Mplus model75latent 模型讲解

来自图书《MPlus中介调节模型》

复杂调节中介模型 Mplus 教程

• 理论模型：解释模型背后的概念框架，明确变量之间的关系和研究假设。
• 数学模型：将理论关系转化为具体的统计方程，方便模型构建和分析。
• 数学推导：详细展示模型参数的估计过程，包括如何计算直接效应、间接效应和调节效应。
• 代码解读：逐行解释 Mplus 代码，说明每一部分的功能和意义，确保用户能够理解并运行代码。

大家好，欢迎来到Data Sense的Mplus教程。今天我们将学习如何使用Mplus分析一个复杂的调节中介模型。这个模型包含一个潜变量预测变量，一个潜变量中介变量，两个潜变量调节变量，以及一个潜变量结果变量。这个模型允许我们考察调节变量如何影响预测变量到中介变量的路径，以及中介变量到结果变量的路径。我们教程的结构主要分为四个部分：首先，我们会介绍模型的理论框架，明确变量间的关系和研究假设；接着，我们会将理论框架转化为具体的数学方程，方便模型的构建和分析；然后，我们会详细展示模型参数的估计过程，以及如何计算直接效应、间接效应和调节效应；最后，我们会逐行解读Mplus代码，说明每一部分的功能和意义。希望通过本教程，大家能够掌握复杂调节中介模型的分析方法。如有任何统计咨询需求，欢迎联系我们。

理论模型

我们来看，图中展示了一个网络，它有五个节点。X分别指向M和Y，M指向Y。W分别指向X、M和Y，Z也分别指向X、M和Y。

数学模型

这张图展示了我们模型的数学关系。圆圈代表变量，箭头代表影响方向。X、W 和 Z 分别是我们的三个起始变量。它们通过 a1、a2 和 a3 的路径影响中间变量 M。另外，X 与 W 的组合变量 XW 通过 a4 影响 M，X 与 Z 的组合变量 XZ 通过 a5 影响 M。M 通过 b1 影响结果变量 Y。同时，W、Z 分别通过 b2 和 b3 直接影响 Y。M 和 W 的组合变量 MW 通过 b4 影响 Y，M 和 Z 的组合变量 MZ 通过 b5 影响 Y。最后，X 也通过 c’ 直接影响 Y。图中箭头旁的字母代表了不同路径的系数。

数学公式1

1. 因变量 Y 的模型：
   Y = b0 + b1M + b2W + b3Z + b4MW + b5MZ + c'X

首先，我们定义因变量Y的模型，它受到中介变量M，两个调节变量W和Z，以及M与W的交互项MW，M与Z的交互项MZ以及自变量X的直接影响。b0是截距，b1到b5和c’是系数。

数学公式2

1. 因变量 Y 的模型：
   Y = b0 + b1M + b2W + b3Z + b4MW + b5MZ + c'X
2. 中介变量 M 的模型：
   M = a0 + a1X + a2W + a3Z + a4XW + a5XZ

接下来，我们定义中介变量M的模型，它受到自变量X，两个调节变量W和Z，以及X与W的交互项XW，X与Z的交互项XZ的影响。a0是截距，a1到a5是系数。

数学公式3

1. 因变量 Y 的模型：
   Y = b0 + b1M + b2W + b3Z + b4MW + b5MZ + c'X
2. 中介变量 M 的模型：
   M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
将 M 的表达式代入 Y 的表达式：
   Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2W + b3Z + b4(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + b5(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Z + c'X

为了分析X如何通过M影响Y，我们将M的表达式代入到Y的表达式中。

数学公式4

1. 因变量 Y 的模型：
   Y = b0 + b1M + b2W + b3Z + b4MW + b5MZ + c'X
2. 中介变量 M 的模型：
   M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
将 M 的表达式代入 Y 的表达式：
   Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2W + b3Z + b4(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + b5(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Z + c'X
展开括号：
   Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2W + b3Z + a0b4W + a1b4XW + a2b4WW + a3b4ZW + a4b4XWW + a5b4XZW + a0b5Z + a1b5XZ + a2b5WZ + a3b5ZZ + a4b5XWZ + a5b5XZZ + c'X

然后，我们将所有括号展开，得到一个更为复杂的表达式。

数学公式5

1. 因变量 Y 的模型：
   Y = b0 + b1M + b2W + b3Z + b4MW + b5MZ + c'X
2. 中介变量 M 的模型：
   M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
将 M 的表达式代入 Y 的表达式：
   Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2W + b3Z + b4(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + b5(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Z + c'X
展开括号：
   Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2W + b3Z + a0b4W + a1b4XW + a2b4WW + a3b4ZW + a4b4XWW + a5b4XZW + a0b5Z + a1b5XZ + a2b5WZ + a3b5ZZ + a4b5XWZ + a5b5XZZ + c'X
整理，分离含X项：
  Y = (b0 + a0b1 + a2b1W + a3b1Z + b2W + b3Z + a0b4W + a2b4WW + a3b4ZW + a0b5Z + a2b5WZ + a3b5ZZ) + (a1b1 + a4b1W + a5b1Z + a1b4W + a4b4WW + a5b4ZW + a1b5Z + a4b5WZ + a5b5ZZ + c')X

