Mplus model6latent 模型讲解

来自图书《MPlus中介调节模型》

使用Mplus分析具有多个串联中介变量的模型

  • 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 + b1M1 + b2M2 + c'X
M1 = a01 + a1X
M2 = a02 + a2X + d1M1

数学公式2

Y = b0 + b1M1 + b2M2 + c'X
M1 = a01 + a1X
M2 = a02 + a2X + d1M1
Y = b0 + b1(a01 + a1X) + b2M2 + c'X

数学公式3

Y = b0 + b1M1 + b2M2 + c'X
M1 = a01 + a1X
M2 = a02 + a2X + d1M1
Y = b0 + b1(a01 + a1X) + b2M2 + c'X
Y = b0 + b1(a01 + a1X) + b2(a02 + a2X + d1M1) + c'X

数学公式4

Y = b0 + b1M1 + b2M2 + c'X
M1 = a01 + a1X
M2 = a02 + a2X + d1M1
Y = b0 + b1(a01 + a1X) + b2M2 + c'X
Y = b0 + b1(a01 + a1X) + b2(a02 + a2X + d1M1) + c'X
Y = b0 + b1(a01 + a1X) + b2(a02 + a2X + d1(a01 + a1X)) + c'X

数学公式5

Y = b0 + b1M1 + b2M2 + c'X
M1 = a01 + a1X
M2 = a02 + a2X + d1M1
Y = b0 + b1(a01 + a1X) + b2M2 + c'X
Y = b0 + b1(a01 + a1X) + b2(a02 + a2X + d1M1) + c'X
Y = b0 + b1(a01 + a1X) + b2(a02 + a2X + d1(a01 + a1X)) + c'X
Y = b0 + a01b1 + a1b1X + a02b2 + a2b2X + a01d1b2 + a1d1b2X + c'X

数学公式6

Y = b0 + b1M1 + b2M2 + c'X
M1 = a01 + a1X
M2 = a02 + a2X + d1M1
Y = b0 + b1(a01 + a1X) + b2M2 + c'X
Y = b0 + b1(a01 + a1X) + b2(a02 + a2X + d1M1) + c'X
Y = b0 + b1(a01 + a1X) + b2(a02 + a2X + d1(a01 + a1X)) + c'X
Y = b0 + a01b1 + a1b1X + a02b2 + a2b2X + a01d1b2 + a1d1b2X + c'X
Y = (b0 + a01b1 + a02b2 + a01d1b2) + (a1b1 + a2b2 + a1d1b2 + c')X

数学公式7

Y = b0 + b1M1 + b2M2 + c'X
M1 = a01 + a1X
M2 = a02 + a2X + d1M1
Y = b0 + b1(a01 + a1X) + b2M2 + c'X
Y = b0 + b1(a01 + a1X) + b2(a02 + a2X + d1M1) + c'X
Y = b0 + b1(a01 + a1X) + b2(a02 + a2X + d1(a01 + a1X)) + c'X
Y = b0 + a01b1 + a1b1X + a02b2 + a2b2X + a01d1b2 + a1d1b2X + c'X
Y = (b0 + a01b1 + a02b2 + a01d1b2) + (a1b1 + a2b2 + a1d1b2 + c')X
间接效应：a1b1, a2b2, a1d1b2
直接效应：c'

代码解读1

USEVARIABLES = X1 X2 X3 X4 M1_1 M1_2 M1_3 M1_4 M2_1 M2_2 M2_3 M2_4 Y1 Y2 Y3 Y4;

代码解读2

USEVARIABLES = X1 X2 X3 X4 M1_1 M1_2 M1_3 M1_4 M2_1 M2_2 M2_3 M2_4 Y1 Y2 Y3 Y4;
ANALYSIS: TYPE = GENERAL; ESTIMATOR = ML; BOOTSTRAP = 10000;

代码解读3

USEVARIABLES = X1 X2 X3 X4 M1_1 M1_2 M1_3 M1_4 M2_1 M2_2 M2_3 M2_4 Y1 Y2 Y3 Y4;
ANALYSIS: TYPE = GENERAL; ESTIMATOR = ML; BOOTSTRAP = 10000;
MODEL: X BY X1 X2 X3 X4; M1 BY M1_1 M1_2 M1_3 M1_4; M2 BY M2_1 M2_2 M2_3 M2_4; Y BY Y1 Y2 Y3 Y4;

