Mplus model92 模型讲解

来自图书《MPlus中介调节模型》

PPT标题：Mplus复杂模型分析教程结构

• 理论模型：理解模型背后的概念和关系
• 数学模型：将理论模型转化为数学方程
• 数学推导：详细展示模型参数估计的数学原理
• 代码解读：分析Mplus代码，并解释每一部分的功能和作用

大家好，今天我将向大家介绍本教程的结构。为了帮助大家更好地掌握复杂模型分析，我们将从四个方面入手。首先，我们会深入理解理论模型，明确变量间的概念和相互关系。接下来，我们会将理论模型转化为具体的数学方程，为后续的推导和计算奠定基础。然后，我们会详细展示模型参数估计的数学原理，让大家理解这些参数是如何计算得到的。最后，我们会仔细解读Mplus代码，帮助大家理解每一部分代码的功能和作用，最终能够根据自己的研究需要，灵活运用Mplus进行复杂模型的分析。希望这个结构能帮助大家更有效地学习和掌握Mplus。

理论模型

我们来看，这张图展示了一个比较复杂的理论模型。这里有五个变量，分别是X、M1、M2、W和Y。大家可以看到，它们之间通过箭头相互连接。X影响着M1、M2和Y。M1影响着M2和Y。M2影响着Y。另外，W也同时影响着X、M1、M2和Y。这些箭头表示了它们之间复杂的相互作用关系。

数学模型

这张图展示了一个比较复杂的模型，里面包含变量X、W、M1、M2和Y。变量X会影响M1，影响的路径是a1，也会影响M2，影响的路径是a2。变量W也会影响M1，路径是a3，同时也会影响M2，路径是a5。X和W的交互作用会影响M1，路径是a4，也会影响M2，路径是a6。M1还会通过路径d1影响M2。M1和W的交互作用还会通过路径d2影响M2。M1会通过路径b1影响Y，M2也会通过路径b2影响Y。M1和W的交互作用会通过路径b3影响Y，M2和W的交互作用会通过路径b4影响Y。变量X也会直接影响Y，路径是c1’。变量W也会直接影响Y，路径是c2’。X和W的交互作用也会直接影响Y，路径是c3’。

数学公式1

模型方程:
Y = b0 + b1M1 + b2M2 + b3M1W + b4M2W + c1'X + c2'W + c3'XW
M1 = a01 + a1X + a3W + a4XW
M2 = a02 + a2X + a5W + a6XW + d1M1 + d2M1W

首先，我们定义了三个模型方程。Y是因变量，M1和M2是两个中介变量，X是自变量，W是调节变量。这些方程描述了它们之间的复杂关系，其中包含了交互效应。

数学公式2

模型方程:
Y = b0 + b1M1 + b2M2 + b3M1W + b4M2W + c1'X + c2'W + c3'XW
M1 = a01 + a1X + a3W + a4XW
M2 = a02 + a2X + a5W + a6XW + d1M1 + d2M1W
替换:
Y = b0 + b1(a01 + a1X + a3W + a4XW) + b2(a02 + a2X + a5W + a6XW + d1(a01 + a1X + a3W + a4XW) + d2(a01 + a1X + a3W + a4XW)W) + b3(a01 + a1X + a3W + a4XW)W + b4(a02 + a2X + a5W + a6XW + d1(a01 + a1X + a3W + a4XW) + d2(a01 + a1X + a3W + a4XW)W)W + c1'X + c2'W + c3'XW