接下来，我们将所有包含X的项和不包含X的项分开，整理成Y = a + bX的形式，其中a代表截距，b代表X对Y的总影响。

数学公式6

1. 因变量 Y 的模型：
   Y = b0 + b1M + b2W + b3Z + b4MW + b5MZ + c'X
2. 中介变量 M 的模型：
   M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
将 M 的表达式代入 Y 的表达式：
   Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2W + b3Z + b4(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + b5(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Z + c'X
展开括号：
   Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2W + b3Z + a0b4W + a1b4XW + a2b4WW + a3b4ZW + a4b4XWW + a5b4XZW + a0b5Z + a1b5XZ + a2b5WZ + a3b5ZZ + a4b5XWZ + a5b5XZZ + c'X
整理，分离含X项：
  Y = (b0 + a0b1 + a2b1W + a3b1Z + b2W + b3Z + a0b4W + a2b4WW + a3b4ZW + a0b5Z + a2b5WZ + a3b5ZZ) + (a1b1 + a4b1W + a5b1Z + a1b4W + a4b4WW + a5b4ZW + a1b5Z + a4b5WZ + a5b5ZZ + c')X
X 对 Y 的间接影响 (conditional indirect effect)：
(a1 + a4W + a5Z)(b1 + b4W + b5Z)

X对Y的间接影响，也就是通过M产生的影响，取决于调节变量W和Z的值，具体形式为(a1 + a4W + a5Z)乘以(b1 + b4W + b5Z).

数学公式7

1. 因变量 Y 的模型：
   Y = b0 + b1M + b2W + b3Z + b4MW + b5MZ + c'X
2. 中介变量 M 的模型：
   M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
将 M 的表达式代入 Y 的表达式：
   Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2W + b3Z + b4(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + b5(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Z + c'X
展开括号：
   Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2W + b3Z + a0b4W + a1b4XW + a2b4WW + a3b4ZW + a4b4XWW + a5b4XZW + a0b5Z + a1b5XZ + a2b5WZ + a3b5ZZ + a4b5XWZ + a5b5XZZ + c'X
整理，分离含X项：
  Y = (b0 + a0b1 + a2b1W + a3b1Z + b2W + b3Z + a0b4W + a2b4WW + a3b4ZW + a0b5Z + a2b5WZ + a3b5ZZ) + (a1b1 + a4b1W + a5b1Z + a1b4W + a4b4WW + a5b4ZW + a1b5Z + a4b5WZ + a5b5ZZ + c')X
X 对 Y 的间接影响 (conditional indirect effect)：
(a1 + a4W + a5Z)(b1 + b4W + b5Z)
X 对 Y 的直接影响：
 c'

X对Y的直接影响，也就是不通过M产生的影响，由系数c’表示。

代码解读1

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;

首先，我们定义模型中用到的所有观测变量。X1到X4是自变量X的观测指标，M1到M4是中介变量M的观测指标。W1到W4是调节变量W的观测指标，Z1到Z4是调节变量Z的观测指标，Y1到Y4是因变量Y的观测指标。

代码解读2

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
 TYPE = GENERAL RANDOM;
 ESTIMATOR = ML;
 ALGORITHM = INTEGRATION;

接下来，在分析部分，我们指定了分析的类型和方法。TYPE = GENERAL RANDOM，表示我们使用的是广义随机模型，这允许模型包含潜在变量。ESTIMATOR = ML，表示使用最大似然估计方法来估计模型参数。ALGORITHM = INTEGRATION，表示使用积分算法处理潜在变量的积分。

代码解读3

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
 TYPE = GENERAL RANDOM;
 ESTIMATOR = ML;
 ALGORITHM = INTEGRATION;
MODEL:
! Measurement model

! Identify moderator factors by fixing variance = 1 (instead of first loading)

! This makes these factors standardised

 X BY X1 X2 X3 X4;
 M BY M1 M2 M3 M4;
 W BY W1* W2 W3 W4;
 Z BY Z1* Z2 Z3 Z4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;

在模型部分，我们定义了模型的结构。X BY X1 X2 X3 X4，表示潜在变量X由观测变量X1到X4测量。M BY M1 M2 M3 M4，表示潜在变量M由观测变量M1到M4测量。W BY W1星 W2 W3 W4，表示潜在变量W由观测变量W1到W4测量，其中W1的载荷被固定为1。Z BY Z1星 Z2 Z3 Z4，表示潜在变量Z由观测变量Z1到Z4测量，其中Z1的载荷被固定为1。Y BY Y1 Y2 Y3 Y4，表示潜在变量Y由观测变量Y1到Y4测量。最后，W@1和Z@1将潜在变量W和Z的方差固定为1，使得它们标准化。

代码解读4

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
 TYPE = GENERAL RANDOM;
 ESTIMATOR = ML;
 ALGORITHM = INTEGRATION;
MODEL:
! Measurement model

! Identify moderator factors by fixing variance = 1 (instead of first loading)

! This makes these factors standardised

 X BY X1 X2 X3 X4;
 M BY M1 M2 M3 M4;
 W BY W1* W2 W3 W4;
 Z BY Z1* Z2 Z3 Z4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;
! Create latent interactions

 MW | M XWITH W;
 MZ | M XWITH Z;
 XW | X XWITH W;
 XZ | X XWITH Z;