代码解读4

USEVARIABLES = X1 X2 X3 X4 M1_1 M1_2 M1_3 M1_4 M2_1 M2_2 M2_3 M2_4 Y1 Y2 Y3 Y4;
ANALYSIS: TYPE = GENERAL; ESTIMATOR = ML; BOOTSTRAP = 10000;
MODEL: X BY X1 X2 X3 X4; M1 BY M1_1 M1_2 M1_3 M1_4; M2 BY M2_1 M2_2 M2_3 M2_4; Y BY Y1 Y2 Y3 Y4;
[Y] (b0); Y ON M1 (b1); Y ON M2 (b2); Y ON X (cdash);

代码解读5

USEVARIABLES = X1 X2 X3 X4 M1_1 M1_2 M1_3 M1_4 M2_1 M2_2 M2_3 M2_4 Y1 Y2 Y3 Y4;
ANALYSIS: TYPE = GENERAL; ESTIMATOR = ML; BOOTSTRAP = 10000;
MODEL: X BY X1 X2 X3 X4; M1 BY M1_1 M1_2 M1_3 M1_4; M2 BY M2_1 M2_2 M2_3 M2_4; Y BY Y1 Y2 Y3 Y4;
[Y] (b0); Y ON M1 (b1); Y ON M2 (b2); Y ON X (cdash);
M1 ON X (a1); M2 ON X (a2); M2 ON M1 (d1);

代码解读6

USEVARIABLES = X1 X2 X3 X4 M1_1 M1_2 M1_3 M1_4 M2_1 M2_2 M2_3 M2_4 Y1 Y2 Y3 Y4;
ANALYSIS: TYPE = GENERAL; ESTIMATOR = ML; BOOTSTRAP = 10000;
MODEL: X BY X1 X2 X3 X4; M1 BY M1_1 M1_2 M1_3 M1_4; M2 BY M2_1 M2_2 M2_3 M2_4; Y BY Y1 Y2 Y3 Y4;
[Y] (b0); Y ON M1 (b1); Y ON M2 (b2); Y ON X (cdash);
M1 ON X (a1); M2 ON X (a2); M2 ON M1 (d1);
MODEL CONSTRAINT: NEW(a1b1 a2b2 a1d1b2 TOTALIND TOTAL);

代码解读7

USEVARIABLES = X1 X2 X3 X4 M1_1 M1_2 M1_3 M1_4 M2_1 M2_2 M2_3 M2_4 Y1 Y2 Y3 Y4;
ANALYSIS: TYPE = GENERAL; ESTIMATOR = ML; BOOTSTRAP = 10000;
MODEL: X BY X1 X2 X3 X4; M1 BY M1_1 M1_2 M1_3 M1_4; M2 BY M2_1 M2_2 M2_3 M2_4; Y BY Y1 Y2 Y3 Y4;
[Y] (b0); Y ON M1 (b1); Y ON M2 (b2); Y ON X (cdash);
M1 ON X (a1); M2 ON X (a2); M2 ON M1 (d1);
MODEL CONSTRAINT: NEW(a1b1 a2b2 a1d1b2 TOTALIND TOTAL);
a1b1 = a1*b1; a2b2 = a2*b2; a1d1b2 = a1*d1*b2; TOTALIND = a1*b1 + a2*b2 + a1*d1*b2; TOTAL = a1*b1 + a2*b2 + a1*d1*b2 + cdash;

代码解读8

USEVARIABLES = X1 X2 X3 X4 M1_1 M1_2 M1_3 M1_4 M2_1 M2_2 M2_3 M2_4 Y1 Y2 Y3 Y4;
ANALYSIS: TYPE = GENERAL; ESTIMATOR = ML; BOOTSTRAP = 10000;
MODEL: X BY X1 X2 X3 X4; M1 BY M1_1 M1_2 M1_3 M1_4; M2 BY M2_1 M2_2 M2_3 M2_4; Y BY Y1 Y2 Y3 Y4;
[Y] (b0); Y ON M1 (b1); Y ON M2 (b2); Y ON X (cdash);
M1 ON X (a1); M2 ON X (a2); M2 ON M1 (d1);
MODEL CONSTRAINT: NEW(a1b1 a2b2 a1d1b2 TOTALIND TOTAL);
a1b1 = a1*b1; a2b2 = a2*b2; a1d1b2 = a1*d1*b2; TOTALIND = a1*b1 + a2*b2 + a1*d1*b2; TOTAL = a1*b1 + a2*b2 + a1*d1*b2 + cdash;
OUTPUT: STAND CINT(bcbootstrap);

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