Mplus model501 模型讲解

来自图书《MPlus中介调节模型》

多重中介效应分析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

模型公式:

1.  Y = b0 + b1M + c1'X1 + c2'X2;
2.  M = a0 + a1X1 + a2X2;

数学公式2

模型公式:

1.  Y = b0 + b1M + c1'X1 + c2'X2;
2.  M = a0 + a1X1 + a2X2;
代入与化简:

将 M = a0 + a1X1 + a2X2  代入  Y = b0 + b1M + c1'X1 + c2'X2， 得到:

Y = b0 + b1(a0 + a1X1 + a2X2) + c1'X1 + c2'X2

展开括号，得到:

Y = b0 + a0b1 + a1b1X1 + a2b1X2 + c1'X1 + c2'X2

数学公式3

模型公式:

1.  Y = b0 + b1M + c1'X1 + c2'X2;
2.  M = a0 + a1X1 + a2X2;
代入与化简:

将 M = a0 + a1X1 + a2X2  代入  Y = b0 + b1M + c1'X1 + c2'X2， 得到:

Y = b0 + b1(a0 + a1X1 + a2X2) + c1'X1 + c2'X2

展开括号，得到:

Y = b0 + a0b1 + a1b1X1 + a2b1X2 + c1'X1 + c2'X2
重组公式:

Y = (b0 + a0b1) + (a1b1 + c1')X1 + (a2b1 + c2')X2

数学公式4

模型公式:

1.  Y = b0 + b1M + c1'X1 + c2'X2;
2.  M = a0 + a1X1 + a2X2;
代入与化简:

将 M = a0 + a1X1 + a2X2  代入  Y = b0 + b1M + c1'X1 + c2'X2， 得到:

Y = b0 + b1(a0 + a1X1 + a2X2) + c1'X1 + c2'X2

展开括号，得到:

Y = b0 + a0b1 + a1b1X1 + a2b1X2 + c1'X1 + c2'X2
重组公式:

Y = (b0 + a0b1) + (a1b1 + c1')X1 + (a2b1 + c2')X2
效应计算:

* X1 对 Y 的间接效应: a1b1
* X2 对 Y 的间接效应: a2b1
* X1 对 Y 的直接效应: c1'
* X2 对 Y 的直接效应: c2'

代码解读1

USEVARIABLES = X1 X2 M Y;

代码解读2

USEVARIABLES = X1 X2 M Y;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;

代码解读3

USEVARIABLES = X1 X2 M Y;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
 Y ON M (b1);
 Y ON X1 (cdash1);
 Y ON X2 (cdash2);
 M ON X1 (a1);
 M ON X2 (a2);

代码解读4

USEVARIABLES = X1 X2 M Y;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
 Y ON M (b1);
 Y ON X1 (cdash1);
 Y ON X2 (cdash2);
 M ON X1 (a1);
 M ON X2 (a2);
! Use model constraint to calculate indirect and total effects
MODEL CONSTRAINT:
 NEW(a1b1 a2b1 TOTALX1 TOTALX2);
 a1b1 = a1*b1;
 a2b1 = a2*b1;
 TOTALX1 = a1*b1 + cdash1;
 TOTALX2 = a2*b1 + cdash2;

代码解读5

USEVARIABLES = X1 X2 M Y;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
! In model statement name each path using parentheses
MODEL:
 Y ON M (b1);
 Y ON X1 (cdash1);
 Y ON X2 (cdash2);
 M ON X1 (a1);
 M ON X2 (a2);
! Use model constraint to calculate indirect and total effects
MODEL CONSTRAINT:
 NEW(a1b1 a2b1 TOTALX1 TOTALX2);
 a1b1 = a1*b1;
 a2b1 = a2*b1;
 TOTALX1 = a1*b1 + cdash1;
 TOTALX2 = a2*b1 + cdash2;
OUTPUT:
 STAND CINT(bcbootstrap);

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