Mplus model20latent 模型讲解

来自图书《MPlus中介调节模型》

使用Mplus构建复杂调节中介模型

  • 理论模型
  • 数学模型
  • 代码解读
  • 模型结果与可视化

理论模型

数学模型

数学公式1

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'V + c3'XV

数学公式2

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'V + c3'XV
M = a0 + a1X

数学公式3

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'V + c3'XV
M = a0 + a1X
Y = b0 + b1(a0 + a1X) + b2Q + b3(a0 + a1X)V + b4(a0 + a1X)Q + b5VQ + b6(a0 + a1X)VQ + c1'X + c2'V + c3'XV

数学公式4

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'V + c3'XV
M = a0 + a1X
Y = b0 + b1(a0 + a1X) + b2Q + b3(a0 + a1X)V + b4(a0 + a1X)Q + b5VQ + b6(a0 + a1X)VQ + c1'X + c2'V + c3'XV
Y = b0 + a0b1 + a1b1X + b2Q + a0b3V + a1b3XV + a0b4Q + a1b4XQ + b5VQ + a0b6VQ + a1b6XVQ + c1'X + c2'V + c3'XV

数学公式5

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'V + c3'XV
M = a0 + a1X
Y = b0 + b1(a0 + a1X) + b2Q + b3(a0 + a1X)V + b4(a0 + a1X)Q + b5VQ + b6(a0 + a1X)VQ + c1'X + c2'V + c3'XV
Y = b0 + a0b1 + a1b1X + b2Q + a0b3V + a1b3XV + a0b4Q + a1b4XQ + b5VQ + a0b6VQ + a1b6XVQ + c1'X + c2'V + c3'XV
Y = (b0 + a0b1 + b2Q + a0b3V + a0b4Q + b5VQ + a0b6VQ + c2'V) + (a1b1 + a1b3V + a1b4Q + a1b6VQ + c1' + c3'V)X

数学公式6

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'V + c3'XV
M = a0 + a1X
Y = b0 + b1(a0 + a1X) + b2Q + b3(a0 + a1X)V + b4(a0 + a1X)Q + b5VQ + b6(a0 + a1X)VQ + c1'X + c2'V + c3'XV
Y = b0 + a0b1 + a1b1X + b2Q + a0b3V + a1b3XV + a0b4Q + a1b4XQ + b5VQ + a0b6VQ + a1b6XVQ + c1'X + c2'V + c3'XV
Y = (b0 + a0b1 + b2Q + a0b3V + a0b4Q + b5VQ + a0b6VQ + c2'V) + (a1b1 + a1b3V + a1b4Q + a1b6VQ + c1' + c3'V)X
条件间接效应 (X 对 Y 的间接效应，取决于 V 和 Q)：a1b1 + a1b3V + a1b4Q + a1b6VQ = a1(b1 + b3V + b4Q + b6VQ)

数学公式7

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'V + c3'XV
M = a0 + a1X
Y = b0 + b1(a0 + a1X) + b2Q + b3(a0 + a1X)V + b4(a0 + a1X)Q + b5VQ + b6(a0 + a1X)VQ + c1'X + c2'V + c3'XV
Y = b0 + a0b1 + a1b1X + b2Q + a0b3V + a1b3XV + a0b4Q + a1b4XQ + b5VQ + a0b6VQ + a1b6XVQ + c1'X + c2'V + c3'XV
Y = (b0 + a0b1 + b2Q + a0b3V + a0b4Q + b5VQ + a0b6VQ + c2'V) + (a1b1 + a1b3V + a1b4Q + a1b6VQ + c1' + c3'V)X
条件间接效应 (X 对 Y 的间接效应，取决于 V 和 Q)：a1b1 + a1b3V + a1b4Q + a1b6VQ = a1(b1 + b3V + b4Q + b6VQ)
条件直接效应 (X 对 Y 的直接效应，取决于 V)：c1' + c3'V

代码解读1

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 V1 V2 V3 V4 Q1 Q2 Q3 Q4 Y1 Y2 Y3 Y4;

代码解读2

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 V1 V2 V3 V4 Q1 Q2 Q3 Q4 Y1 Y2 Y3 Y4;
ANALYSIS: 
TYPE = GENERAL RANDOM; 
ESTIMATOR = ML; 
ALGORITHM = INTEGRATION;

