Mplus model88 模型讲解

来自图书《MPlus中介调节模型》

Mplus 调节中介模型分析教程结构

• 理论模型
• 数学模型
• 数学推导
• 代码解读

大家好，欢迎来到 Data Sense 的 Mplus 调节中介模型分析教程。本教程为了帮助大家快速掌握复杂模型分析，结构非常清晰。我们首先会讲解模型的理论背景，帮助大家理解模型背后的逻辑。接着，我们会用数学公式来精确描述模型，并提供必要的数学推导，让大家深入理解模型运作的机制。最后，我们会详细讲解 Mplus 代码的含义，以及如何根据自己的研究修改代码。本教程旨在提供一个实用而高效的学习体验，让大家可以快速上手，将模型应用到自己的研究中。

理论模型

我们来看，这个图显示了几个变量之间的关系。X 影响 M1，M1 又影响 M2。M2 和 W 都影响 Y，M1 也直接影响 Y。同时，X 也直接影响 Y，W 也直接影响 Y。这就是我们理论模型的大致框架。

数学模型

这张图展示了一个复杂的统计模型。我们可以看到，X 通过两条路径影响 Y。第一条路径，X 先影响 M1，M1 再影响 Y；第二条路径，X 先影响 M1，M1 再影响 M2，M2 再影响 Y。同时，W 这个变量会调节 M1 和 M2 对 Y 的影响。具体来说，M1 和 W 的交互项 M1W 以及 M2 和 W 的交互项 M2W 都会影响 Y。图中还显示了 X 直接影响 Y 的路径，用 c’ 表示。箭头表示变量之间的影响方向，箭头旁的 a1、a2、b1、b2、b3、b4、b5、d1 和 c’ 代表了这些影响的大小。

数学公式1

模型方程:

Y = b0 + b1M1 + b2M2 + b3W + b4M1W + b5M2W + c'X
M1 = a01 + a1X
M2 = a02 + a2X + d1M1

首先，我们定义了模型中变量之间的关系。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。我们的目标是将Y表示为X的函数，从而研究X对Y的总效应和间接效应。

数学公式2

模型方程:

Y = b0 + b1M1 + b2M2 + b3W + b4M1W + b5M2W + c'X
M1 = a01 + a1X
M2 = a02 + a2X + d1M1
代入化简:

Y = b0 + b1(a01 + a1X) + b2(a02 + a2X + d1(a01 + a1X)) + b3W + b4(a01 + a1X)W + b5(a02 + a2X + d1(a01 + a1X))W + c'X

接下来，我们将M1和M2的表达式代入Y的方程中。这一步是为了将Y完全表示为X和其他已知变量的函数。

数学公式3

模型方程:

Y = b0 + b1M1 + b2M2 + b3W + b4M1W + b5M2W + c'X
M1 = a01 + a1X
M2 = a02 + a2X + d1M1
代入化简:

Y = b0 + b1(a01 + a1X) + b2(a02 + a2X + d1(a01 + a1X)) + b3W + b4(a01 + a1X)W + b5(a02 + a2X + d1(a01 + a1X))W + c'X
Y = b0 + a01b1 + a1b1X + a02b2 + a2b2X + a01d1b2 + a1d1b2X + b3W + a01b4W + a1b4XW + a02b5 + a2b5X + a01d1b5W + a1d1b5XW + c'X

然后，我们展开括号，以便将各项整理成更容易分析的形式。这一步只是简单的代数运算。

数学公式4

模型方程:

Y = b0 + b1M1 + b2M2 + b3W + b4M1W + b5M2W + c'X
M1 = a01 + a1X
M2 = a02 + a2X + d1M1
代入化简:

Y = b0 + b1(a01 + a1X) + b2(a02 + a2X + d1(a01 + a1X)) + b3W + b4(a01 + a1X)W + b5(a02 + a2X + d1(a01 + a1X))W + c'X
Y = b0 + a01b1 + a1b1X + a02b2 + a2b2X + a01d1b2 + a1d1b2X + b3W + a01b4W + a1b4XW + a02b5 + a2b5X + a01d1b5W + a1d1b5XW + c'X
整理:

Y = (b0 + a01b1 + a02b2 + a01d1b2 + b3W + a01b4W + a02b5 + a01d1b5W) + (a1b1 + a2b2 + a2b5W + a1d1b2 + a1b4W + a1d1b5W + c')X

现在，我们将各项整理成Y = a + bX的形式，其中a是不包含X的项，b是X的系数。这样可以更清晰地看到X如何影响Y。

数学公式5

模型方程:

Y = b0 + b1M1 + b2M2 + b3W + b4M1W + b5M2W + c'X
M1 = a01 + a1X
M2 = a02 + a2X + d1M1
代入化简:

Y = b0 + b1(a01 + a1X) + b2(a02 + a2X + d1(a01 + a1X)) + b3W + b4(a01 + a1X)W + b5(a02 + a2X + d1(a01 + a1X))W + c'X
Y = b0 + a01b1 + a1b1X + a02b2 + a2b2X + a01d1b2 + a1d1b2X + b3W + a01b4W + a1b4XW + a02b5 + a2b5X + a01d1b5W + a1d1b5XW + c'X
整理:

Y = (b0 + a01b1 + a02b2 + a01d1b2 + b3W + a01b4W + a02b5 + a01d1b5W) + (a1b1 + a2b2 + a2b5W + a1d1b2 + a1b4W + a1d1b5W + c')X
结果:

间接效应 (conditional on W):
*  a1(b1 + b4W)
*  a2(b2 + b5W)
*  a1d1(b2 + b5W)

直接效应:
*  c'

最后，我们得到了Y关于X的表达式，从中我们可以提取出三个间接效应和一个直接效应。间接效应表示X通过中介变量M1和M2对Y的影响，并且这些影响会受到调节变量W的影响。直接效应表示X直接对Y的影响，不通过中介变量。

代码解读1

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y

首先，我们看到的是一些注释行，它们定义了我们模型中使用的变量。X是预测变量，M1和M2是中介变量，W是调节变量，Y是结果变量。这些注释帮助我们理解代码的含义。

代码解读2

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;

接下来，USEVARIABLES 命令指定了分析中将要使用的所有变量。除了原始变量X、M1、M2、W和Y之外，还包括了交互项M1W和M2W，这些交互项会在后面进行定义。

代码解读3

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above

这里是一些注释，提醒我们需要创建交互项，并且这些交互项需要在 USEVARIABLES 子命令之后定义。

代码解读4

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;

DEFINE 命令开始定义新的变量。我们在这里定义了交互项。M1W等于M1乘以W，M2W等于M2乘以W。这些交互项将用于捕捉调节效应。

代码解读5

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;

ANALYSIS 命令开始定义分析的参数。TYPE = GENERAL 指定进行一般模型分析。ESTIMATOR = ML 指定使用最大似然估计方法。BOOTSTRAP = 10000 指定使用bootstrap方法进行参数估计，抽样次数为10000次，用于计算置信区间。

代码解读6

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:

这里是一个注释，提醒在MODEL命令中，每个路径都使用括号命名。MODEL命令开始定义模型的结构。

代码解读7

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);

这些代码定义了Y对其他变量的回归路径。例如，Y ON M1 (b1)定义了Y对M1的回归路径，并命名为b1。Y ON X (cdash) 定义了X对Y的直接效应，并命名为cdash。这些回归系数表示变量之间的关系强度。

代码解读8

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);
! direct effect of X on Y
M1 ON X (a1);
M2 ON X (a2);
M2 ON M1 (d1);

