Mplus model47 模型讲解

来自图书《MPlus中介调节模型》

Mplus 中介、调节和调节中介模型构建指南

  • 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

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ

数学公式2

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2V + b3Q + b4(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + b5(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Q + b6VQ + b7(a0 + a1X + a2W + a3Z + a4XW + a5XZ)VQ + c'X

数学公式3

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2V + b3Q + b4(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + b5(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Q + b6VQ + b7(a0 + a1X + a2W + a3Z + a4XW + a5XZ)VQ + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + b3Q + a0b4V + a1b4XV + a2b4WV + a3b4ZV + a4b4XWV + a5b4XZV + a0b5Q + a1b5XQ + a2b5WQ + a3b5ZQ + a4b5XWQ + a5b5XZQ + b6VQ + a0b7VQ + a1b7XVQ + a2b7WVQ + a3b7ZVQ + a4b7XWVQ + a5b7XZVQ + c'X

数学公式4

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2V + b3Q + b4(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + b5(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Q + b6VQ + b7(a0 + a1X + a2W + a3Z + a4XW + a5XZ)VQ + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + b3Q + a0b4V + a1b4XV + a2b4WV + a3b4ZV + a4b4XWV + a5b4XZV + a0b5Q + a1b5XQ + a2b5WQ + a3b5ZQ + a4b5XWQ + a5b5XZQ + b6VQ + a0b7VQ + a1b7XVQ + a2b7WVQ + a3b7ZVQ + a4b7XWVQ + a5b7XZVQ + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + b2V + b3Q + a0b4V + a2b4WV + a3b4ZV + a0b5Q + a2b5WQ + a3b5ZQ + b6VQ + a0b7VQ + a2b7WVQ + a3b7ZVQ) + (a1b1 + a4b1W + a5b1Z + a1b4V + a4b4WV + a5b4ZV + a1b5Q + a4b5WQ + a5b5ZQ + a1b7VQ + a4b7WVQ + a5b7ZVQ + c')X

数学公式5

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2V + b3Q + b4(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + b5(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Q + b6VQ + b7(a0 + a1X + a2W + a3Z + a4XW + a5XZ)VQ + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + b3Q + a0b4V + a1b4XV + a2b4WV + a3b4ZV + a4b4XWV + a5b4XZV + a0b5Q + a1b5XQ + a2b5WQ + a3b5ZQ + a4b5XWQ + a5b5XZQ + b6VQ + a0b7VQ + a1b7XVQ + a2b7WVQ + a3b7ZVQ + a4b7XWVQ + a5b7XZVQ + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + b2V + b3Q + a0b4V + a2b4WV + a3b4ZV + a0b5Q + a2b5WQ + a3b5ZQ + b6VQ + a0b7VQ + a2b7WVQ + a3b7ZVQ) + (a1b1 + a4b1W + a5b1Z + a1b4V + a4b4WV + a5b4ZV + a1b5Q + a4b5WQ + a5b5ZQ + a1b7VQ + a4b7WVQ + a5b7ZVQ + c')X
X对Y的间接效应 (在W, Z, V, Q的条件下)：
a1b1 + a4b1W + a5b1Z + a1b4V + a4b4WV + a5b4ZV + a1b5Q + a4b5WQ + a5b5ZQ + a1b7VQ + a4b7WVQ + a5b7ZVQ = (a1 + a4W + a5Z)(b1 + b4V + b5Q + b7VQ)
X对Y的直接效应：
c'

代码解读1

USEVARIABLES = X M W Z V Q Y XW XZ VQ MV MQ MVQ;

代码解读2

USEVARIABLES = X M W Z V Q Y XW XZ VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XZ = X*Z;
 VQ = V*Q;
 MVQ = M*V*Q;

代码解读3

USEVARIABLES = X M W Z V Q Y XW XZ VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XZ = X*Z;
 VQ = V*Q;
 MVQ = M*V*Q;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;

代码解读4

USEVARIABLES = X M W Z V Q Y XW XZ VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XZ = X*Z;
 VQ = V*Q;
 MVQ = M*V*Q;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 Y ON VQ (b6);
 Y ON MVQ (b7);
 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);

代码解读5

USEVARIABLES = X M W Z V Q Y XW XZ VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XZ = X*Z;
 VQ = V*Q;
 MVQ = M*V*Q;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 Y ON VQ (b6);
 Y ON MVQ (b7);
 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);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z LOW_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q ... );
 LOW_W = #LOWW;
 ...
 ILLLL = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b4*LOW_V + ... ;
 ...

代码解读6

USEVARIABLES = X M W Z V Q Y XW XZ VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XZ = X*Z;
 VQ = V*Q;
 MVQ = M*V*Q;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 Y ON VQ (b6);
 Y ON MVQ (b7);
 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);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z LOW_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q ... );
 LOW_W = #LOWW;
 ...
 ILLLL = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b4*LOW_V + ... ;
 ...
PLOT(...);
 LOOP(XVAL,1,5,0.1);
 PLLLL = ILLLL*XVAL;
 ...

代码解读7

USEVARIABLES = X M W Z V Q Y XW XZ VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XZ = X*Z;
 VQ = V*Q;
 MVQ = M*V*Q;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 Y ON VQ (b6);
 Y ON MVQ (b7);
 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);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z LOW_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q ... );
 LOW_W = #LOWW;
 ...
 ILLLL = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b4*LOW_V + ... ;
 ...
PLOT(...);
 LOOP(XVAL,1,5,0.1);
 PLLLL = ILLLL*XVAL;
 ...
OUTPUT:
 STAND CINT(bcbootstrap);

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