Mplus model25 模型讲解

Mplus中介、调节与调节中介模型构建教程

理论模型
数学模型
数学推导
Mplus代码解读

大家好，欢迎来到本教程。本教程将手把手教大家如何使用Mplus构建包含中介、调节和调节中介效应的复杂模型。我们将以一个具体的案例为例，逐步讲解模型的构建过程。首先，我们将介绍模型的理论基础，也就是理论模型部分，帮助大家理解中介、调节和调节中介效应的概念和逻辑关系。接下来，我们会深入探讨模型的数学表达形式，也就是数学模型部分，了解模型中各个参数的含义以及它们之间的关系。然后，我们会进行数学推导，展示如何推导出模型中的关键参数，例如间接效应和总效应。最后，我们将重点讲解Mplus代码的编写和结果解读，帮助大家掌握使用Mplus软件分析数据的技巧。本教程涵盖了多个调节变量及其交互作用，并演示如何计算在不同调节变量取值下的条件间接效应和总效应。大家可以根据自己的需要选择性地学习教程的各个部分。如有任何问题，欢迎随时提出！

理论模型

数学模型

数学公式1

模型方程式：
Y = b0 + b1M + b2V + b3MV + c'X

数学公式2

模型方程式：
Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ

数学公式3

模型方程式：
Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)V + c'X

数学公式4

模型方程式：
Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)V + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + b2V + a0b3V + a1b3XV + a2b3WV + a3b3ZV + a4b3XWV + a5b3XZV + a6b3WZV + a7b3XWZV + c'X

数学公式5

模型方程式：
Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)V + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + b2V + a0b3V + a1b3XV + a2b3WV + a3b3ZV + a4b3XWV + a5b3XZV + a6b3WZV + a7b3XWZV + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + b2V + a0b3V + a2b3WV + a3b3ZV + a6b3WZV) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b3V + a4b3WV + a5b3ZV + a7b3WZV + c')X

数学公式6

模型方程式：
Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)V + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + b2V + a0b3V + a1b3XV + a2b3WV + a3b3ZV + a4b3XWV + a5b3XZV + a6b3WZV + a7b3XWZV + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + b2V + a0b3V + a2b3WV + a3b3ZV + a6b3WZV) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b3V + a4b3WV + a5b3ZV + a7b3WZV + c')X
X对Y的一个间接效应（在W, Z, V条件下）：
(a1 + a4W + a5Z + a7WZ)(b1 + b3V)

数学公式7

模型方程式：
Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)V + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + b2V + a0b3V + a1b3XV + a2b3WV + a3b3ZV + a4b3XWV + a5b3XZV + a6b3WZV + a7b3XWZV + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + b2V + a0b3V + a2b3WV + a3b3ZV + a6b3WZV) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b3V + a4b3WV + a5b3ZV + a7b3WZV + c')X
X对Y的一个间接效应（在W, Z, V条件下）：
(a1 + a4W + a5Z + a7WZ)(b1 + b3V)
X对Y的一个直接效应：
c'

代码解读1

USEVARIABLES = X M W Z V Y XW XZ WZ MV XWZ;

代码解读2

USEVARIABLES = X M W Z V Y XW XZ WZ MV XWZ;
DEFINE:
 MV = M*V;
 XW = X*W;
 XZ = X*Z;
 WZ = W*Z;
 XWZ = X*W*Z;

代码解读3

USEVARIABLES = X M W Z V Y XW XZ WZ MV XWZ;
DEFINE:
 MV = M*V;
 XW = X*W;
 XZ = X*Z;
 WZ = W*Z;
 XWZ = X*W*Z;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;

代码解读4

USEVARIABLES = X M W Z V Y XW XZ WZ MV XWZ;
DEFINE:
 MV = M*V;
 XW = X*W;
 XZ = X*Z;
 WZ = W*Z;
 XWZ = X*W*Z;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON MV (b3);
 Y ON X (cdash);
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON Z (a3);
 M ON XW (a4);
 M ON XZ (a5);
 M ON WZ (a6);
 M ON XWZ (a7);

代码解读5

USEVARIABLES = X M W Z V Y XW XZ WZ MV XWZ;
DEFINE:
 MV = M*V;
 XW = X*W;
 XZ = X*Z;
 WZ = W*Z;
 XWZ = X*W*Z;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON MV (b3);
 Y ON X (cdash);
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON Z (a3);
 M ON XW (a4);
 M ON XZ (a5);
 M ON WZ (a6);
 M ON XWZ (a7);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z LOW_V MED_V HIGH_V ... );
 LOW_W = #LOWW;
 ...
 ILWLZLV = a1*b1 + a4*b1*LOW_W + ... ;
 ...
 TLWLZLV = ILWLZLV + cdash;

代码解读6

USEVARIABLES = X M W Z V Y XW XZ WZ MV XWZ;
DEFINE:
 MV = M*V;
 XW = X*W;
 XZ = X*Z;
 WZ = W*Z;
 XWZ = X*W*Z;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON MV (b3);
 Y ON X (cdash);
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON Z (a3);
 M ON XW (a4);
 M ON XZ (a5);
 M ON WZ (a6);
 M ON XWZ (a7);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z LOW_V MED_V HIGH_V ... );
 LOW_W = #LOWW;
 ...
 ILWLZLV = a1*b1 + a4*b1*LOW_W + ... ;
 ...
 TLWLZLV = ILWLZLV + cdash;
PLOT(...);
 LOOP(XVAL,1,5,0.1);
 ...
 PLOT:
 TYPE = plot2;

代码解读7

USEVARIABLES = X M W Z V Y XW XZ WZ MV XWZ;
DEFINE:
 MV = M*V;
 XW = X*W;
 XZ = X*Z;
 WZ = W*Z;
 XWZ = X*W*Z;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON MV (b3);
 Y ON X (cdash);
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON Z (a3);
 M ON XW (a4);
 M ON XZ (a5);
 M ON WZ (a6);
 M ON XWZ (a7);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z LOW_V MED_V HIGH_V ... );
 LOW_W = #LOWW;
 ...
 ILWLZLV = a1*b1 + a4*b1*LOW_W + ... ;
 ...
 TLWLZLV = ILWLZLV + cdash;
PLOT(...);
 LOOP(XVAL,1,5,0.1);
 ...
 PLOT:
 TYPE = plot2;
OUTPUT:
 STAND CINT(bcbootstrap);

资源汇总

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