接下来，我们将中介变量M1和M2的方程代入因变量Y的方程中。这一步的目的是为了消除M1和M2，从而可以直接考察自变量X对因变量Y的总效应。

数学公式3

模型方程:
Y = b0 + b1M1 + b2M2 + b3M1W + b4M2W + c1'X + c2'W + c3'XW
M1 = a01 + a1X + a3W + a4XW
M2 = a02 + a2X + a5W + a6XW + d1M1 + d2M1W
替换:
Y = b0 + b1(a01 + a1X + a3W + a4XW) + b2(a02 + a2X + a5W + a6XW + d1(a01 + a1X + a3W + a4XW) + d2(a01 + a1X + a3W + a4XW)W) + b3(a01 + a1X + a3W + a4XW)W + b4(a02 + a2X + a5W + a6XW + d1(a01 + a1X + a3W + a4XW) + d2(a01 + a1X + a3W + a4XW)W)W + c1'X + c2'W + c3'XW
展开:
Y = b0 + a01b1 + a1b1X + a3b1W + a02b2 + a2b2X + a5b2W + a6b2XW + a01d1b2 + a1d1b2X + a3d1b2W + a4d1b2XW + a01d2b2W + a1d2b2XW + a3d2b2WW + a4d2b2XWW + a01b3W + a1b3XW + a3b3WW + a4b3XWW + a02b4W + a2b4XW + a5b4WW + a6b4XWW + a01d1b4W + a1d1b4XW + a3d1b4WW + a4d1b4XWW + a01d2b4WW + a1d2b4XWW + a3d2b4WWW + a4d2b4XWWW + c1'X + c2'W + c3'XW

然后，我们对上一步得到的方程进行展开，将所有括号都去掉，以便后续进行整理和分组。这一步可能会显得比较繁琐，但它对于我们理解变量之间的关系至关重要。

数学公式4

模型方程:
Y = b0 + b1M1 + b2M2 + b3M1W + b4M2W + c1'X + c2'W + c3'XW
M1 = a01 + a1X + a3W + a4XW
M2 = a02 + a2X + a5W + a6XW + d1M1 + d2M1W
替换:
Y = b0 + b1(a01 + a1X + a3W + a4XW) + b2(a02 + a2X + a5W + a6XW + d1(a01 + a1X + a3W + a4XW) + d2(a01 + a1X + a3W + a4XW)W) + b3(a01 + a1X + a3W + a4XW)W + b4(a02 + a2X + a5W + a6XW + d1(a01 + a1X + a3W + a4XW) + d2(a01 + a1X + a3W + a4XW)W)W + c1'X + c2'W + c3'XW
展开:
Y = b0 + a01b1 + a1b1X + a3b1W + a02b2 + a2b2X + a5b2W + a6b2XW + a01d1b2 + a1d1b2X + a3d1b2W + a4d1b2XW + a01d2b2W + a1d2b2XW + a3d2b2WW + a4d2b2XWW + a01b3W + a1b3XW + a3b3WW + a4b3XWW + a02b4W + a2b4XW + a5b4WW + a6b4XWW + a01d1b4W + a1d1b4XW + a3d1b4WW + a4d1b4XWW + a01d2b4WW + a1d2b4XWW + a3d2b4WWW + a4d2b4XWWW + c1'X + c2'W + c3'XW
分组:
Y = b0 + a01b1 + a3b1W + a02b2 + a5b2W + a01d1b2 + a3d1b2W + a01d2b2W + a3d2b2WW + a01b3W + a3b3WW + a02b4W + a5b4WW + a01d1b4W + a3d1b4WW + a01d2b4WW + a3d2b4WWW + c2'W + (a1b1 + a4b1W + a2b2 + a6b2W + a1d1b2+ a4d1b2W + a1d2b2W + a4d2b2WW + a1b3W + a4b3WW + a2b4W + a6b4WW + a1d1b4W + a4d1b4WW + a1d2b4WW + a4d2b4WWW + c1' + c3'W)X