这里是一个注释，说明上一行代码是X对Y的直接效应。接下来的代码定义了中介变量的回归路径。M1 ON X (a1)定义了M1对X的回归路径，命名为a1。M2 ON X (a2)定义了M2对X的回归路径，命名为a2。M2 ON M1 (d1)定义了M2对M1的回归路径，命名为d1。

代码解读9

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);
! direct effect of X on Y
M1 ON X (a1);
M2 ON X (a2);
M2 ON M1 (d1);
! Use model constraint subcommand to test simple slopes
! You need to pick low, medium and high moderator values,
! for example, of 1 SD below mean, mean, 1 SD above mean
! Also calc total effects at lo, med, hi values of moderator

这些注释说明接下来的模型约束子命令用于测试简单斜率。我们需要选择调节变量W的低、中、高三个值（例如，均值上下一个标准差），并计算不同调节变量值下的总效应。

代码解读10

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);
! direct effect of X on Y
M1 ON X (a1);
M2 ON X (a2);
M2 ON M1 (d1);
! Use model constraint subcommand to test simple slopes
! You need to pick low, medium and high moderator values,
! for example, of 1 SD below mean, mean, 1 SD above mean
! Also calc total effects at lo, med, hi values of moderator
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W
LWa1b1 MWa1b1 HWa1b1
LWa2b2 MWa2b2 HWa2b2
LWa1d1b2 MWa1d1b2 HWa1d1b2
IMM_A IMM_B IMM_C
TOT_LOWW TOT_MEDW TOT_HIW);

MODEL CONSTRAINT 命令开始定义模型约束和计算。NEW 子命令定义新的变量，用于存储调节变量W的低、中、高值以及计算出的条件间接效应和总效应。

代码解读11

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);
! direct effect of X on Y
M1 ON X (a1);
M2 ON X (a2);
M2 ON M1 (d1);
! Use model constraint subcommand to test simple slopes
! You need to pick low, medium and high moderator values,
! for example, of 1 SD below mean, mean, 1 SD above mean
! Also calc total effects at lo, med, hi values of moderator
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W
LWa1b1 MWa1b1 HWa1b1
LWa2b2 MWa2b2 HWa2b2
LWa1d1b2 MWa1d1b2 HWa1d1b2
IMM_A IMM_B IMM_C
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

这里定义了调节变量W的低、中、高值。例如，LOW_W = #LOWW 定义 LOW_W 为 W 的低值，#LOWW 是占位符，实际使用时需要替换为具体的数值。注释提醒用户需要将 #LOWW 等占位符替换为 W 的实际低、中、高值。

代码解读12

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);
! direct effect of X on Y
M1 ON X (a1);
M2 ON X (a2);
M2 ON M1 (d1);
! Use model constraint subcommand to test simple slopes
! You need to pick low, medium and high moderator values,
! for example, of 1 SD below mean, mean, 1 SD above mean
! Also calc total effects at lo, med, hi values of moderator
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W
LWa1b1 MWa1b1 HWa1b1
LWa2b2 MWa2b2 HWa2b2
LWa1d1b2 MWa1d1b2 HWa1d1b2
IMM_A IMM_B IMM_C
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 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 + a1*b4*LOW_W;
MWa1b1 = a1*b1 + a1*b4*MED_W;
HWa1b1 = a1*b1 + a1*b4*HIGH_W;

这里开始计算不同调节变量值下的间接效应和总效应。例如，LWa1b1 = a1*b1 + a1*b4*LOW_W 计算W取低值时，通过M1的条件间接效应。注释说明下面计算的是通过 M1 的条件间接效应。