这部分定义了潜在变量之间的交互作用。MW | M XWITH W，创建了M和W之间的交互项MW。MZ | M XWITH Z，创建了M和Z之间的交互项MZ。XW | X XWITH W，创建了X和W之间的交互项XW。XZ | X XWITH Z，创建了X和Z之间的交互项XZ。

代码解读5

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
 TYPE = GENERAL RANDOM;
 ESTIMATOR = ML;
 ALGORITHM = INTEGRATION;
MODEL:
! Measurement model

! Identify moderator factors by fixing variance = 1 (instead of first loading)

! This makes these factors standardised

 X BY X1 X2 X3 X4;
 M BY M1 M2 M3 M4;
 W BY W1* W2 W3 W4;
 Z BY Z1* Z2 Z3 Z4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;
! Create latent interactions

 MW | M XWITH W;
 MZ | M XWITH Z;
 XW | X XWITH W;
 XZ | X XWITH Z;
! Fit structural model and name parameters


! Note that intercepts of M, Y are fixed = 0 since they are latent vars


! so no code to state and name them as parameters

 Y ON M (b1);
 Y ON W (b2);
 Y ON Z (b3);
 Y ON MW (b4);
 Y ON MZ (b5);
 Y ON X(cdash);
 M ON X (a1);
 M ON W (a2);
 M ON Z (a3);
 M ON XW (a4);
 M ON XZ (a5);

接下来，我们定义了结构模型，描述了潜在变量之间的路径关系，并给每个路径指定了名称。例如，Y ON M (b1)，表示M对Y的回归路径，回归系数命名为b1。Y ON X(cdash)，表示X对Y的直接回归路径，系数名为cdash。M ON X (a1)，表示X对M的回归路径，系数名为a1。这里要注意，M和Y的截距被固定为0，因为它们是潜在变量，不需要额外代码指定。

代码解读6

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
 TYPE = GENERAL RANDOM;
 ESTIMATOR = ML;
 ALGORITHM = INTEGRATION;
MODEL:
! Measurement model

! Identify moderator factors by fixing variance = 1 (instead of first loading)

! This makes these factors standardised

 X BY X1 X2 X3 X4;
 M BY M1 M2 M3 M4;
 W BY W1* W2 W3 W4;
 Z BY Z1* Z2 Z3 Z4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;
! Create latent interactions

 MW | M XWITH W;
 MZ | M XWITH Z;
 XW | X XWITH W;
 XZ | X XWITH Z;
! Fit structural model and name parameters


! Note that intercepts of M, Y are fixed = 0 since they are latent vars


! so no code to state and name them as parameters

 Y ON M (b1);
 Y ON W (b2);
 Y ON Z (b3);
 Y ON MW (b4);
 Y ON MZ (b5);
 Y ON X(cdash);
 M ON X (a1);
 M ON W (a2);
 M ON Z (a3);
 M ON XW (a4);
 M ON XZ (a5);
! Use model constraint subcommand to test conditional indirect effects


! You need to pick low, medium and high moderator values for W, Z


! for example, of 1 SD below mean, mean, 1 SD above mean
! 2 moderators, 3 values for each, gives 9 combinations


! arbitrary naming convention for conditional indirect and total effects used below:


! MEV_LOQ = medium value of V and low value of Q, etc.
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z
 ILOW_LOZ IMEW_LOZ IHIW_LOZ ILOW_MEZ IMEW_MEZ IHIW_MEZ
 ILOW_HIZ IMEW_HIZ IHIW_HIZ
 TLOW_LOZ TMEW_LOZ THIW_LOZ TLOW_MEZ TMEW_MEZ THIW_MEZ
 TLOW_HIZ TMEW_HIZ THIW_HIZ);
 LOW_W = -1;
! -1 SD below mean value of W

 MED_W = 0;
! mean value of W

 HIGH_W = 1;
! +1 SD above mean value of W
 LOW_Z = -1;
! -1 SD below mean value of Z

 MED_Z = 0;
! mean value of Z

 HIGH_Z = 1;
! +1 SD above mean value of Z

在模型约束部分，我们计算模型的约束参数，比如条件间接效应和总效应。我们定义了W和Z的低、中、高值，分别用-1、0和1表示，这通常代表均值以下一个标准差、均值和均值以上一个标准差。同时，我们定义了不同条件下间接效应和总效应的名称。

代码解读7

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
 TYPE = GENERAL RANDOM;
 ESTIMATOR = ML;
 ALGORITHM = INTEGRATION;
MODEL:
! Measurement model

! Identify moderator factors by fixing variance = 1 (instead of first loading)

! This makes these factors standardised

 X BY X1 X2 X3 X4;
 M BY M1 M2 M3 M4;
 W BY W1* W2 W3 W4;
 Z BY Z1* Z2 Z3 Z4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;
! Create latent interactions

 MW | M XWITH W;
 MZ | M XWITH Z;
 XW | X XWITH W;
 XZ | X XWITH Z;
! Fit structural model and name parameters


! Note that intercepts of M, Y are fixed = 0 since they are latent vars


! so no code to state and name them as parameters

 Y ON M (b1);
 Y ON W (b2);
 Y ON Z (b3);
 Y ON MW (b4);
 Y ON MZ (b5);
 Y ON X(cdash);
 M ON X (a1);
 M ON W (a2);
 M ON Z (a3);
 M ON XW (a4);
 M ON XZ (a5);
! Use model constraint subcommand to test conditional indirect effects