现在，我们将展开的方程按照是否包含自变量X进行分组，将其整理成Y = a + bX的形式。其中，a部分不包含X，而b部分则是X的系数，代表着X对Y的总效应。

数学公式5

模型方程:
Y = b0 + b1M1 + b2M2 + b3M1W + b4M2W + c1'X + c2'W + c3'XW
M1 = a01 + a1X + a3W + a4XW
M2 = a02 + a2X + a5W + a6XW + d1M1 + d2M1W
替换:
Y = b0 + b1(a01 + a1X + a3W + a4XW) + b2(a02 + a2X + a5W + a6XW + d1(a01 + a1X + a3W + a4XW) + d2(a01 + a1X + a3W + a4XW)W) + b3(a01 + a1X + a3W + a4XW)W + b4(a02 + a2X + a5W + a6XW + d1(a01 + a1X + a3W + a4XW) + d2(a01 + a1X + a3W + a4XW)W)W + c1'X + c2'W + c3'XW
展开:
Y = b0 + a01b1 + a1b1X + a3b1W + a02b2 + a2b2X + a5b2W + a6b2XW + a01d1b2 + a1d1b2X + a3d1b2W + a4d1b2XW + a01d2b2W + a1d2b2XW + a3d2b2WW + a4d2b2XWW + a01b3W + a1b3XW + a3b3WW + a4b3XWW + a02b4W + a2b4XW + a5b4WW + a6b4XWW + a01d1b4W + a1d1b4XW + a3d1b4WW + a4d1b4XWW + a01d2b4WW + a1d2b4XWW + a3d2b4WWW + a4d2b4XWWW + c1'X + c2'W + c3'XW
分组:
Y = b0 + a01b1 + a3b1W + a02b2 + a5b2W + a01d1b2 + a3d1b2W + a01d2b2W + a3d2b2WW + a01b3W + a3b3WW + a02b4W + a5b4WW + a01d1b4W + a3d1b4WW + a01d2b4WW + a3d2b4WWW + c2'W + (a1b1 + a4b1W + a2b2 + a6b2W + a1d1b2+ a4d1b2W + a1d2b2W + a4d2b2WW + a1b3W + a4b3WW + a2b4W + a6b4WW + a1d1b4W + a4d1b4WW + a1d2b4WW + a4d2b4WWW + c1' + c3'W)X
间接效应:
(a1 + a4W)(b1 + b3W)
(a2 + a6W)(b2 + b4W)
(a1 + a4W)(d1 + d2W)(b2 + b4W)

直接效应:
c1' + c3'W

通过以上推导，我们最终可以得出X对Y的条件间接效应和条件直接效应的表达式。这些效应都受到调节变量W的影响，因此是条件性的。其中，间接效应是通过中介变量M1和M2传递的，而直接效应则是不通过中介变量直接影响Y的。 这些表达式清晰地展示了复杂关系中各个路径的效应大小。

代码解读1

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

首先，我们看到的是代码的注释部分。这里定义了模型中各个变量的角色。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 XW M1W M2W;

接下来，USEVARIABLES语句指定了模型中要用到的所有变量。除了原始的X、M1、M2、W和Y之外，还包括了交互项XW、M1W和M2W。这些交互项是通过将原始变量相乘得到的，用于考察调节效应。

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 XW M1W M2W;
DEFINE:

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

在DEFINE部分，我们定义了交互项的具体计算方式。XW等于X乘以W，M1W等于M1乘以W，M2W等于M2乘以W。这些是模型中要用到的交互效应项。

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 XW M1W M2W;
DEFINE:

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

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

在ANALYSIS部分，我们指定了分析的设置。TYPE = GENERAL表示这是一个一般的模型。ESTIMATOR = ML表示使用最大似然法进行参数估计。BOOTSTRAP = 10000表示使用自助法重复抽样10000次，用于计算参数估计的置信区间。

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 XW M1W M2W;
DEFINE:

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

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

Y ON M1 (b1);
Y ON M2 (b2);
Y ON M1W (b3);
Y ON M2W (b4);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
M1 ON X (a1);
M2 ON X (a2);
M1 ON W (a3);
M1 ON XW (a4);
M2 ON W (a5);
M2 ON XW (a6);
M2 ON M1 (d1);
M2 ON M1W (d2);

MODEL语句定义了模型中的路径关系。例如，Y ON M1 (b1)表示Y回归M1，路径系数命名为b1。其他类似语句定义了Y对其他变量、M1和M2的回归关系，以及M1和M2之间的回归关系。括号里的名称是路径系数的标签，方便后续使用。

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 XW M1W M2W;
DEFINE:

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

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

Y ON M1 (b1);
Y ON M2 (b2);
Y ON M1W (b3);
Y ON M2W (b4);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
M1 ON X (a1);
M2 ON X (a2);
M1 ON W (a3);
M1 ON XW (a4);
M2 ON W (a5);
M2 ON XW (a6);
M2 ON M1 (d1);
M2 ON M1W (d2);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1
 LWa2b2 MWa2b2 HWa2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_ALW IMM_AMW IMM_AHW IMM_BLW IMM_BMW IMM_BHW IMM_CLW IMM_CMW IMM_CHW
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);