代码解读13

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);
! direct effect of X on Y
M1 ON X (a1);
M2 ON X (a2);
M2 ON M1 (d1);
! Use model constraint subcommand to test simple slopes
! You need to pick low, medium and high moderator values,
! for example, of 1 SD below mean, mean, 1 SD above mean
! Also calc total effects at lo, med, hi values of moderator
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W
LWa1b1 MWa1b1 HWa1b1
LWa2b2 MWa2b2 HWa2b2
LWa1d1b2 MWa1d1b2 HWa1d1b2
IMM_A IMM_B IMM_C
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 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 + a1*b4*LOW_W;
MWa1b1 = a1*b1 + a1*b4*MED_W;
HWa1b1 = a1*b1 + a1*b4*HIGH_W;
! Conditional indirect effects of X on Y via M2 only given values of W

LWa2b2 = a2*b2 + a2*b5*LOW_W;
MWa2b2 = a2*b2 + a2*b5*MED_W;
HWa2b2 = a2*b2 + a2*b5*HIGH_W;

这里计算通过M2的条件间接效应。例如，LWa2b2 = a2*b2 + a2*b5*LOW_W 计算W取低值时，通过M2的条件间接效应。注释说明下面计算的是通过 M2 的条件间接效应。

代码解读14

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);
! direct effect of X on Y
M1 ON X (a1);
M2 ON X (a2);
M2 ON M1 (d1);
! Use model constraint subcommand to test simple slopes
! You need to pick low, medium and high moderator values,
! for example, of 1 SD below mean, mean, 1 SD above mean
! Also calc total effects at lo, med, hi values of moderator
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W
LWa1b1 MWa1b1 HWa1b1
LWa2b2 MWa2b2 HWa2b2
LWa1d1b2 MWa1d1b2 HWa1d1b2
IMM_A IMM_B IMM_C
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 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 + a1*b4*LOW_W;
MWa1b1 = a1*b1 + a1*b4*MED_W;
HWa1b1 = a1*b1 + a1*b4*HIGH_W;
! Conditional indirect effects of X on Y via M2 only given values of W

LWa2b2 = a2*b2 + a2*b5*LOW_W;
MWa2b2 = a2*b2 + a2*b5*MED_W;
HWa2b2 = a2*b2 + a2*b5*HIGH_W;
! Conditional indirect effects of X on Y via M1 and M2 given values of W

LWa1d1b2 = a1*d1*b2 + a1*d1*b5*LOW_W;
MWa1d1b2 = a1*d1*b2 + a1*d1*b5*MED_W;
HWa1d1b2 = a1*d1*b2 + a1*d1*b5*HIGH_W;

这里计算通过M1和M2的串行条件间接效应。例如，LWa1d1b2 = a1*d1*b2 + a1*d1*b5*LOW_W 计算W取低值时，通过M1和M2的条件间接效应。注释说明下面计算的是通过 M1 和 M2 的串行条件间接效应。

代码解读15

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);
! direct effect of X on Y
M1 ON X (a1);
M2 ON X (a2);
M2 ON M1 (d1);
! Use model constraint subcommand to test simple slopes
! You need to pick low, medium and high moderator values,
! for example, of 1 SD below mean, mean, 1 SD above mean
! Also calc total effects at lo, med, hi values of moderator
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W
LWa1b1 MWa1b1 HWa1b1
LWa2b2 MWa2b2 HWa2b2
LWa1d1b2 MWa1d1b2 HWa1d1b2
IMM_A IMM_B IMM_C
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 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 + a1*b4*LOW_W;
MWa1b1 = a1*b1 + a1*b4*MED_W;
HWa1b1 = a1*b1 + a1*b4*HIGH_W;
! Conditional indirect effects of X on Y via M2 only given values of W

LWa2b2 = a2*b2 + a2*b5*LOW_W;
MWa2b2 = a2*b2 + a2*b5*MED_W;
HWa2b2 = a2*b2 + a2*b5*HIGH_W;
! Conditional indirect effects of X on Y via M1 and M2 given values of W

LWa1d1b2 = a1*d1*b2 + a1*d1*b5*LOW_W;
MWa1d1b2 = a1*d1*b2 + a1*d1*b5*MED_W;
HWa1d1b2 = a1*d1*b2 + a1*d1*b5*HIGH_W;
! Indices of Moderated Mediation