! You need to pick low, medium and high moderator values for W, Z


! for example, of 1 SD below mean, mean, 1 SD above mean
! 2 moderators, 3 values for each, gives 9 combinations


! arbitrary naming convention for conditional indirect and total effects used below:


! MEV_LOQ = medium value of V and low value of Q, etc.
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z
 ILOW_LOZ IMEW_LOZ IHIW_LOZ ILOW_MEZ IMEW_MEZ IHIW_MEZ
 ILOW_HIZ IMEW_HIZ IHIW_HIZ
 TLOW_LOZ TMEW_LOZ THIW_LOZ TLOW_MEZ TMEW_MEZ THIW_MEZ
 TLOW_HIZ TMEW_HIZ THIW_HIZ);
 LOW_W = -1;
! -1 SD below mean value of W

 MED_W = 0;
! mean value of W

 HIGH_W = 1;
! +1 SD above mean value of W
 LOW_Z = -1;
! -1 SD below mean value of Z

 MED_Z = 0;
! mean value of Z

 HIGH_Z = 1;
! +1 SD above mean value of Z
! Calc conditional indirect effects for each combination of moderator values
 ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b4*LOW_W +
 a4*b4*LOW_W*LOW_W + a5*b4*LOW_Z*LOW_W + a1*b5*LOW_Z +
 a4*b5*LOW_W*LOW_Z + a5*b5*LOW_Z*LOW_Z;
 IMEW_LOZ = a1*b1 + a4*b1*MED_W + a5*b1*LOW_Z + a1*b4*MED_W +
 a4*b4*MED_W*MED_W + a5*b4*LOW_Z*MED_W + a1*b5*LOW_Z +
 a4*b5*MED_W*LOW_Z + a5*b5*LOW_Z*LOW_Z;
 IHIW_LOZ = a1*b1 + a4*b1*HIGH_W + a5*b1*LOW_Z + a1*b4*HIGH_W +
 a4*b4*HIGH_W*HIGH_W + a5*b4*LOW_Z*HIGH_W + a1*b5*LOW_Z +
 a4*b5*HIGH_W*LOW_Z + a5*b5*LOW_Z*LOW_Z;
 ILOW_MEZ = a1*b1 + a4*b1*LOW_W + a5*b1*MED_Z + a1*b4*LOW_W +
 a4*b4*LOW_W*LOW_W + a5*b4*MED_Z*LOW_W + a1*b5*MED_Z +
 a4*b5*LOW_W*MED_Z + a5*b5*MED_Z*MED_Z;
 IMEW_MEZ = a1*b1 + a4*b1*MED_W + a5*b1*MED_Z + a1*b4*MED_W +
 a4*b4*MED_W*MED_W + a5*b4*MED_Z*MED_W + a1*b5*MED_Z +
 a4*b5*MED_W*MED_Z + a5*b5*MED_Z*MED_Z;
 IHIW_MEZ = a1*b1 + a4*b1*HIGH_W + a5*b1*MED_Z + a1*b4*HIGH_W +
 a4*b4*HIGH_W*HIGH_W + a5*b4*MED_Z*HIGH_W + a1*b5*MED_Z +
 a4*b5*HIGH_W*MED_Z + a5*b5*MED_Z*MED_Z;
 ILOW_HIZ = a1*b1 + a4*b1*LOW_W + a5*b1*HIGH_Z + a1*b4*LOW_W +
 a4*b4*LOW_W*LOW_W + a5*b4*HIGH_Z*LOW_W + a1*b5*HIGH_Z +
 a4*b5*LOW_W*HIGH_Z + a5*b5*HIGH_Z*HIGH_Z;
 IMEW_HIZ = a1*b1 + a4*b1*MED_W + a5*b1*HIGH_Z + a1*b4*MED_W +
 a4*b4*MED_W*MED_W + a5*b4*HIGH_Z*MED_W + a1*b5*HIGH_Z +
 a4*b5*MED_W*HIGH_Z + a5*b5*HIGH_Z*HIGH_Z;
 IHIW_HIZ = a1*b1 + a4*b1*HIGH_W + a5*b1*HIGH_Z + a1*b4*HIGH_W +
 a4*b4*HIGH_W*HIGH_W + a5*b4*HIGH_Z*HIGH_W + a1*b5*HIGH_Z +
 a4*b5*HIGH_W*HIGH_Z + a5*b5*HIGH_Z*HIGH_Z;

这里，我们计算在不同调节变量水平下，X对Y的条件间接效应。例如，ILOW_LOZ计算了当W和Z都取低值时的间接效应。公式来自于之前推导的(a1 + a4W + a5Z)乘以(b1 + b4W + b5Z)。这部分代码为W和Z的每种组合都计算了相应的间接效应。

代码解读8

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
 TYPE = GENERAL RANDOM;
 ESTIMATOR = ML;
 ALGORITHM = INTEGRATION;
MODEL:
! Measurement model

! Identify moderator factors by fixing variance = 1 (instead of first loading)

! This makes these factors standardised

 X BY X1 X2 X3 X4;
 M BY M1 M2 M3 M4;
 W BY W1* W2 W3 W4;
 Z BY Z1* Z2 Z3 Z4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;
! Create latent interactions