在MODEL CONSTRAINT部分，我们首先定义了一些新的变量，用于存储计算结果，比如调节变量W的低、中、高值，以及不同条件下的间接效应、直接效应和总效应等。这些变量在后面的计算中会被用到。

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 XW M1W M2W;
DEFINE:

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

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

Y ON M1 (b1);
Y ON M2 (b2);
Y ON M1W (b3);
Y ON M2W (b4);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
M1 ON X (a1);
M2 ON X (a2);
M1 ON W (a3);
M1 ON XW (a4);
M2 ON W (a5);
M2 ON XW (a6);
M2 ON M1 (d1);
M2 ON M1W (d2);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1
 LWa2b2 MWa2b2 HWa2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_ALW IMM_AMW IMM_AHW IMM_BLW IMM_BMW IMM_BHW IMM_CLW IMM_CMW IMM_CHW
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = #LOWW;
MED_W = #MEDW;
HIGH_W = #HIGHW;

接下来，我们定义调节变量W的低、中、高水平。这里需要将#LOWW、#MEDW和#HIGHW替换为实际的数值。一般情况下，我们会选择平均值加减一个标准差作为低值和高值。

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 XW M1W M2W;
DEFINE:

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

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

Y ON M1 (b1);
Y ON M2 (b2);
Y ON M1W (b3);
Y ON M2W (b4);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
M1 ON X (a1);
M2 ON X (a2);
M1 ON W (a3);
M1 ON XW (a4);
M2 ON W (a5);
M2 ON XW (a6);
M2 ON M1 (d1);
M2 ON M1W (d2);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1
 LWa2b2 MWa2b2 HWa2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_ALW IMM_AMW IMM_AHW IMM_BLW IMM_BMW IMM_BHW IMM_CLW IMM_CMW IMM_CHW
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = #LOWW;
MED_W = #MEDW;
HIGH_W = #HIGHW;
LWa1b1 = (a1 + a4*LOW_W)*(b1 + b3*LOW_W);
MWa1b1 = (a1 + a4*MED_W)*(b1 + b3*MED_W);
HWa1b1 = (a1 + a4*HIGH_W)*(b1 + b3*HIGH_W);

LWa2b2 = (a2 + a6*LOW_W)*(b2 + b4*LOW_W);
MWa2b2 = (a2 + a6*MED_W)*(b2 + b4*MED_W);
HWa2b2 = (a2 + a6*HIGH_W)*(b2 + b4*HIGH_W);

LWa1d1b2 = (a1 + a4*LOW_W)*(d1 + d2*LOW_W)*(b2 + b4*LOW_W);
MWa1d1b2 = (a1 + a4*MED_W)*(d1 + d2*MED_W)*(b2 + b4*MED_W);
HWa1d1b2 = (a1 + a4*HIGH_W)*(d1 + d2*HIGH_W)*(b2 + b4*HIGH_W);

这部分代码计算了不同调节变量W水平下的条件间接效应。例如，LWa1b1表示W取低值时，X通过M1对Y的间接效应。这些计算使用了之前在MODEL部分定义的路径系数。

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 XW M1W M2W;
DEFINE:

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

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

Y ON M1 (b1);
Y ON M2 (b2);
Y ON M1W (b3);
Y ON M2W (b4);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
M1 ON X (a1);
M2 ON X (a2);
M1 ON W (a3);
M1 ON XW (a4);
M2 ON W (a5);
M2 ON XW (a6);
M2 ON M1 (d1);
M2 ON M1W (d2);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1
 LWa2b2 MWa2b2 HWa2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_ALW IMM_AMW IMM_AHW IMM_BLW IMM_BMW IMM_BHW IMM_CLW IMM_CMW IMM_CHW
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = #LOWW;
MED_W = #MEDW;
HIGH_W = #HIGHW;
LWa1b1 = (a1 + a4*LOW_W)*(b1 + b3*LOW_W);
MWa1b1 = (a1 + a4*MED_W)*(b1 + b3*MED_W);
HWa1b1 = (a1 + a4*HIGH_W)*(b1 + b3*HIGH_W);

