Mplus model60latent 模型讲解

Mplus模型60（潜变量）：包含中介、调节和调节中介效应的模型构建教程

理论模型
数学模型
代码解读
条件间接效应计算与作图

大家好，欢迎来到本教程。这个PPT页面概述了我们Mplus模型60教程的结构。本教程将带你一步步构建一个复杂的模型，它包含中介效应、调节效应以及更复杂的调节中介效应。首先，我们会介绍模型的理论基础，也就是理论模型部分，让你理解模型背后的逻辑和假设。接下来，我们会用数学公式表达这个复杂的模型，这就是数学模型部分，这部分会比较精简，重点在于理解模型结构。然后，我们将直接进入代码解读部分，详细讲解Mplus代码的每一行，包括测量模型、结构模型，以及如何通过模型约束来计算和可视化条件间接效应。最后，我们会重点讲解如何利用Mplus代码计算不同调节变量水平下的条件间接效应，并通过作图直观地展现结果。本教程旨在提供一个快速参考，你可以根据自己的需要选择性地阅读相关部分。感谢Figure it out统计咨询公司的支持！

理论模型

数学模型

数学公式1

Y = b0 + b1M + b2W + b3MW + c'X

数学公式2

Y = b0 + b1M + b2W + b3MW + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ

数学公式3

Y = b0 + b1M + b2W + b3MW + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2W + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + c'X

数学公式4

Y = b0 + b1M + b2W + b3MW + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2W + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2W + a0b3W + a1b3XW + a2b3WW + a3b3ZW + a4b3XWW + a5b3XZW + c'X

数学公式5

Y = b0 + b1M + b2W + b3MW + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2W + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2W + a0b3W + a1b3XW + a2b3WW + a3b3ZW + a4b3XWW + a5b3XZW + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + b2W + a0b3W + a2b3WW + a3b3ZW) + (a1b1 + a4b1W + a5b1Z + a1b3W + a4b3WW + a5b3ZW + c')X

数学公式6

Y = b0 + b1M + b2W + b3MW + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2W + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2W + a0b3W + a1b3XW + a2b3WW + a3b3ZW + a4b3XWW + a5b3XZW + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + b2W + a0b3W + a2b3WW + a3b3ZW) + (a1b1 + a4b1W + a5b1Z + a1b3W + a4b3WW + a5b3ZW + c')X
条件于 W 和 Z 的 X 对 Y 的间接效应为：(a1 + a4W + a5Z)(b1 + b3W)

数学公式7

Y = b0 + b1M + b2W + b3MW + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2W + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2W + a0b3W + a1b3XW + a2b3WW + a3b3ZW + a4b3XWW + a5b3XZW + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + b2W + a0b3W + a2b3WW + a3b3ZW) + (a1b1 + a4b1W + a5b1Z + a1b3W + a4b3WW + a5b3ZW + c')X
条件于 W 和 Z 的 X 对 Y 的间接效应为：(a1 + a4W + a5Z)(b1 + b3W)
X 对 Y 的直接效应为：c'

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;

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;

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:
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;

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:
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;

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

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:
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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON W (b2);
Y ON MW (b3);
Y ON X (cdash);

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:
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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON W (b2);
Y ON MW (b3);
Y ON X (cdash);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);

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:
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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON W (b2);
Y ON MW (b3);
Y ON X (cdash);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z ...);
LOW_W = -1; ...

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:
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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON W (b2);
Y ON MW (b3);
Y ON X (cdash);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z ...);
LOW_W = -1; ...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b3*LOW_W + a4*b3*LOW_W*LOW_W + a5*b3*LOW_Z*LOW_W; ...

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:
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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON W (b2);
Y ON MW (b3);
Y ON X (cdash);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z ...);
LOW_W = -1; ...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b3*LOW_W + a4*b3*LOW_W*LOW_W + a5*b3*LOW_Z*LOW_W; ...
TLOW_LOZ = ILOW_LOZ + cdash; ...

代码解读11

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:
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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON W (b2);
Y ON MW (b3);
Y ON X (cdash);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z ...);
LOW_W = -1; ...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b3*LOW_W + a4*b3*LOW_W*LOW_W + a5*b3*LOW_Z*LOW_W; ...
TLOW_LOZ = ILOW_LOZ + cdash; ...
PLOT(PLOW_LOZ PMEW_LOZ PHIW_LOZ ...);
LOOP(XVAL,-3,3,0.1); ...

代码解读12

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:
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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON W (b2);
Y ON MW (b3);
Y ON X (cdash);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z ...);
LOW_W = -1; ...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b3*LOW_W + a4*b3*LOW_W*LOW_W + a5*b3*LOW_Z*LOW_W; ...
TLOW_LOZ = ILOW_LOZ + cdash; ...
PLOT(PLOW_LOZ PMEW_LOZ PHIW_LOZ ...);
LOOP(XVAL,-3,3,0.1); ...
OUTPUT: CINT;

资源汇总

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