 MW | M XWITH W;
 MZ | M XWITH Z;
 XW | X XWITH W;
 XZ | X XWITH Z;
! Fit structural model and name parameters


! Note that intercepts of M, Y are fixed = 0 since they are latent vars


! so no code to state and name them as parameters

 Y ON M (b1);
 Y ON W (b2);
 Y ON Z (b3);
 Y ON MW (b4);
 Y ON MZ (b5);
 Y ON X(cdash);
 M ON X (a1);
 M ON W (a2);
 M ON Z (a3);
 M ON XW (a4);
 M ON XZ (a5);
! Use model constraint subcommand to test conditional indirect effects


! You need to pick low, medium and high moderator values for W, Z


! for example, of 1 SD below mean, mean, 1 SD above mean
! 2 moderators, 3 values for each, gives 9 combinations


! arbitrary naming convention for conditional indirect and total effects used below:


! MEV_LOQ = medium value of V and low value of Q, etc.
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z
 ILOW_LOZ IMEW_LOZ IHIW_LOZ ILOW_MEZ IMEW_MEZ IHIW_MEZ
 ILOW_HIZ IMEW_HIZ IHIW_HIZ
 TLOW_LOZ TMEW_LOZ THIW_LOZ TLOW_MEZ TMEW_MEZ THIW_MEZ
 TLOW_HIZ TMEW_HIZ THIW_HIZ);
 LOW_W = -1;
! -1 SD below mean value of W

 MED_W = 0;
! mean value of W

 HIGH_W = 1;
! +1 SD above mean value of W
 LOW_Z = -1;
! -1 SD below mean value of Z

 MED_Z = 0;
! mean value of Z

 HIGH_Z = 1;
! +1 SD above mean value of Z
! Calc conditional indirect effects for each combination of moderator values
 ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b4*LOW_W +
 a4*b4*LOW_W*LOW_W + a5*b4*LOW_Z*LOW_W + a1*b5*LOW_Z +
 a4*b5*LOW_W*LOW_Z + a5*b5*LOW_Z*LOW_Z;
 IMEW_LOZ = a1*b1 + a4*b1*MED_W + a5*b1*LOW_Z + a1*b4*MED_W +
 a4*b4*MED_W*MED_W + a5*b4*LOW_Z*MED_W + a1*b5*LOW_Z +
 a4*b5*MED_W*LOW_Z + a5*b5*LOW_Z*LOW_Z;
 IHIW_LOZ = a1*b1 + a4*b1*HIGH_W + a5*b1*LOW_Z + a1*b4*HIGH_W +
 a4*b4*HIGH_W*HIGH_W + a5*b4*LOW_Z*HIGH_W + a1*b5*LOW_Z +
 a4*b5*HIGH_W*LOW_Z + a5*b5*LOW_Z*LOW_Z;
 ILOW_MEZ = a1*b1 + a4*b1*LOW_W + a5*b1*MED_Z + a1*b4*LOW_W +
 a4*b4*LOW_W*LOW_W + a5*b4*MED_Z*LOW_W + a1*b5*MED_Z +
 a4*b5*LOW_W*MED_Z + a5*b5*MED_Z*MED_Z;
 IMEW_MEZ = a1*b1 + a4*b1*MED_W + a5*b1*MED_Z + a1*b4*MED_W +
 a4*b4*MED_W*MED_W + a5*b4*MED_Z*MED_W + a1*b5*MED_Z +
 a4*b5*MED_W*MED_Z + a5*b5*MED_Z*MED_Z;
 IHIW_MEZ = a1*b1 + a4*b1*HIGH_W + a5*b1*MED_Z + a1*b4*HIGH_W +
 a4*b4*HIGH_W*HIGH_W + a5*b4*MED_Z*HIGH_W + a1*b5*MED_Z +
 a4*b5*HIGH_W*MED_Z + a5*b5*MED_Z*MED_Z;
 ILOW_HIZ = a1*b1 + a4*b1*LOW_W + a5*b1*HIGH_Z + a1*b4*LOW_W +
 a4*b4*LOW_W*LOW_W + a5*b4*HIGH_Z*LOW_W + a1*b5*HIGH_Z +
 a4*b5*LOW_W*HIGH_Z + a5*b5*HIGH_Z*HIGH_Z;
 IMEW_HIZ = a1*b1 + a4*b1*MED_W + a5*b1*HIGH_Z + a1*b4*MED_W +
 a4*b4*MED_W*MED_W + a5*b4*HIGH_Z*MED_W + a1*b5*HIGH_Z +
 a4*b5*MED_W*HIGH_Z + a5*b5*HIGH_Z*HIGH_Z;
 IHIW_HIZ = a1*b1 + a4*b1*HIGH_W + a5*b1*HIGH_Z + a1*b4*HIGH_W +
 a4*b4*HIGH_W*HIGH_W + a5*b4*HIGH_Z*HIGH_W + a1*b5*HIGH_Z +
 a4*b5*HIGH_W*HIGH_Z + a5*b5*HIGH_Z*HIGH_Z;
! Calc conditional total effects for each combination of moderator values
 TLOW_LOZ = ILOW_LOZ + cdash;
 TMEW_LOZ = IMEW_LOZ + cdash;
 THIW_LOZ = IHIW_LOZ + cdash;
 TLOW_MEZ = ILOW_MEZ + cdash;
 TMEW_MEZ = IMEW_MEZ + cdash;
 THIW_MEZ = IHIW_MEZ + cdash;
 TLOW_HIZ = ILOW_HIZ + cdash;
 TMEW_HIZ = IMEW_HIZ + cdash;
 THIW_HIZ = IHIW_HIZ + cdash;