LWa2b2 = (a2 + a6*LOW_W)*(b2 + b4*LOW_W);
MWa2b2 = (a2 + a6*MED_W)*(b2 + b4*MED_W);
HWa2b2 = (a2 + a6*HIGH_W)*(b2 + b4*HIGH_W);

LWa1d1b2 = (a1 + a4*LOW_W)*(d1 + d2*LOW_W)*(b2 + b4*LOW_W);
MWa1d1b2 = (a1 + a4*MED_W)*(d1 + d2*MED_W)*(b2 + b4*MED_W);
HWa1d1b2 = (a1 + a4*HIGH_W)*(d1 + d2*HIGH_W)*(b2 + b4*HIGH_W);
IMM_ALW = a1*b3 + a4*b1 + a4*b3*LOW_W;
IMM_AMW = a1*b3 + a4*b1 + a4*b3*MED_W;
IMM_AHW = a1*b3 + a4*b1 + a4*b3*HIGH_W;

IMM_BLW = a2*b4 + a6*b2 + a6*b4*LOW_W;
IMM_BMW = a2*b4 + a6*b2 + a6*b4*MED_W;
IMM_BHW = a2*b4 + a6*b2 + a6*b4*HIGH_W;

IMM_CLW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2
 + a1*d2*b3*LOW_W + a4*d1*b3*LOW_W + a4*d2*b2*LOW_W + a4*d2*b3*LOW_W*LOW_W;
IMM_CMW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2 
+ a1*d2*b3*MED_W + a4*d1*b3*MED_W + a4*d2*b2*MED_W + a4*d2*b3*MED_W*MED_W;
IMM_CHW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2 
+ a1*d2*b3*HIGH_W + a4*d1*b3*HIGH_W + a4*d2*b2*HIGH_W + a4*d2*b3*HIGH_W*HIGH_W;

这部分计算的是调节中介效应指数，也就是IMM。IMM_ALW表示调节变量W对X到M1到Y这条路径的调节效应指数，其他IMM类似。这些指数可以帮助我们理解调节效应的含义。

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 XW M1W M2W;
DEFINE:

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

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

Y ON M1 (b1);
Y ON M2 (b2);
Y ON M1W (b3);
Y ON M2W (b4);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
M1 ON X (a1);
M2 ON X (a2);
M1 ON W (a3);
M1 ON XW (a4);
M2 ON W (a5);
M2 ON XW (a6);
M2 ON M1 (d1);
M2 ON M1W (d2);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1
 LWa2b2 MWa2b2 HWa2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_ALW IMM_AMW IMM_AHW IMM_BLW IMM_BMW IMM_BHW IMM_CLW IMM_CMW IMM_CHW
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = #LOWW;
MED_W = #MEDW;
HIGH_W = #HIGHW;
LWa1b1 = (a1 + a4*LOW_W)*(b1 + b3*LOW_W);
MWa1b1 = (a1 + a4*MED_W)*(b1 + b3*MED_W);
HWa1b1 = (a1 + a4*HIGH_W)*(b1 + b3*HIGH_W);

LWa2b2 = (a2 + a6*LOW_W)*(b2 + b4*LOW_W);
MWa2b2 = (a2 + a6*MED_W)*(b2 + b4*MED_W);
HWa2b2 = (a2 + a6*HIGH_W)*(b2 + b4*HIGH_W);

LWa1d1b2 = (a1 + a4*LOW_W)*(d1 + d2*LOW_W)*(b2 + b4*LOW_W);
MWa1d1b2 = (a1 + a4*MED_W)*(d1 + d2*MED_W)*(b2 + b4*MED_W);
HWa1d1b2 = (a1 + a4*HIGH_W)*(d1 + d2*HIGH_W)*(b2 + b4*HIGH_W);
IMM_ALW = a1*b3 + a4*b1 + a4*b3*LOW_W;
IMM_AMW = a1*b3 + a4*b1 + a4*b3*MED_W;
IMM_AHW = a1*b3 + a4*b1 + a4*b3*HIGH_W;

IMM_BLW = a2*b4 + a6*b2 + a6*b4*LOW_W;
IMM_BMW = a2*b4 + a6*b2 + a6*b4*MED_W;
IMM_BHW = a2*b4 + a6*b2 + a6*b4*HIGH_W;