IMM_A = a1*b4;
IMM_B = a1*d1*b5;
IMM_C = a2*b5;

这里计算调节中介效应的指标。IMM_A = a1*b4计算M1对W调节的中介作用的指标，IMM_B = a1*d1*b5计算 M1 和 M2 的串行中介路径中，M2 对 W 调节的中介作用的指标， IMM_C = a2*b5 计算 M2 对 W 调节的中介作用的指标。注释说明下面计算的是调节中介效应的指标。

代码解读16

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);
! direct effect of X on Y
M1 ON X (a1);
M2 ON X (a2);
M2 ON M1 (d1);
! Use model constraint subcommand to test simple slopes
! You need to pick low, medium and high moderator values,
! for example, of 1 SD below mean, mean, 1 SD above mean
! Also calc total effects at lo, med, hi values of moderator
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W
LWa1b1 MWa1b1 HWa1b1
LWa2b2 MWa2b2 HWa2b2
LWa1d1b2 MWa1d1b2 HWa1d1b2
IMM_A IMM_B IMM_C
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 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 + a1*b4*LOW_W;
MWa1b1 = a1*b1 + a1*b4*MED_W;
HWa1b1 = a1*b1 + a1*b4*HIGH_W;
! Conditional indirect effects of X on Y via M2 only given values of W

LWa2b2 = a2*b2 + a2*b5*LOW_W;
MWa2b2 = a2*b2 + a2*b5*MED_W;
HWa2b2 = a2*b2 + a2*b5*HIGH_W;
! Conditional indirect effects of X on Y via M1 and M2 given values of W

LWa1d1b2 = a1*d1*b2 + a1*d1*b5*LOW_W;
MWa1d1b2 = a1*d1*b2 + a1*d1*b5*MED_W;
HWa1d1b2 = a1*d1*b2 + a1*d1*b5*HIGH_W;
! Indices of Moderated Mediation

IMM_A = a1*b4;
IMM_B = a1*d1*b5;
IMM_C = a2*b5;
! Conditional total effects of X on Y given values of W

TOT_LOWW = LWa1d1b2 + LWa2b2 + LWa1b1 + cdash;
TOT_MEDW = MWa1d1b2 + MWa2b2 + MWa1b1 + cdash ;
TOT_HIW = HWa1d1b2 + HWa2b2 + HWa1b1 + cdash;

这里计算不同W值下X对Y的条件总效应。例如，TOT_LOWW = LWa1d1b2 + LWa2b2 + LWa1b1 + cdash计算W取低值时，X对Y的总效应。注释说明下面计算的是不同 W 值下 X 对 Y 的条件总效应。

代码解读17

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);
! direct effect of X on Y
M1 ON X (a1);
M2 ON X (a2);
M2 ON M1 (d1);
! Use model constraint subcommand to test simple slopes
! You need to pick low, medium and high moderator values,
! for example, of 1 SD below mean, mean, 1 SD above mean
! Also calc total effects at lo, med, hi values of moderator
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W
LWa1b1 MWa1b1 HWa1b1
LWa2b2 MWa2b2 HWa2b2
LWa1d1b2 MWa1d1b2 HWa1d1b2
IMM_A IMM_B IMM_C
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 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 + a1*b4*LOW_W;
MWa1b1 = a1*b1 + a1*b4*MED_W;
HWa1b1 = a1*b1 + a1*b4*HIGH_W;
! Conditional indirect effects of X on Y via M2 only given values of W

LWa2b2 = a2*b2 + a2*b5*LOW_W;
MWa2b2 = a2*b2 + a2*b5*MED_W;
HWa2b2 = a2*b2 + a2*b5*HIGH_W;
! Conditional indirect effects of X on Y via M1 and M2 given values of W

