Mplus model27 模型讲解

Mplus中介、调节和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，欢迎学习本教程！本教程将手把手教大家如何用Mplus构建复杂的模型，包括中介效应、调节效应以及两者兼具的调节中介效应。我们将以一个包含一个自变量、一个中介变量、三个调节变量和一个因变量的案例为例，一步步讲解模型的构建过程。

首先，我们会讲解模型的理论基础，也就是理论模型部分，让大家理解模型的逻辑和假设。接下来，我们会用数学公式表达这个模型，也就是数学模型部分，并详细推导公式，帮助大家理解模型背后的数学原理，这就是数学推导部分。最后，我们将展示具体的Mplus代码，并逐行解释代码的含义和作用，这就是Mplus代码解读部分。

通过本教程，即使没有扎实的统计学基础，也能轻松掌握Mplus的使用，并将其作为快速查找和应用工具。教程中会提供应对不同类型变量（例如二元变量）的参考建议。希望大家能学有所获！有任何问题，欢迎联系Data Sense咨询。

理论模型

数学模型

数学公式1

Y = b0 + b1M + b2V + b3MV + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ

数学公式2

Y = b0 + b1M + b2V + b3MV + c1'X + c2'W + c3'XW
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 + c1'X + c2'W + c3'XW

数学公式3

Y = b0 + b1M + b2V + b3MV + c1'X + c2'W + c3'XW
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 + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + b2V + a0b3V + a1b3XV + a2b3WV + a3b3ZV + a4b3XWV + a5b3XZV + a6b3WZV + a7b3XWZV + c1'X + c2'W + c3'XW

数学公式4

Y = b0 + b1M + b2V + b3MV + c1'X + c2'W + c3'XW
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 + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + b2V + a0b3V + a1b3XV + a2b3WV + a3b3ZV + a4b3XWV + a5b3XZV + a6b3WZV + a7b3XWZV + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + b2V + a0b3V + a2b3WV + a3b3ZV + a6b3WZV + c2'W) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b3V + a4b3WV + a5b3ZV + a7b3WZV + c1' + c3'W)X

数学公式5

Y = b0 + b1M + b2V + b3MV + c1'X + c2'W + c3'XW
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 + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + b2V + a0b3V + a1b3XV + a2b3WV + a3b3ZV + a4b3XWV + a5b3XZV + a6b3WZV + a7b3XWZV + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + b2V + a0b3V + a2b3WV + a3b3ZV + a6b3WZV + c2'W) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b3V + a4b3WV + a5b3ZV + a7b3WZV + c1' + c3'W)X
X对Y的间接效应为：(a1 + a4W + a5Z + a7WZ)(b1 + b3V)
X对Y的直接效应为：c1' + c3'W

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 (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 [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 (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 [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 + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z + a1*b3*LOW_V + a4*b3*LOW_W*LOW_V + a5*b3*LOW_Z*LOW_V + a7*b3*LOW_W*LOW_Z*LOW_V; ...

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 (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 [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 + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z + a1*b3*LOW_V + a4*b3*LOW_W*LOW_V + a5*b3*LOW_Z*LOW_V + a7*b3*LOW_W*LOW_Z*LOW_V; ...
PLOT(PLWLZLV PMWLZLV ...);
 LOOP(XVAL,1,5,0.1);
 PLWLZLV = ILWLZLV*XVAL; ...

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 (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 [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 + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z + a1*b3*LOW_V + a4*b3*LOW_W*LOW_V + a5*b3*LOW_Z*LOW_V + a7*b3*LOW_W*LOW_Z*LOW_V; ...
PLOT(PLWLZLV PMWLZLV ...);
 LOOP(XVAL,1,5,0.1);
 PLWLZLV = ILWLZLV*XVAL; ...
OUTPUT:
 STAND CINT(bcbootstrap);

资源汇总

本视频讲义地址: https://mlln.cn/mplus-model-templates/model27.html
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