接下来，我们计算X对Y的条件总效应，这是通过将条件间接效应加上直接效应cdash来计算的。例如，TLOW_LOZ是W和Z都取低值时的总效应，它是ILOW_LOZ加上cdash的结果。

代码解读9

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
 TYPE = GENERAL RANDOM;
 ESTIMATOR = ML;
 ALGORITHM = INTEGRATION;
MODEL:
! Measurement model

! Identify moderator factors by fixing variance = 1 (instead of first loading)

! This makes these factors standardised

 X BY X1 X2 X3 X4;
 M BY M1 M2 M3 M4;
 W BY W1* W2 W3 W4;
 Z BY Z1* Z2 Z3 Z4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;
! Create latent interactions

 MW | M XWITH W;
 MZ | M XWITH Z;
 XW | X XWITH W;
 XZ | X XWITH Z;
! Fit structural model and name parameters


! Note that intercepts of M, Y are fixed = 0 since they are latent vars


! so no code to state and name them as parameters

 Y ON M (b1);
 Y ON W (b2);
 Y ON Z (b3);
 Y ON MW (b4);
 Y ON MZ (b5);
 Y ON X(cdash);
 M ON X (a1);
 M ON W (a2);
 M ON Z (a3);
 M ON XW (a4);
 M ON XZ (a5);
! Use model constraint subcommand to test conditional indirect effects


! You need to pick low, medium and high moderator values for W, Z


! for example, of 1 SD below mean, mean, 1 SD above mean
! 2 moderators, 3 values for each, gives 9 combinations


! arbitrary naming convention for conditional indirect and total effects used below:


! MEV_LOQ = medium value of V and low value of Q, etc.
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z
 ILOW_LOZ IMEW_LOZ IHIW_LOZ ILOW_MEZ IMEW_MEZ IHIW_MEZ
 ILOW_HIZ IMEW_HIZ IHIW_HIZ
 TLOW_LOZ TMEW_LOZ THIW_LOZ TLOW_MEZ TMEW_MEZ THIW_MEZ
 TLOW_HIZ TMEW_HIZ THIW_HIZ);
 LOW_W = -1;
! -1 SD below mean value of W

 MED_W = 0;
! mean value of W

 HIGH_W = 1;
! +1 SD above mean value of W
 LOW_Z = -1;
! -1 SD below mean value of Z

 MED_Z = 0;
! mean value of Z

 HIGH_Z = 1;
! +1 SD above mean value of Z
! Calc conditional indirect effects for each combination of moderator values
 ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b4*LOW_W +
 a4*b4*LOW_W*LOW_W + a5*b4*LOW_Z*LOW_W + a1*b5*LOW_Z +
 a4*b5*LOW_W*LOW_Z + a5*b5*LOW_Z*LOW_Z;
 IMEW_LOZ = a1*b1 + a4*b1*MED_W + a5*b1*LOW_Z + a1*b4*MED_W +
 a4*b4*MED_W*MED_W + a5*b4*LOW_Z*MED_W + a1*b5*LOW_Z +
 a4*b5*MED_W*LOW_Z + a5*b5*LOW_Z*LOW_Z;
 IHIW_LOZ = a1*b1 + a4*b1*HIGH_W + a5*b1*LOW_Z + a1*b4*HIGH_W +
 a4*b4*HIGH_W*HIGH_W + a5*b4*LOW_Z*HIGH_W + a1*b5*LOW_Z +
 a4*b5*HIGH_W*LOW_Z + a5*b5*LOW_Z*LOW_Z;
 ILOW_MEZ = a1*b1 + a4*b1*LOW_W + a5*b1*MED_Z + a1*b4*LOW_W +
 a4*b4*LOW_W*LOW_W + a5*b4*MED_Z*LOW_W + a1*b5*MED_Z +
 a4*b5*LOW_W*MED_Z + a5*b5*MED_Z*MED_Z;
 IMEW_MEZ = a1*b1 + a4*b1*MED_W + a5*b1*MED_Z + a1*b4*MED_W +
 a4*b4*MED_W*MED_W + a5*b4*MED_Z*MED_W + a1*b5*MED_Z +
 a4*b5*MED_W*MED_Z + a5*b5*MED_Z*MED_Z;
 IHIW_MEZ = a1*b1 + a4*b1*HIGH_W + a5*b1*MED_Z + a1*b4*HIGH_W +
 a4*b4*HIGH_W*HIGH_W + a5*b4*MED_Z*HIGH_W + a1*b5*MED_Z +
 a4*b5*HIGH_W*MED_Z + a5*b5*MED_Z*MED_Z;
 ILOW_HIZ = a1*b1 + a4*b1*LOW_W + a5*b1*HIGH_Z + a1*b4*LOW_W +
 a4*b4*LOW_W*LOW_W + a5*b4*HIGH_Z*LOW_W + a1*b5*HIGH_Z +
 a4*b5*LOW_W*HIGH_Z + a5*b5*HIGH_Z*HIGH_Z;
 IMEW_HIZ = a1*b1 + a4*b1*MED_W + a5*b1*HIGH_Z + a1*b4*MED_W +
 a4*b4*MED_W*MED_W + a5*b4*HIGH_Z*MED_W + a1*b5*HIGH_Z +
 a4*b5*MED_W*HIGH_Z + a5*b5*HIGH_Z*HIGH_Z;
 IHIW_HIZ = a1*b1 + a4*b1*HIGH_W + a5*b1*HIGH_Z + a1*b4*HIGH_W +
 a4*b4*HIGH_W*HIGH_W + a5*b4*HIGH_Z*HIGH_W + a1*b5*HIGH_Z +
 a4*b5*HIGH_W*HIGH_Z + a5*b5*HIGH_Z*HIGH_Z;
! Calc conditional total effects for each combination of moderator values
 TLOW_LOZ = ILOW_LOZ + cdash;
 TMEW_LOZ = IMEW_LOZ + cdash;
 THIW_LOZ = IHIW_LOZ + cdash;
 TLOW_MEZ = ILOW_MEZ + cdash;
 TMEW_MEZ = IMEW_MEZ + cdash;
 THIW_MEZ = IHIW_MEZ + cdash;
 TLOW_HIZ = ILOW_HIZ + cdash;
 TMEW_HIZ = IMEW_HIZ + cdash;
 THIW_HIZ = IHIW_HIZ + cdash;
! Use loop plot to plot conditional indirect effect of X on Y for each combination of low, med, high moderator values
! Could be edited to show conditional direct or conditional total effects instead
! NOTE - values from -3 to 3 in LOOP() statement since
! X is factor with mean set at default of 0
 PLOT(PLOW_LOZ PMEW_LOZ PHIW_LOZ PLOW_MEZ PMEW_MEZ PHIW_MEZ
 PLOW_HIZ PMEW_HIZ PHIW_HIZ);
 LOOP(XVAL,-3,3,0.1);
 PLOW_LOZ = ILOW_LOZ*XVAL;
 PMEW_LOZ = IMEW_LOZ*XVAL;
 PHIW_LOZ = IHIW_LOZ*XVAL;
 PLOW_MEZ = ILOW_MEZ*XVAL;
 PMEW_MEZ = IMEW_MEZ*XVAL;
 PHIW_MEZ = IHIW_MEZ*XVAL;
 PLOW_HIZ = ILOW_HIZ*XVAL;
 PMEW_HIZ = IMEW_HIZ*XVAL;
 PHIW_HIZ = IHIW_HIZ*XVAL;

