影响M1和Y。

数学模型

这张图展示了一个复杂的变量关系模型。这里有四个自变量，分别是XW、W和X。它们会影响两个中介变量M1和M2，也会直接影响因变量Y。M1和M2之间也存在影响，M1影响M2，并且M1和M2都会影响Y。图中用a1、a2、a3、a4、b1、b2、c1’、c2’、c3’和d1这些系数来表示各个变量之间的影响强度。我们接下来会详细分析这些路径以及它们所代表的意义。

数学公式1

模型方程:

1.  Y = b0 + b1M1 + b2M2 + c1'X + c2'W + c3'XW
2.  M1 = a01 + a1X + a3W + a4XW
3.  M2 = a02 + a2X + d1M1

首先，我们来看一下模型方程。这里有三个方程，它们描述了变量之间的关系。Y是结果变量，X是预测变量，M1和M2是中介变量，W是调节变量。方程1表示Y受到M1、M2、X、W以及X和W交互项的影响；方程2表示M1受到X、W以及X和W交互项的影响；方程3表示M2受到X和M1的影响。

数学公式2

模型方程:

1.  Y = b0 + b1M1 + b2M2 + c1'X + c2'W + c3'XW
2.  M1 = a01 + a1X + a3W + a4XW
3.  M2 = a02 + a2X + d1M1
代入和展开:

M2 = a02 + a2X + d1(a01 + a1X + a3W + a4XW)

Y = b0 + b1(a01 + a1X + a3W + a4XW) + b2(a02 + a2X + d1(a01 + a1X + a3W + a4XW)) + c1'X + c2'W + c3'XW

Y = b0 + a01b1 + a1b1X + a3b1W + a4b1XW + a02b2 + a2b2X + a01d1b2 + a1d1b2X + a3d1b2W + a4d1b2XW + c1'X + c2'W + c3'XW

接下来，我们将进行代入和展开。首先，我们将M1的方程代入M2的方程。然后，再将M1和M2的展开式代入Y的方程中。最后，我们展开所有的括号，得到Y的一个完全展开式。

数学公式3

模型方程:

1.  Y = b0 + b1M1 + b2M2 + c1'X + c2'W + c3'XW
2.  M1 = a01 + a1X + a3W + a4XW
3.  M2 = a02 + a2X + d1M1
代入和展开:

M2 = a02 + a2X + d1(a01 + a1X + a3W + a4XW)

Y = b0 + b1(a01 + a1X + a3W + a4XW) + b2(a02 + a2X + d1(a01 + a1X + a3W + a4XW)) + c1'X + c2'W + c3'XW

Y = b0 + a01b1 + a1b1X + a3b1W + a4b1XW + a02b2 + a2b2X + a01d1b2 + a1d1b2X + a3d1b2W + a4d1b2XW + c1'X + c2'W + c3'XW
整理和分组:

Y = (b0 + a01b1 + a02b2 + a01d1b2 + a3b1W  + a3d1b2W + c2'W) + (a1b1 + a2b2 + a1d1b2 + a4b1W + a4d1b2W + c1' + c3'W)X

现在，我们对Y的展开式进行整理和分组。我们将不包含X的项放在一起，作为截距；将包含X的项提取出X，剩下的部分作为斜率。这样，我们就将Y表示成了 Y = a + bX 的形式。

数学公式4

模型方程:

1.  Y = b0 + b1M1 + b2M2 + c1'X + c2'W + c3'XW
2.  M1 = a01 + a1X + a3W + a4XW
3.  M2 = a02 + a2X + d1M1
代入和展开:

M2 = a02 + a2X + d1(a01 + a1X + a3W + a4XW)

Y = b0 + b1(a01 + a1X + a3W + a4XW) + b2(a02 + a2X + d1(a01 + a1X + a3W + a4XW)) + c1'X + c2'W + c3'XW

Y = b0 + a01b1 + a1b1X + a3b1W + a4b1XW + a02b2 + a2b2X + a01d1b2 + a1d1b2X + a3d1b2W + a4d1b2XW + c1'X + c2'W + c3'XW
整理和分组:

Y = (b0 + a01b1 + a02b2 + a01d1b2 + a3b1W  + a3d1b2W + c2'W) + (a1b1 + a2b2 + a1d1b2 + a4b1W + a4d1b2W + c1' + c3'W)X
总结:

a (截距) = b0 + a01b1 + a02b2 + a01d1b2 + a3b1W  + a3d1b2W + c2'W

b (斜率) = a1b1 + a2b2 + a1d1b2 + a4b1W + a4d1b2W + c1' + c3'W

这里，我们总结了Y与X的关系式。其中，a是截距部分，b是斜率部分。截距包含了所有不包含X的项，斜率包含了所有X的系数。

数学公式5

模型方程:

1.  Y = b0 + b1M1 + b2M2 + c1'X + c2'W + c3'XW
2.  M1 = a01 + a1X + a3W + a4XW
3.  M2 = a02 + a2X + d1M1
代入和展开:

M2 = a02 + a2X + d1(a01 + a1X + a3W + a4XW)

Y = b0 + b1(a01 + a1X + a3W + a4XW) + b2(a02 + a2X + d1(a01 + a1X + a3W + a4XW)) + c1'X + c2'W + c3'XW

Y = b0 + a01b1 + a1b1X + a3b1W + a4b1XW + a02b2 + a2b2X + a01d1b2 + a1d1b2X + a3d1b2W + a4d1b2XW + c1'X + c2'W + c3'XW
整理和分组:

Y = (b0 + a01b1 + a02b2 + a01d1b2 + a3b1W  + a3d1b2W + c2'W) + (a1b1 + a2b2 + a1d1b2 + a4b1W + a4d1b2W + c1' + c3'W)X
总结:

a (截距) = b0 + a01b1 + a02b2 + a01d1b2 + a3b1W  + a3d1b2W + c2'W

b (斜率) = a1b1 + a2b2 + a1d1b2 + a4b1W + a4d1b2W + c1' + c3'W
间接效应和直接效应:

* X 通过 M1 对 Y 的间接效应 (条件效应): (a1 + a4W)b1
* X 通过 M2 对 Y 的间接效应: a2b2
* X 通过 M1 和 M2 对 Y 的间接效应 (条件效应): (a1 + a4W)d1b2
* X 对 Y 的直接效应 (条件效应): c1' + c3'W

最后，我们分析X对Y的各种效应。X通过M1对Y的间接效应是(a1+a4W)b1；X通过M2对Y的间接效应是a2b2；X通过M1和M2对Y的间接效应是(a1+a4W)d1b2；X对Y的直接效应是c1’+c3’W。这里的间接效应，又称作中介效应，它表示X通过中介变量M对Y的影响。直接效应表示X直接对Y的影响。请注意，条件效应是随着调节变量W的变化而变化的。

代码解读1

USEVARIABLES = X M1 M2 W Y XW;
! Create interaction term

大家好，现在我们开始解读Mplus代码。首先，第一步是定义要使用的变量。这里，我们用USEVARIABLES声明了X，作为预测变量；M1和M2，是两个中介变量；W，是调节变量；Y，是结果变量；XW，是X和W的交互项。叹号后面是注释，说明这里要创建一个交互项，但实际上交互项的创建在后面的步骤。

代码解读2

USEVARIABLES = X M1 M2 W Y XW;
! Create interaction term
DEFINE:
 XW = X*W;

第二步，使用DEFINE语句定义新的变量。这里我们创建了X和W的交互项，命名为XW。它通过将X和W相乘得到，代表了X和W的共同作用。

代码解读3

USEVARIABLES = X M1 M2 W Y XW;
! Create interaction term
DEFINE:
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;

接下来，我们设定分析的类型和方法。TYPE=GENERAL表示使用一般的分析类型，适用于多种模型。ESTIMATOR=ML指定使用最大似然估计方法，这是一种常用的参数估计方法。最后，BOOTSTRAP=10000表示使用bootstrap方法进行参数估计，并通过10000次重采样来评估结果的稳定性。

代码解读4

USEVARIABLES = X M1 M2 W Y XW;
! Create interaction term
DEFINE:
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 Y ON M1 (b1);
 Y ON M2 (b2);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 M1 ON X (a1);
 M1 ON W (a3);
 M1 ON XW (a4);
 M2 ON X (a2);
 M2 ON M1 (d1);

第四步，定义模型中变量之间的关系。Y对M1的回归系数命名为b1，Y对M2的回归系数命名为b2。Y对X的直接回归系数是cdash1，Y对W的直接回归系数是cdash2，Y对XW的回归系数是cdash3。M1对X的回归系数是a1，M1对W的回归系数是a3，M1对XW的回归系数是a4。M2对X的回归系数是a2，M2对M1的回归系数是d1。这些语句共同构建了模型中各变量之间的路径关系。