代码解读3

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 V1 V2 V3 V4 Q1 Q2 Q3 Q4 Y1 Y2 Y3 Y4;
ANALYSIS: 
TYPE = GENERAL RANDOM; 
ESTIMATOR = ML; 
ALGORITHM = INTEGRATION;
MODEL: 
X BY X1 X2 X3 X4; 
M BY M1 M2 M3 M4; 
V BY V1* V2 V3 V4; 
Q BY Q1* Q2 Q3 Q4; 
Y BY Y1 Y2 Y3 Y4; 
V@1; Q@1;

代码解读4

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 V1 V2 V3 V4 Q1 Q2 Q3 Q4 Y1 Y2 Y3 Y4;
ANALYSIS: 
TYPE = GENERAL RANDOM; 
ESTIMATOR = ML; 
ALGORITHM = INTEGRATION;
MODEL: 
X BY X1 X2 X3 X4; 
M BY M1 M2 M3 M4; 
V BY V1* V2 V3 V4; 
Q BY Q1* Q2 Q3 Q4; 
Y BY Y1 Y2 Y3 Y4; 
V@1; Q@1;
MV | M XWITH V; 
MQ | M XWITH Q; 
XV | X XWITH V; 
VQ | V XWITH Q; 
MVQ | M XWITH VQ;

代码解读5

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 V1 V2 V3 V4 Q1 Q2 Q3 Q4 Y1 Y2 Y3 Y4;
ANALYSIS: 
TYPE = GENERAL RANDOM; 
ESTIMATOR = ML; 
ALGORITHM = INTEGRATION;
MODEL: 
X BY X1 X2 X3 X4; 
M BY M1 M2 M3 M4; 
V BY V1* V2 V3 V4; 
Q BY Q1* Q2 Q3 Q4; 
Y BY Y1 Y2 Y3 Y4; 
V@1; Q@1;
MV | M XWITH V; 
MQ | M XWITH Q; 
XV | X XWITH V; 
VQ | V XWITH Q; 
MVQ | M XWITH VQ;
Y ON M (b1); 
Y ON Q (b2); 
Y ON MV (b3); 
Y ON MQ (b4); 
Y ON VQ (b5); 
Y ON MVQ (b6); 
Y ON X (cdash1); 
Y ON V (cdash2); 
Y ON XV (cdash3); 
M ON X (a1);

代码解读6

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 V1 V2 V3 V4 Q1 Q2 Q3 Q4 Y1 Y2 Y3 Y4;
ANALYSIS: 
TYPE = GENERAL RANDOM; 
ESTIMATOR = ML; 
ALGORITHM = INTEGRATION;
MODEL: 
X BY X1 X2 X3 X4; 
M BY M1 M2 M3 M4; 
V BY V1* V2 V3 V4; 
Q BY Q1* Q2 Q3 Q4; 
Y BY Y1 Y2 Y3 Y4; 
V@1; Q@1;
MV | M XWITH V; 
MQ | M XWITH Q; 
XV | X XWITH V; 
VQ | V XWITH Q; 
MVQ | M XWITH VQ;
Y ON M (b1); 
Y ON Q (b2); 
Y ON MV (b3); 
Y ON MQ (b4); 
Y ON VQ (b5); 
Y ON MVQ (b6); 
Y ON X (cdash1); 
Y ON V (cdash2); 
Y ON XV (cdash3); 
M ON X (a1);
MODEL CONSTRAINT: 
NEW(LOW_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q ...); 
LOW_V = -1; MED_V = 0; HIGH_V = 1; ...