这部分代码用于生成条件间接效应的绘图。我们定义了要绘制的变量名称，然后使用循环，XVAL从-3变化到3，步长为0.1。 这是因为潜在变量X的均值默认为0。接下来的代码在不同的调节变量水平下，将X的不同值XVAL乘以相应的条件间接效应，以生成用于绘制的变量。

代码解读10

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
Y1 Y2 Y3 Y4;
ANALYSIS:
 TYPE = GENERAL RANDOM;
 ESTIMATOR = ML;
 ALGORITHM = INTEGRATION;
MODEL:
! Measurement model

! Identify moderator factors by fixing variance = 1 (instead of first loading)

! This makes these factors standardised

 X BY X1 X2 X3 X4;
 M BY M1 M2 M3 M4;
 W BY W1* W2 W3 W4;
 Z BY Z1* Z2 Z3 Z4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;
! Create latent interactions

 MW | M XWITH W;
 MZ | M XWITH Z;
 XW | X XWITH W;
 XZ | X XWITH Z;
! Fit structural model and name parameters


! Note that intercepts of M, Y are fixed = 0 since they are latent vars


! so no code to state and name them as parameters

 Y ON M (b1);
 Y ON W (b2);
 Y ON Z (b3);
 Y ON MW (b4);
 Y ON MZ (b5);
 Y ON X(cdash);
 M ON X (a1);
 M ON W (a2);
 M ON Z (a3);
 M ON XW (a4);
 M ON XZ (a5);
! Use model constraint subcommand to test conditional indirect effects


! You need to pick low, medium and high moderator values for W, Z


! for example, of 1 SD below mean, mean, 1 SD above mean
! 2 moderators, 3 values for each, gives 9 combinations


! arbitrary naming convention for conditional indirect and total effects used below:


! MEV_LOQ = medium value of V and low value of Q, etc.
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z
 ILOW_LOZ IMEW_LOZ IHIW_LOZ ILOW_MEZ IMEW_MEZ IHIW_MEZ
 ILOW_HIZ IMEW_HIZ IHIW_HIZ
 TLOW_LOZ TMEW_LOZ THIW_LOZ TLOW_MEZ TMEW_MEZ THIW_MEZ
 TLOW_HIZ TMEW_HIZ THIW_HIZ);
 LOW_W = -1;
! -1 SD below mean value of W

 MED_W = 0;
! mean value of W

 HIGH_W = 1;
! +1 SD above mean value of W
 LOW_Z = -1;
! -1 SD below mean value of Z