代码解读5

USEVARIABLES = X M1 M2 W Y XW;
! Create interaction term
DEFINE:
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 Y ON M1 (b1);
 Y ON M2 (b2);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 M1 ON X (a1);
 M1 ON W (a3);
 M1 ON XW (a4);
 M2 ON X (a2);
 M2 ON M1 (d1);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1 a2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_A IMM_B
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);
 LOW_W = #LOWW;
! replace #LOWW in the code with your chosen low value of W
 MED_W = #MEDW;
! replace #MEDW in the code with your chosen medium value of W
 HIGH_W = #HIGHW;
! replace #HIGHW in the code with your chosen high value of W

第五步，我们使用模型约束来计算不同调节变量水平下的效应。首先使用NEW定义了一系列新的参数，包括调节变量W的低、中、高值，以及在不同W值下的间接效应、直接效应和总效应等。接着，将用户指定的值赋值给LOW_W, MED_W和HIGH_W。 注意，代码中 #LOWW, #MEDW, 和 #HIGHW需要替换为你选择的实际数值。

代码解读6

USEVARIABLES = X M1 M2 W Y XW;
! Create interaction term
DEFINE:
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 Y ON M1 (b1);
 Y ON M2 (b2);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 M1 ON X (a1);
 M1 ON W (a3);
 M1 ON XW (a4);
 M2 ON X (a2);
 M2 ON M1 (d1);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1 a2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_A IMM_B
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);
 LOW_W = #LOWW;
! replace #LOWW in the code with your chosen low value of W
 MED_W = #MEDW;
! replace #MEDW in the code with your chosen medium value of W
 HIGH_W = #HIGHW;
! replace #HIGHW in the code with your chosen high value of W
! Now calc indirect, direct and total effects for each value of W
! Conditional indirect effects of X on Y via M1 only given values of W
 LWa1b1 = a1*b1 + a4*b1*LOW_W;
 MWa1b1 = a1*b1 + a4*b1*MED_W;
 HWa1b1 = a1*b1 + a4*b1*HIGH_W;
 a2b2 = a2*b2 ;
! indirect effects of X on Y via M2 only
! Conditional indirect effects of X on Y via M1 and M2 given values of W
 LWa1d1b2 = a1*d1*b2 + a4*d1*b2*LOW_W;
 MWa1d1b2 = a1*d1*b2 + a4*d1*b2*MED_W;
 HWa1d1b2 = a1*d1*b2 + a4*d1*b2*HIGH_W;

接下来，我们计算不同W值下的各种效应。这里计算了X通过M1对Y的间接效应，使用了LWa1b1, MWa1b1和HWa1b1来分别表示W的低、中、高值下的条件间接效应。a2b2表示X通过M2对Y的间接效应。 LWa1d1b2, MWa1d1b2和HWa1d1b2则表示X通过M1和M2对Y的间接效应在不同W值下的条件效应。公式中使用了前面定义的回归系数和W的取值。

代码解读7

USEVARIABLES = X M1 M2 W Y XW;
! Create interaction term
DEFINE:
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 Y ON M1 (b1);
 Y ON M2 (b2);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 M1 ON X (a1);
 M1 ON W (a3);
 M1 ON XW (a4);
 M2 ON X (a2);
 M2 ON M1 (d1);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1 a2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_A IMM_B
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);
 LOW_W = #LOWW;
! replace #LOWW in the code with your chosen low value of W
 MED_W = #MEDW;
! replace #MEDW in the code with your chosen medium value of W
 HIGH_W = #HIGHW;
! replace #HIGHW in the code with your chosen high value of W
! Now calc indirect, direct and total effects for each value of W
! Conditional indirect effects of X on Y via M1 only given values of W
 LWa1b1 = a1*b1 + a4*b1*LOW_W;
 MWa1b1 = a1*b1 + a4*b1*MED_W;
 HWa1b1 = a1*b1 + a4*b1*HIGH_W;
 a2b2 = a2*b2 ;
! indirect effects of X on Y via M2 only
! Conditional indirect effects of X on Y via M1 and M2 given values of W
 LWa1d1b2 = a1*d1*b2 + a4*d1*b2*LOW_W;
 MWa1d1b2 = a1*d1*b2 + a4*d1*b2*MED_W;
 HWa1d1b2 = a1*d1*b2 + a4*d1*b2*HIGH_W;
! Indices of Moderated Mediation
 IMM_A = a4*b1;
 IMM_B = a4*d1*b2;
! Conditional direct effects of X on Y given values of W
 DIR_LW = cdash1 + cdash3*LOW_W;
 DIR_MW = cdash1 + cdash3*MED_W;
 DIR_HW = cdash1 + cdash3*HIGH_W;
! Conditional total effects of X on Y given values of W
 TOT_LOWW = LWa1d1b2 + LWa1b1 + a2b2 + DIR_LW;
 TOT_MEDW = MWa1d1b2 + MWa1b1 + a2b2 + DIR_MW;
 TOT_HIW = HWa1d1b2 + HWa1b1 + a2b2 + DIR_HW;