IMM_CLW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2
 + a1*d2*b3*LOW_W + a4*d1*b3*LOW_W + a4*d2*b2*LOW_W + a4*d2*b3*LOW_W*LOW_W;
IMM_CMW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2 
+ a1*d2*b3*MED_W + a4*d1*b3*MED_W + a4*d2*b2*MED_W + a4*d2*b3*MED_W*MED_W;
IMM_CHW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2 
+ a1*d2*b3*HIGH_W + a4*d1*b3*HIGH_W + a4*d2*b2*HIGH_W + a4*d2*b3*HIGH_W*HIGH_W;
DIR_LW = cdash1 + cdash3*LOW_W;
DIR_MW = cdash + cdash3*MED_W;
DIR_HW = cdash + cdash3*HIGH_W;

这里计算的是不同调节变量W水平下的X对Y的直接效应。DIR_LW表示W取低值时的直接效应，其他类似。

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 XW M1W M2W;
DEFINE:

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

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

Y ON M1 (b1);
Y ON M2 (b2);
Y ON M1W (b3);
Y ON M2W (b4);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
M1 ON X (a1);
M2 ON X (a2);
M1 ON W (a3);
M1 ON XW (a4);
M2 ON W (a5);
M2 ON XW (a6);
M2 ON M1 (d1);
M2 ON M1W (d2);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1
 LWa2b2 MWa2b2 HWa2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_ALW IMM_AMW IMM_AHW IMM_BLW IMM_BMW IMM_BHW IMM_CLW IMM_CMW IMM_CHW
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = #LOWW;
MED_W = #MEDW;
HIGH_W = #HIGHW;
LWa1b1 = (a1 + a4*LOW_W)*(b1 + b3*LOW_W);
MWa1b1 = (a1 + a4*MED_W)*(b1 + b3*MED_W);
HWa1b1 = (a1 + a4*HIGH_W)*(b1 + b3*HIGH_W);

LWa2b2 = (a2 + a6*LOW_W)*(b2 + b4*LOW_W);
MWa2b2 = (a2 + a6*MED_W)*(b2 + b4*MED_W);
HWa2b2 = (a2 + a6*HIGH_W)*(b2 + b4*HIGH_W);

LWa1d1b2 = (a1 + a4*LOW_W)*(d1 + d2*LOW_W)*(b2 + b4*LOW_W);
MWa1d1b2 = (a1 + a4*MED_W)*(d1 + d2*MED_W)*(b2 + b4*MED_W);
HWa1d1b2 = (a1 + a4*HIGH_W)*(d1 + d2*HIGH_W)*(b2 + b4*HIGH_W);
IMM_ALW = a1*b3 + a4*b1 + a4*b3*LOW_W;
IMM_AMW = a1*b3 + a4*b1 + a4*b3*MED_W;
IMM_AHW = a1*b3 + a4*b1 + a4*b3*HIGH_W;

IMM_BLW = a2*b4 + a6*b2 + a6*b4*LOW_W;
IMM_BMW = a2*b4 + a6*b2 + a6*b4*MED_W;
IMM_BHW = a2*b4 + a6*b2 + a6*b4*HIGH_W;

IMM_CLW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2
 + a1*d2*b3*LOW_W + a4*d1*b3*LOW_W + a4*d2*b2*LOW_W + a4*d2*b3*LOW_W*LOW_W;
IMM_CMW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2 
+ a1*d2*b3*MED_W + a4*d1*b3*MED_W + a4*d2*b2*MED_W + a4*d2*b3*MED_W*MED_W;
IMM_CHW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2 
+ a1*d2*b3*HIGH_W + a4*d1*b3*HIGH_W + a4*d2*b2*HIGH_W + a4*d2*b3*HIGH_W*HIGH_W;
DIR_LW = cdash1 + cdash3*LOW_W;
DIR_MW = cdash + cdash3*MED_W;
DIR_HW = cdash + cdash3*HIGH_W;
TOT_LOWW = LWa1d1b2 + LWa2b2 + LWa1b1 + DIR_LW;
TOT_MEDW = MWa1d1b2 + MWa2b2 + MWa1b1 + DIR_MW;
TOT_HIW = HWa1d1b2 + HWa2b2 + HWa1b1 + DIR_HW;