LWa1d1b2 = a1*d1*b2 + a1*d1*b5*LOW_W;
MWa1d1b2 = a1*d1*b2 + a1*d1*b5*MED_W;
HWa1d1b2 = a1*d1*b2 + a1*d1*b5*HIGH_W;
! Indices of Moderated Mediation

IMM_A = a1*b4;
IMM_B = a1*d1*b5;
IMM_C = a2*b5;
! Conditional total effects of X on Y given values of W

TOT_LOWW = LWa1d1b2 + LWa2b2 + LWa1b1 + cdash;
TOT_MEDW = MWa1d1b2 + MWa2b2 + MWa1b1 + cdash ;
TOT_HIW = HWa1d1b2 + HWa2b2 + HWa1b1 + cdash;
! 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);

这里开始定义如何绘制X对Y的总效应在不同W值下的变化。 PLOT(LOMOD MEDMOD HIMOD)指定要绘制的变量，这些变量在接下来的循环中计算。注释说明需要将LOOP中的1和5替换为X的实际最小值和最大值。

代码解读18

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);
! direct effect of X on Y
M1 ON X (a1);
M2 ON X (a2);
M2 ON M1 (d1);
! Use model constraint subcommand to test simple slopes
! You need to pick low, medium and high moderator values,
! for example, of 1 SD below mean, mean, 1 SD above mean
! Also calc total effects at lo, med, hi values of moderator
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W
LWa1b1 MWa1b1 HWa1b1
LWa2b2 MWa2b2 HWa2b2
LWa1d1b2 MWa1d1b2 HWa1d1b2
IMM_A IMM_B IMM_C
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 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 + a1*b4*LOW_W;
MWa1b1 = a1*b1 + a1*b4*MED_W;
HWa1b1 = a1*b1 + a1*b4*HIGH_W;
! Conditional indirect effects of X on Y via M2 only given values of W

LWa2b2 = a2*b2 + a2*b5*LOW_W;
MWa2b2 = a2*b2 + a2*b5*MED_W;
HWa2b2 = a2*b2 + a2*b5*HIGH_W;
! Conditional indirect effects of X on Y via M1 and M2 given values of W

LWa1d1b2 = a1*d1*b2 + a1*d1*b5*LOW_W;
MWa1d1b2 = a1*d1*b2 + a1*d1*b5*MED_W;
HWa1d1b2 = a1*d1*b2 + a1*d1*b5*HIGH_W;
! Indices of Moderated Mediation

IMM_A = a1*b4;
IMM_B = a1*d1*b5;
IMM_C = a2*b5;
! Conditional total effects of X on Y given values of W

TOT_LOWW = LWa1d1b2 + LWa2b2 + LWa1b1 + cdash;
TOT_MEDW = MWa1d1b2 + MWa2b2 + MWa1b1 + cdash ;
TOT_HIW = HWa1d1b2 + HWa2b2 + HWa1b1 + cdash;
! 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;

LOOP(XVAL,1,5,0.1) 定义一个循环，变量为XVAL，从1变化到5，步长为0.1。这些值需要根据实际数据替换。接下来的代码计算不同W值下的总效应乘以X的值，用于绘制散点图。

代码解读19

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);
! direct effect of X on Y
M1 ON X (a1);
M2 ON X (a2);
M2 ON M1 (d1);
! Use model constraint subcommand to test simple slopes
! You need to pick low, medium and high moderator values,
! for example, of 1 SD below mean, mean, 1 SD above mean
! Also calc total effects at lo, med, hi values of moderator
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W
LWa1b1 MWa1b1 HWa1b1
LWa2b2 MWa2b2 HWa2b2
LWa1d1b2 MWa1d1b2 HWa1d1b2
IMM_A IMM_B IMM_C
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 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 + a1*b4*LOW_W;
MWa1b1 = a1*b1 + a1*b4*MED_W;
HWa1b1 = a1*b1 + a1*b4*HIGH_W;
! Conditional indirect effects of X on Y via M2 only given values of W

