Mplus model74 模型讲解

来自图书《MPlus中介调节模型》

有调节的中介效应分析 (模型 74) Mplus 教程

  • 理论模型
  • 数学模型
  • 数学推导
  • 代码解读

理论模型

数学模型

数学公式1

模型方程：

Y = b0 + b1M + c1'X + c2'MX
M = a0 + a1X

数学公式2

模型方程：

Y = b0 + b1M + c1'X + c2'MX
M = a0 + a1X
代入M的表达式：

Y = b0 + b1(a0 + a1X) + c1'X + c2'(a0 + a1X)X

数学公式3

模型方程：

Y = b0 + b1M + c1'X + c2'MX
M = a0 + a1X
代入M的表达式：

Y = b0 + b1(a0 + a1X) + c1'X + c2'(a0 + a1X)X
展开括号：

Y = b0 + a0b1 + a1b1X + c1'X + a0c2'X + a1c2'XX

数学公式4

模型方程：

Y = b0 + b1M + c1'X + c2'MX
M = a0 + a1X
代入M的表达式：

Y = b0 + b1(a0 + a1X) + c1'X + c2'(a0 + a1X)X
展开括号：

Y = b0 + a0b1 + a1b1X + c1'X + a0c2'X + a1c2'XX
整理方程：

Y = (b0 + a0b1) + (a1b1 + c1' + a0c2' + a1c2'X)X

数学公式5

模型方程：

Y = b0 + b1M + c1'X + c2'MX
M = a0 + a1X
代入M的表达式：

Y = b0 + b1(a0 + a1X) + c1'X + c2'(a0 + a1X)X
展开括号：

Y = b0 + a0b1 + a1b1X + c1'X + a0c2'X + a1c2'XX
整理方程：

Y = (b0 + a0b1) + (a1b1 + c1' + a0c2' + a1c2'X)X
条件间接效应：

a1b1 + a1c2'X  

或  a1(b1 + c2'X)

代码解读1

USEVARIABLES = X M Y XM;

代码解读2

USEVARIABLES = X M Y XM;
DEFINE:

 XM = X*M;

代码解读3

USEVARIABLES = X M Y XM;
DEFINE:

 XM = X*M;
ANALYSIS:

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

代码解读4

USEVARIABLES = X M Y XM;
DEFINE:

 XM = X*M;
ANALYSIS:

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

 Y ON M (b1);
 Y ON X (cdash1);
 Y ON XM (cdash2);
 [M] (a0);
 M ON X (a1);

代码解读5

USEVARIABLES = X M Y XM;
DEFINE:

 XM = X*M;
ANALYSIS:

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

 Y ON M (b1);
 Y ON X (cdash1);
 Y ON XM (cdash2);
 [M] (a0);
 M ON X (a1);
MODEL CONSTRAINT:
 NEW(LOW_X MED_X HIGH_X IND_LOWX IND_MEDX IND_HIX);
 LOW_X = #LOWX;
 MED_X = #MEDX;
 HIGH_X = #HIGHX;
 IND_LOWX = a1*b1 + a1*cdash2*LOW_X;
 IND_MEDX = a1*b1 + a1*cdash2*MED_X;
 IND_HIX = a1*b1 + a1*cdash2*HIGH_X;

代码解读6

USEVARIABLES = X M Y XM;
DEFINE:

 XM = X*M;
ANALYSIS:

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

 Y ON M (b1);
 Y ON X (cdash1);
 Y ON XM (cdash2);
 [M] (a0);
 M ON X (a1);
MODEL CONSTRAINT:
 NEW(LOW_X MED_X HIGH_X IND_LOWX IND_MEDX IND_HIX);
 LOW_X = #LOWX;
 MED_X = #MEDX;
 HIGH_X = #HIGHX;
 IND_LOWX = a1*b1 + a1*cdash2*LOW_X;
 IND_MEDX = a1*b1 + a1*cdash2*MED_X;
 IND_HIX = a1*b1 + a1*cdash2*HIGH_X;
PLOT(INDX);
LOOP(XVAL,1,5,0.1);
 INDX = (a1*b1 + a1*cdash2*XVAL)*XVAL;

代码解读7

USEVARIABLES = X M Y XM;
DEFINE:

 XM = X*M;
ANALYSIS:

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

 Y ON M (b1);
 Y ON X (cdash1);
 Y ON XM (cdash2);
 [M] (a0);
 M ON X (a1);
MODEL CONSTRAINT:
 NEW(LOW_X MED_X HIGH_X IND_LOWX IND_MEDX IND_HIX);
 LOW_X = #LOWX;
 MED_X = #MEDX;
 HIGH_X = #HIGHX;
 IND_LOWX = a1*b1 + a1*cdash2*LOW_X;
 IND_MEDX = a1*b1 + a1*cdash2*MED_X;
 IND_HIX = a1*b1 + a1*cdash2*HIGH_X;
PLOT(INDX);
LOOP(XVAL,1,5,0.1);
 INDX = (a1*b1 + a1*cdash2*XVAL)*XVAL;
PLOT:

 TYPE = plot2;

代码解读8

USEVARIABLES = X M Y XM;
DEFINE:

 XM = X*M;
ANALYSIS:

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

 Y ON M (b1);
 Y ON X (cdash1);
 Y ON XM (cdash2);
 [M] (a0);
 M ON X (a1);
MODEL CONSTRAINT:
 NEW(LOW_X MED_X HIGH_X IND_LOWX IND_MEDX IND_HIX);
 LOW_X = #LOWX;
 MED_X = #MEDX;
 HIGH_X = #HIGHX;
 IND_LOWX = a1*b1 + a1*cdash2*LOW_X;
 IND_MEDX = a1*b1 + a1*cdash2*MED_X;
 IND_HIX = a1*b1 + a1*cdash2*HIGH_X;
PLOT(INDX);
LOOP(XVAL,1,5,0.1);
 INDX = (a1*b1 + a1*cdash2*XVAL)*XVAL;
PLOT:

 TYPE = plot2;
OUTPUT:

 STAND CINT(bcbootstrap);

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