这部分计算的是不同调节变量W水平下的X对Y的总效应，总效应等于间接效应加上直接效应。

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 XW M1W M2W;
DEFINE:

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

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

Y ON M1 (b1);
Y ON M2 (b2);
Y ON M1W (b3);
Y ON M2W (b4);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
M1 ON X (a1);
M2 ON X (a2);
M1 ON W (a3);
M1 ON XW (a4);
M2 ON W (a5);
M2 ON XW (a6);
M2 ON M1 (d1);
M2 ON M1W (d2);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1
 LWa2b2 MWa2b2 HWa2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_ALW IMM_AMW IMM_AHW IMM_BLW IMM_BMW IMM_BHW IMM_CLW IMM_CMW IMM_CHW
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = #LOWW;
MED_W = #MEDW;
HIGH_W = #HIGHW;
LWa1b1 = (a1 + a4*LOW_W)*(b1 + b3*LOW_W);
MWa1b1 = (a1 + a4*MED_W)*(b1 + b3*MED_W);
HWa1b1 = (a1 + a4*HIGH_W)*(b1 + b3*HIGH_W);

LWa2b2 = (a2 + a6*LOW_W)*(b2 + b4*LOW_W);
MWa2b2 = (a2 + a6*MED_W)*(b2 + b4*MED_W);
HWa2b2 = (a2 + a6*HIGH_W)*(b2 + b4*HIGH_W);

LWa1d1b2 = (a1 + a4*LOW_W)*(d1 + d2*LOW_W)*(b2 + b4*LOW_W);
MWa1d1b2 = (a1 + a4*MED_W)*(d1 + d2*MED_W)*(b2 + b4*MED_W);
HWa1d1b2 = (a1 + a4*HIGH_W)*(d1 + d2*HIGH_W)*(b2 + b4*HIGH_W);
IMM_ALW = a1*b3 + a4*b1 + a4*b3*LOW_W;
IMM_AMW = a1*b3 + a4*b1 + a4*b3*MED_W;
IMM_AHW = a1*b3 + a4*b1 + a4*b3*HIGH_W;

IMM_BLW = a2*b4 + a6*b2 + a6*b4*LOW_W;
IMM_BMW = a2*b4 + a6*b2 + a6*b4*MED_W;
IMM_BHW = a2*b4 + a6*b2 + a6*b4*HIGH_W;

IMM_CLW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2
 + a1*d2*b3*LOW_W + a4*d1*b3*LOW_W + a4*d2*b2*LOW_W + a4*d2*b3*LOW_W*LOW_W;
IMM_CMW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2 
+ a1*d2*b3*MED_W + a4*d1*b3*MED_W + a4*d2*b2*MED_W + a4*d2*b3*MED_W*MED_W;
IMM_CHW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2 
+ a1*d2*b3*HIGH_W + a4*d1*b3*HIGH_W + a4*d2*b2*HIGH_W + a4*d2*b3*HIGH_W*HIGH_W;
DIR_LW = cdash1 + cdash3*LOW_W;
DIR_MW = cdash + cdash3*MED_W;
DIR_HW = cdash + cdash3*HIGH_W;
TOT_LOWW = LWa1d1b2 + LWa2b2 + LWa1b1 + DIR_LW;
TOT_MEDW = MWa1d1b2 + MWa2b2 + MWa1b1 + DIR_MW;
TOT_HIW = HWa1d1b2 + HWa2b2 + HWa1b1 + DIR_HW;
PLOT(LOMOD MEDMOD HIMOD);
LOOP(XVAL,1,5,0.1);
LOMOD = TOT_LOWW*XVAL;
MEDMOD = TOT_MEDW*XVAL;
HIMOD = TOT_HIW*XVAL;

这段代码准备绘制图形。PLOT语句指定要绘制的变量。LOOP语句创建一个循环，让XVAL从1变化到5，步长为0.1。然后计算在不同的XVAL值下，调节变量W取低、中、高值时的Y值，用于绘图。

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 XW M1W M2W;
DEFINE:

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

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

Y ON M1 (b1);
Y ON M2 (b2);
Y ON M1W (b3);
Y ON M2W (b4);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
M1 ON X (a1);
M2 ON X (a2);
M1 ON W (a3);
M1 ON XW (a4);
M2 ON W (a5);
M2 ON XW (a6);
M2 ON M1 (d1);
M2 ON M1W (d2);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W
 LWa1b1 MWa1b1 HWa1b1
 LWa2b2 MWa2b2 HWa2b2
 LWa1d1b2 MWa1d1b2 HWa1d1b2
 IMM_ALW IMM_AMW IMM_AHW IMM_BLW IMM_BMW IMM_BHW IMM_CLW IMM_CMW IMM_CHW
 DIR_LW DIR_MW DIR_HW
 TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = #LOWW;
MED_W = #MEDW;
HIGH_W = #HIGHW;
LWa1b1 = (a1 + a4*LOW_W)*(b1 + b3*LOW_W);
MWa1b1 = (a1 + a4*MED_W)*(b1 + b3*MED_W);
HWa1b1 = (a1 + a4*HIGH_W)*(b1 + b3*HIGH_W);

LWa2b2 = (a2 + a6*LOW_W)*(b2 + b4*LOW_W);
MWa2b2 = (a2 + a6*MED_W)*(b2 + b4*MED_W);
HWa2b2 = (a2 + a6*HIGH_W)*(b2 + b4*HIGH_W);

LWa1d1b2 = (a1 + a4*LOW_W)*(d1 + d2*LOW_W)*(b2 + b4*LOW_W);
MWa1d1b2 = (a1 + a4*MED_W)*(d1 + d2*MED_W)*(b2 + b4*MED_W);
HWa1d1b2 = (a1 + a4*HIGH_W)*(d1 + d2*HIGH_W)*(b2 + b4*HIGH_W);
IMM_ALW = a1*b3 + a4*b1 + a4*b3*LOW_W;
IMM_AMW = a1*b3 + a4*b1 + a4*b3*MED_W;
IMM_AHW = a1*b3 + a4*b1 + a4*b3*HIGH_W;

IMM_BLW = a2*b4 + a6*b2 + a6*b4*LOW_W;
IMM_BMW = a2*b4 + a6*b2 + a6*b4*MED_W;
IMM_BHW = a2*b4 + a6*b2 + a6*b4*HIGH_W;

IMM_CLW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2
 + a1*d2*b3*LOW_W + a4*d1*b3*LOW_W + a4*d2*b2*LOW_W + a4*d2*b3*LOW_W*LOW_W;
IMM_CMW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2 
+ a1*d2*b3*MED_W + a4*d1*b3*MED_W + a4*d2*b2*MED_W + a4*d2*b3*MED_W*MED_W;
IMM_CHW = a1*d1*b3 + a1*d2*b2 + a4*d1*b2 
+ a1*d2*b3*HIGH_W + a4*d1*b3*HIGH_W + a4*d2*b2*HIGH_W + a4*d2*b3*HIGH_W*HIGH_W;
DIR_LW = cdash1 + cdash3*LOW_W;
DIR_MW = cdash + cdash3*MED_W;
DIR_HW = cdash + cdash3*HIGH_W;
TOT_LOWW = LWa1d1b2 + LWa2b2 + LWa1b1 + DIR_LW;
TOT_MEDW = MWa1d1b2 + MWa2b2 + MWa1b1 + DIR_MW;
TOT_HIW = HWa1d1b2 + HWa2b2 + HWa1b1 + DIR_HW;
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，PLOT语句设置绘图类型为二维图。OUTPUT语句指定输出标准化系数和使用自助法计算的置信区间。这段代码运行后会输出模型的参数估计结果和一些辅助分析，并且可以根据我们设定的变量画出想要的图。

资源汇总

• 本视频讲义地址: https://mlln.cn/mplus-model-templates/model92.html
• 图书《MPlus中介调节模型》打包下载: 点击下载
• 图书《MPlus中介调节模型》在线看: 点击查看
• 视频教程: 点击这里打开视频
• Mplus 模型模板教程列表: https://mlln.cn/mplus-model-templates
• 统计咨询: https://wx.zsxq.com/group/88888188828842

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