Mplus model1d 模型讲解

来自图书《MPlus中介调节模型》

使用Mplus进行简单调节效应分析（含分类调节变量）

  • 理论模型
  • 数学模型
  • 数学推导
  • Mplus代码解读

理论模型

数学模型

数学公式1

Y = b0 + b1X + b2WD1 + b3WD2 + b4XWD1 + b5XWD2

数学公式2

Y = b0 + b1X + b2WD1 + b3WD2 + b4XWD1 + b5XWD2
Y = (b0 + b2WD1 + b3WD2) + (b1 + b4WD1 + b5WD2)X

数学公式3

Y = b0 + b1X + b2WD1 + b3WD2 + b4XWD1 + b5XWD2
Y = (b0 + b2WD1 + b3WD2) + (b1 + b4WD1 + b5WD2)X
b1 + b4WD1 + b5WD2

数学公式4

Y = b0 + b1X + b2WD1 + b3WD2 + b4XWD1 + b5XWD2
Y = (b0 + b2WD1 + b3WD2) + (b1 + b4WD1 + b5WD2)X
b1 + b4WD1 + b5WD2
当 W = 1 时，WD1 = 1, WD2 = 0，则 Y = (b0 + b2) + (b1 + b4)X

数学公式5

Y = b0 + b1X + b2WD1 + b3WD2 + b4XWD1 + b5XWD2
Y = (b0 + b2WD1 + b3WD2) + (b1 + b4WD1 + b5WD2)X
b1 + b4WD1 + b5WD2
当 W = 1 时，WD1 = 1, WD2 = 0，则 Y = (b0 + b2) + (b1 + b4)X
当 W = 2 时，WD1 = 0, WD2 = 1，则 Y = (b0 + b3) + (b1 + b5)X

数学公式6

Y = b0 + b1X + b2WD1 + b3WD2 + b4XWD1 + b5XWD2
Y = (b0 + b2WD1 + b3WD2) + (b1 + b4WD1 + b5WD2)X
b1 + b4WD1 + b5WD2
当 W = 1 时，WD1 = 1, WD2 = 0，则 Y = (b0 + b2) + (b1 + b4)X
当 W = 2 时，WD1 = 0, WD2 = 1，则 Y = (b0 + b3) + (b1 + b5)X
当 W = 3 时，WD1 = 0, WD2 = 0，则 Y = b0 + b1X

代码解读1

USEVARIABLES = X WD1 WD2 Y XWD1 XWD2;

代码解读2

USEVARIABLES = X WD1 WD2 Y XWD1 XWD2;
DEFINE:
XWD1 = X*WD1;
XWD2 = X*WD2;

代码解读3

USEVARIABLES = X WD1 WD2 Y XWD1 XWD2;
DEFINE:
XWD1 = X*WD1;
XWD2 = X*WD2;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;

代码解读4

USEVARIABLES = X WD1 WD2 Y XWD1 XWD2;
DEFINE:
XWD1 = X*WD1;
XWD2 = X*WD2;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
MODEL:
[Y] (b0);
Y ON X (b1);
Y ON WD1 (b2);
Y ON WD2 (b3);
Y ON XWD1 (b4);
Y ON XWD2 (b5);

代码解读5

USEVARIABLES = X WD1 WD2 Y XWD1 XWD2;
DEFINE:
XWD1 = X*WD1;
XWD2 = X*WD2;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
MODEL:
[Y] (b0);
Y ON X (b1);
Y ON WD1 (b2);
Y ON WD2 (b3);
Y ON XWD1 (b4);
Y ON XWD2 (b5);
MODEL CONSTRAINT:
NEW(SIMP_W1 SIMP_W2 SIMP_W3);
SIMP_W1 = b1 + b4;
SIMP_W2 = b1 + b5;
SIMP_W3 = b1;

代码解读6

USEVARIABLES = X WD1 WD2 Y XWD1 XWD2;
DEFINE:
XWD1 = X*WD1;
XWD2 = X*WD2;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
MODEL:
[Y] (b0);
Y ON X (b1);
Y ON WD1 (b2);
Y ON WD2 (b3);
Y ON XWD1 (b4);
Y ON XWD2 (b5);
MODEL CONSTRAINT:
NEW(SIMP_W1 SIMP_W2 SIMP_W3);
SIMP_W1 = b1 + b4;
SIMP_W2 = b1 + b5;
SIMP_W3 = b1;
PLOT(LINE_W1 LINE_W2 LINE_W3);
LOOP(XVAL,1,5,0.1);
LINE_W1 = (b0 + b2) + (b1 + b4)*XVAL;
LINE_W2 = (b0 + b3) + (b1 + b5)*XVAL;
LINE_W3 = b0 + b1*XVAL;

代码解读7

USEVARIABLES = X WD1 WD2 Y XWD1 XWD2;
DEFINE:
XWD1 = X*WD1;
XWD2 = X*WD2;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
MODEL:
[Y] (b0);
Y ON X (b1);
Y ON WD1 (b2);
Y ON WD2 (b3);
Y ON XWD1 (b4);
Y ON XWD2 (b5);
MODEL CONSTRAINT:
NEW(SIMP_W1 SIMP_W2 SIMP_W3);
SIMP_W1 = b1 + b4;
SIMP_W2 = b1 + b5;
SIMP_W3 = b1;
PLOT(LINE_W1 LINE_W2 LINE_W3);
LOOP(XVAL,1,5,0.1);
LINE_W1 = (b0 + b2) + (b1 + b4)*XVAL;
LINE_W2 = (b0 + b3) + (b1 + b5)*XVAL;
LINE_W3 = b0 + b1*XVAL;
PLOT: TYPE = plot2;

代码解读8

USEVARIABLES = X WD1 WD2 Y XWD1 XWD2;
DEFINE:
XWD1 = X*WD1;
XWD2 = X*WD2;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
MODEL:
[Y] (b0);
Y ON X (b1);
Y ON WD1 (b2);
Y ON WD2 (b3);
Y ON XWD1 (b4);
Y ON XWD2 (b5);
MODEL CONSTRAINT:
NEW(SIMP_W1 SIMP_W2 SIMP_W3);
SIMP_W1 = b1 + b4;
SIMP_W2 = b1 + b5;
SIMP_W3 = b1;
PLOT(LINE_W1 LINE_W2 LINE_W3);
LOOP(XVAL,1,5,0.1);
LINE_W1 = (b0 + b2) + (b1 + b4)*XVAL;
LINE_W2 = (b0 + b3) + (b1 + b5)*XVAL;
LINE_W3 = b0 + b1*XVAL;
PLOT: TYPE = plot2;
OUTPUT: STAND CINT;

资源汇总

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