 MED_Z = 0;
! mean value of Z

 HIGH_Z = 1;
! +1 SD above mean value of Z
! Calc conditional indirect effects for each combination of moderator values
 ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b4*LOW_W +
 a4*b4*LOW_W*LOW_W + a5*b4*LOW_Z*LOW_W + a1*b5*LOW_Z +
 a4*b5*LOW_W*LOW_Z + a5*b5*LOW_Z*LOW_Z;
 IMEW_LOZ = a1*b1 + a4*b1*MED_W + a5*b1*LOW_Z + a1*b4*MED_W +
 a4*b4*MED_W*MED_W + a5*b4*LOW_Z*MED_W + a1*b5*LOW_Z +
 a4*b5*MED_W*LOW_Z + a5*b5*LOW_Z*LOW_Z;
 IHIW_LOZ = a1*b1 + a4*b1*HIGH_W + a5*b1*LOW_Z + a1*b4*HIGH_W +
 a4*b4*HIGH_W*HIGH_W + a5*b4*LOW_Z*HIGH_W + a1*b5*LOW_Z +
 a4*b5*HIGH_W*LOW_Z + a5*b5*LOW_Z*LOW_Z;
 ILOW_MEZ = a1*b1 + a4*b1*LOW_W + a5*b1*MED_Z + a1*b4*LOW_W +
 a4*b4*LOW_W*LOW_W + a5*b4*MED_Z*LOW_W + a1*b5*MED_Z +
 a4*b5*LOW_W*MED_Z + a5*b5*MED_Z*MED_Z;
 IMEW_MEZ = a1*b1 + a4*b1*MED_W + a5*b1*MED_Z + a1*b4*MED_W +
 a4*b4*MED_W*MED_W + a5*b4*MED_Z*MED_W + a1*b5*MED_Z +
 a4*b5*MED_W*MED_Z + a5*b5*MED_Z*MED_Z;
 IHIW_MEZ = a1*b1 + a4*b1*HIGH_W + a5*b1*MED_Z + a1*b4*HIGH_W +
 a4*b4*HIGH_W*HIGH_W + a5*b4*MED_Z*HIGH_W + a1*b5*MED_Z +
 a4*b5*HIGH_W*MED_Z + a5*b5*MED_Z*MED_Z;
 ILOW_HIZ = a1*b1 + a4*b1*LOW_W + a5*b1*HIGH_Z + a1*b4*LOW_W +
 a4*b4*LOW_W*LOW_W + a5*b4*HIGH_Z*LOW_W + a1*b5*HIGH_Z +
 a4*b5*LOW_W*HIGH_Z + a5*b5*HIGH_Z*HIGH_Z;
 IMEW_HIZ = a1*b1 + a4*b1*MED_W + a5*b1*HIGH_Z + a1*b4*MED_W +
 a4*b4*MED_W*MED_W + a5*b4*HIGH_Z*MED_W + a1*b5*HIGH_Z +
 a4*b5*MED_W*HIGH_Z + a5*b5*HIGH_Z*HIGH_Z;
 IHIW_HIZ = a1*b1 + a4*b1*HIGH_W + a5*b1*HIGH_Z + a1*b4*HIGH_W +
 a4*b4*HIGH_W*HIGH_W + a5*b4*HIGH_Z*HIGH_W + a1*b5*HIGH_Z +
 a4*b5*HIGH_W*HIGH_Z + a5*b5*HIGH_Z*HIGH_Z;
! Calc conditional total effects for each combination of moderator values
 TLOW_LOZ = ILOW_LOZ + cdash;
 TMEW_LOZ = IMEW_LOZ + cdash;
 THIW_LOZ = IHIW_LOZ + cdash;
 TLOW_MEZ = ILOW_MEZ + cdash;
 TMEW_MEZ = IMEW_MEZ + cdash;
 THIW_MEZ = IHIW_MEZ + cdash;
 TLOW_HIZ = ILOW_HIZ + cdash;
 TMEW_HIZ = IMEW_HIZ + cdash;
 THIW_HIZ = IHIW_HIZ + cdash;
! Use loop plot to plot conditional indirect effect of X on Y for each combination of low, med, high moderator values
! Could be edited to show conditional direct or conditional total effects instead
! NOTE - values from -3 to 3 in LOOP() statement since
! X is factor with mean set at default of 0
 PLOT(PLOW_LOZ PMEW_LOZ PHIW_LOZ PLOW_MEZ PMEW_MEZ PHIW_MEZ
 PLOW_HIZ PMEW_HIZ PHIW_HIZ);
 LOOP(XVAL,-3,3,0.1);
 PLOW_LOZ = ILOW_LOZ*XVAL;
 PMEW_LOZ = IMEW_LOZ*XVAL;
 PHIW_LOZ = IHIW_LOZ*XVAL;
 PLOW_MEZ = ILOW_MEZ*XVAL;
 PMEW_MEZ = IMEW_MEZ*XVAL;
 PHIW_MEZ = IHIW_MEZ*XVAL;
 PLOW_HIZ = ILOW_HIZ*XVAL;
 PMEW_HIZ = IMEW_HIZ*XVAL;
 PHIW_HIZ = IHIW_HIZ*XVAL;
PLOT:

 TYPE = plot2;
OUTPUT:

 CINT;

最后，在绘图部分，我们定义了绘图类型为plot2，表示需要生成一个二维图形。输出部分，CINT表示要求输出参数估计的置信区间。

资源汇总

• 本视频讲义地址: https://mlln.cn/mplus-model-templates/model75latent.html
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• 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
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