然后，计算调节中介的指数，IMM_A和IMM_B分别代表了W如何调节X通过M1和M1、M2的间接效应的大小。接着计算了不同W值下X对Y的直接效应DIR_LW, DIR_MW和DIR_HW。最后，计算了不同W值下X对Y的总效应，TOT_LOWW, TOT_MEDW和TOT_HIW，总效应包含了所有的间接效应和直接效应。

代码解读8

USEVARIABLES = X M1 M2 W Y XW;
! Create interaction term
DEFINE:
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 Y ON M1 (b1);
 Y ON M2 (b2);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 M1 ON X (a1);
 M1 ON W (a3);
 M1 ON XW (a4);
 M2 ON X (a2);
 M2 ON M1 (d1);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1 a2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_A IMM_B
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);
 LOW_W = #LOWW;
! replace #LOWW in the code with your chosen low value of W
 MED_W = #MEDW;
! replace #MEDW in the code with your chosen medium value of W
 HIGH_W = #HIGHW;
! replace #HIGHW in the code with your chosen high value of W
! Now calc indirect, direct and total effects for each value of W
! Conditional indirect effects of X on Y via M1 only given values of W
 LWa1b1 = a1*b1 + a4*b1*LOW_W;
 MWa1b1 = a1*b1 + a4*b1*MED_W;
 HWa1b1 = a1*b1 + a4*b1*HIGH_W;
 a2b2 = a2*b2 ;
! indirect effects of X on Y via M2 only
! Conditional indirect effects of X on Y via M1 and M2 given values of W
 LWa1d1b2 = a1*d1*b2 + a4*d1*b2*LOW_W;
 MWa1d1b2 = a1*d1*b2 + a4*d1*b2*MED_W;
 HWa1d1b2 = a1*d1*b2 + a4*d1*b2*HIGH_W;
! Indices of Moderated Mediation
 IMM_A = a4*b1;
 IMM_B = a4*d1*b2;
! Conditional direct effects of X on Y given values of W
 DIR_LW = cdash1 + cdash3*LOW_W;
 DIR_MW = cdash1 + cdash3*MED_W;
 DIR_HW = cdash1 + cdash3*HIGH_W;
! Conditional total effects of X on Y given values of W
 TOT_LOWW = LWa1d1b2 + LWa1b1 + a2b2 + DIR_LW;
 TOT_MEDW = MWa1d1b2 + MWa1b1 + a2b2 + DIR_MW;
 TOT_HIW = HWa1d1b2 + HWa1b1 + a2b2 + DIR_HW;
! Use loop plot to plot total effect of X on Y for low, med, high values of W
! NOTE - values of 1,5 in LOOP() statement need to be replaced by
! logical min and max limits of predictor X used in analysis
 PLOT(LOMOD MEDMOD HIMOD);
 LOOP(XVAL,1,5,0.1);
 LOMOD = TOT_LOWW*XVAL;
 MEDMOD = TOT_MEDW*XVAL;
 HIMOD = TOT_HIW*XVAL;

第八步，我们设置循环绘图，来可视化X对Y的总效应在不同W值下的变化。代码首先提示用户需要替换LOOP函数中的1和5，用实际的X的最小值和最大值代替。然后，通过循环，计算当X值在指定范围内变化时，在W的低，中，高值下，Y的预测值，结果分别存储在LOMOD, MEDMOD和HIMOD中。