LWa2b2 = a2*b2 + a2*b5*LOW_W;
MWa2b2 = a2*b2 + a2*b5*MED_W;
HWa2b2 = a2*b2 + a2*b5*HIGH_W;
! Conditional indirect effects of X on Y via M1 and M2 given values of W

LWa1d1b2 = a1*d1*b2 + a1*d1*b5*LOW_W;
MWa1d1b2 = a1*d1*b2 + a1*d1*b5*MED_W;
HWa1d1b2 = a1*d1*b2 + a1*d1*b5*HIGH_W;
! Indices of Moderated Mediation

IMM_A = a1*b4;
IMM_B = a1*d1*b5;
IMM_C = a2*b5;
! Conditional total effects of X on Y given values of W

TOT_LOWW = LWa1d1b2 + LWa2b2 + LWa1b1 + cdash;
TOT_MEDW = MWa1d1b2 + MWa2b2 + MWa1b1 + cdash ;
TOT_HIW = HWa1d1b2 + HWa2b2 + HWa1b1 + cdash;
! 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;

PLOT 命令开始定义绘图的参数。TYPE = plot2 指定绘制二维散点图。

代码解读20

! Predictor variable - X
! Mediator variable(s) - M1, M2
! Moderator variable(s) - W
! Outcome variable - Y
USEVARIABLES = X M1 M2 W Y M1W M2W;
! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above
DEFINE:

M1W = M1*W;
M2W = M2*W;
ANALYSIS:

TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
Y ON M1 (b1);
Y ON M2 (b2);
Y ON W (b3);
Y ON M1W (b4);
Y ON M2W (b5);
Y ON X (cdash);
! direct effect of X on Y
M1 ON X (a1);
M2 ON X (a2);
M2 ON M1 (d1);
! Use model constraint subcommand to test simple slopes
! You need to pick low, medium and high moderator values,
! for example, of 1 SD below mean, mean, 1 SD above mean
! Also calc total effects at lo, med, hi values of moderator
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W
LWa1b1 MWa1b1 HWa1b1
LWa2b2 MWa2b2 HWa2b2
LWa1d1b2 MWa1d1b2 HWa1d1b2
IMM_A IMM_B IMM_C
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 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 + a1*b4*LOW_W;
MWa1b1 = a1*b1 + a1*b4*MED_W;
HWa1b1 = a1*b1 + a1*b4*HIGH_W;
! Conditional indirect effects of X on Y via M2 only given values of W

LWa2b2 = a2*b2 + a2*b5*LOW_W;
MWa2b2 = a2*b2 + a2*b5*MED_W;
HWa2b2 = a2*b2 + a2*b5*HIGH_W;
! Conditional indirect effects of X on Y via M1 and M2 given values of W

LWa1d1b2 = a1*d1*b2 + a1*d1*b5*LOW_W;
MWa1d1b2 = a1*d1*b2 + a1*d1*b5*MED_W;
HWa1d1b2 = a1*d1*b2 + a1*d1*b5*HIGH_W;
! Indices of Moderated Mediation

IMM_A = a1*b4;
IMM_B = a1*d1*b5;
IMM_C = a2*b5;
! Conditional total effects of X on Y given values of W

TOT_LOWW = LWa1d1b2 + LWa2b2 + LWa1b1 + cdash;
TOT_MEDW = MWa1d1b2 + MWa2b2 + MWa1b1 + cdash ;
TOT_HIW = HWa1d1b2 + HWa2b2 + HWa1b1 + cdash;
! 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);

OUTPUT 命令开始定义输出内容。STAND 指定输出标准化后的结果，CINT(bcbootstrap)指定使用bias-corrected bootstrap方法计算置信区间。

资源汇总

• 本视频讲义地址: https://mlln.cn/mplus-model-templates/model88.html
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• 视频教程: 点击这里打开视频
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