代码解读9

USEVARIABLES = X M1 M2 W Y XW;
! Create interaction term
DEFINE:
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 Y ON M1 (b1);
 Y ON M2 (b2);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 M1 ON X (a1);
 M1 ON W (a3);
 M1 ON XW (a4);
 M2 ON X (a2);
 M2 ON M1 (d1);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1 a2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_A IMM_B
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);
 LOW_W = #LOWW;
! replace #LOWW in the code with your chosen low value of W
 MED_W = #MEDW;
! replace #MEDW in the code with your chosen medium value of W
 HIGH_W = #HIGHW;
! replace #HIGHW in the code with your chosen high value of W
! Now calc indirect, direct and total effects for each value of W
! Conditional indirect effects of X on Y via M1 only given values of W
 LWa1b1 = a1*b1 + a4*b1*LOW_W;
 MWa1b1 = a1*b1 + a4*b1*MED_W;
 HWa1b1 = a1*b1 + a4*b1*HIGH_W;
 a2b2 = a2*b2 ;
! indirect effects of X on Y via M2 only
! Conditional indirect effects of X on Y via M1 and M2 given values of W
 LWa1d1b2 = a1*d1*b2 + a4*d1*b2*LOW_W;
 MWa1d1b2 = a1*d1*b2 + a4*d1*b2*MED_W;
 HWa1d1b2 = a1*d1*b2 + a4*d1*b2*HIGH_W;
! Indices of Moderated Mediation
 IMM_A = a4*b1;
 IMM_B = a4*d1*b2;
! Conditional direct effects of X on Y given values of W
 DIR_LW = cdash1 + cdash3*LOW_W;
 DIR_MW = cdash1 + cdash3*MED_W;
 DIR_HW = cdash1 + cdash3*HIGH_W;
! Conditional total effects of X on Y given values of W
 TOT_LOWW = LWa1d1b2 + LWa1b1 + a2b2 + DIR_LW;
 TOT_MEDW = MWa1d1b2 + MWa1b1 + a2b2 + DIR_MW;
 TOT_HIW = HWa1d1b2 + HWa1b1 + a2b2 + DIR_HW;
! Use loop plot to plot total effect of X on Y for low, med, high values of W
! NOTE - values of 1,5 in LOOP() statement need to be replaced by
! logical min and max limits of predictor X used in analysis
 PLOT(LOMOD MEDMOD HIMOD);
 LOOP(XVAL,1,5,0.1);
 LOMOD = TOT_LOWW*XVAL;
 MEDMOD = TOT_MEDW*XVAL;
 HIMOD = TOT_HIW*XVAL;
PLOT:
 TYPE = plot2;

第九步，设置绘图的类型。这里TYPE=plot2表示要绘制多条曲线图，用于展示在不同的W值下X对Y的总效应的变化情况。

代码解读10

USEVARIABLES = X M1 M2 W Y XW;
! Create interaction term
DEFINE:
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 Y ON M1 (b1);
 Y ON M2 (b2);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 M1 ON X (a1);
 M1 ON W (a3);
 M1 ON XW (a4);
 M2 ON X (a2);
 M2 ON M1 (d1);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1 a2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_A IMM_B
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);
 LOW_W = #LOWW;
! replace #LOWW in the code with your chosen low value of W
 MED_W = #MEDW;
! replace #MEDW in the code with your chosen medium value of W
 HIGH_W = #HIGHW;
! replace #HIGHW in the code with your chosen high value of W
! Now calc indirect, direct and total effects for each value of W
! Conditional indirect effects of X on Y via M1 only given values of W
 LWa1b1 = a1*b1 + a4*b1*LOW_W;
 MWa1b1 = a1*b1 + a4*b1*MED_W;
 HWa1b1 = a1*b1 + a4*b1*HIGH_W;
 a2b2 = a2*b2 ;
! indirect effects of X on Y via M2 only
! Conditional indirect effects of X on Y via M1 and M2 given values of W
 LWa1d1b2 = a1*d1*b2 + a4*d1*b2*LOW_W;
 MWa1d1b2 = a1*d1*b2 + a4*d1*b2*MED_W;
 HWa1d1b2 = a1*d1*b2 + a4*d1*b2*HIGH_W;
! Indices of Moderated Mediation
 IMM_A = a4*b1;
 IMM_B = a4*d1*b2;
! Conditional direct effects of X on Y given values of W
 DIR_LW = cdash1 + cdash3*LOW_W;
 DIR_MW = cdash1 + cdash3*MED_W;
 DIR_HW = cdash1 + cdash3*HIGH_W;
! Conditional total effects of X on Y given values of W
 TOT_LOWW = LWa1d1b2 + LWa1b1 + a2b2 + DIR_LW;
 TOT_MEDW = MWa1d1b2 + MWa1b1 + a2b2 + DIR_MW;
 TOT_HIW = HWa1d1b2 + HWa1b1 + a2b2 + DIR_HW;
! Use loop plot to plot total effect of X on Y for low, med, high values of W
! NOTE - values of 1,5 in LOOP() statement need to be replaced by
! logical min and max limits of predictor X used in analysis
 PLOT(LOMOD MEDMOD HIMOD);
 LOOP(XVAL,1,5,0.1);
 LOMOD = TOT_LOWW*XVAL;
 MEDMOD = TOT_MEDW*XVAL;
 HIMOD = TOT_HIW*XVAL;
PLOT:
 TYPE = plot2;
OUTPUT:
 STAND CINT(bcbootstrap);

最后一步，指定输出格式。STAND表示输出标准化参数估计，CINT(bcbootstrap)表示输出使用偏差校正的bootstrap方法计算得到的置信区间。这可以帮助我们评估参数估计的可靠性。

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