代码解读7

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 V1 V2 V3 V4 Q1 Q2 Q3 Q4 Y1 Y2 Y3 Y4;
ANALYSIS: 
TYPE = GENERAL RANDOM; 
ESTIMATOR = ML; 
ALGORITHM = INTEGRATION;
MODEL: 
X BY X1 X2 X3 X4; 
M BY M1 M2 M3 M4; 
V BY V1* V2 V3 V4; 
Q BY Q1* Q2 Q3 Q4; 
Y BY Y1 Y2 Y3 Y4; 
V@1; Q@1;
MV | M XWITH V; 
MQ | M XWITH Q; 
XV | X XWITH V; 
VQ | V XWITH Q; 
MVQ | M XWITH VQ;
Y ON M (b1); 
Y ON Q (b2); 
Y ON MV (b3); 
Y ON MQ (b4); 
Y ON VQ (b5); 
Y ON MVQ (b6); 
Y ON X (cdash1); 
Y ON V (cdash2); 
Y ON XV (cdash3); 
M ON X (a1);
MODEL CONSTRAINT: 
NEW(LOW_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q ...); 
LOW_V = -1; MED_V = 0; HIGH_V = 1; ...
ILOV_LOQ = a1*b1 + a1*b3*LOW_V + a1*b4*LOW_Q + a1*b6*LOW_V*LOW_Q; ...

代码解读8

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 V1 V2 V3 V4 Q1 Q2 Q3 Q4 Y1 Y2 Y3 Y4;
ANALYSIS: 
TYPE = GENERAL RANDOM; 
ESTIMATOR = ML; 
ALGORITHM = INTEGRATION;
MODEL: 
X BY X1 X2 X3 X4; 
M BY M1 M2 M3 M4; 
V BY V1* V2 V3 V4; 
Q BY Q1* Q2 Q3 Q4; 
Y BY Y1 Y2 Y3 Y4; 
V@1; Q@1;
MV | M XWITH V; 
MQ | M XWITH Q; 
XV | X XWITH V; 
VQ | V XWITH Q; 
MVQ | M XWITH VQ;
Y ON M (b1); 
Y ON Q (b2); 
Y ON MV (b3); 
Y ON MQ (b4); 
Y ON VQ (b5); 
Y ON MVQ (b6); 
Y ON X (cdash1); 
Y ON V (cdash2); 
Y ON XV (cdash3); 
M ON X (a1);
MODEL CONSTRAINT: 
NEW(LOW_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q ...); 
LOW_V = -1; MED_V = 0; HIGH_V = 1; ...
ILOV_LOQ = a1*b1 + a1*b3*LOW_V + a1*b4*LOW_Q + a1*b6*LOW_V*LOW_Q; ...
DIR_LOWV = cdash1 + cdash3*LOW_V; ... 
TLOV_LOQ = ILOV_LOQ + DIR_LOWV; ...

代码解读9

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 V1 V2 V3 V4 Q1 Q2 Q3 Q4 Y1 Y2 Y3 Y4;
ANALYSIS: 
TYPE = GENERAL RANDOM; 
ESTIMATOR = ML; 
ALGORITHM = INTEGRATION;
MODEL: 
X BY X1 X2 X3 X4; 
M BY M1 M2 M3 M4; 
V BY V1* V2 V3 V4; 
Q BY Q1* Q2 Q3 Q4; 
Y BY Y1 Y2 Y3 Y4; 
V@1; Q@1;
MV | M XWITH V; 
MQ | M XWITH Q; 
XV | X XWITH V; 
VQ | V XWITH Q; 
MVQ | M XWITH VQ;
Y ON M (b1); 
Y ON Q (b2); 
Y ON MV (b3); 
Y ON MQ (b4); 
Y ON VQ (b5); 
Y ON MVQ (b6); 
Y ON X (cdash1); 
Y ON V (cdash2); 
Y ON XV (cdash3); 
M ON X (a1);
MODEL CONSTRAINT: 
NEW(LOW_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q ...); 
LOW_V = -1; MED_V = 0; HIGH_V = 1; ...
ILOV_LOQ = a1*b1 + a1*b3*LOW_V + a1*b4*LOW_Q + a1*b6*LOW_V*LOW_Q; ...
DIR_LOWV = cdash1 + cdash3*LOW_V; ... 
TLOV_LOQ = ILOV_LOQ + DIR_LOWV; ...
PLOT(PLOV_LOQ PMEV_LOQ PHIV_LOQ ...); 
LOOP(XVAL,-3,3,0.1); 
PLOV_LOQ = ILOV_LOQ*XVAL; ...

代码解读10

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 V1 V2 V3 V4 Q1 Q2 Q3 Q4 Y1 Y2 Y3 Y4;
ANALYSIS: 
TYPE = GENERAL RANDOM; 
ESTIMATOR = ML; 
ALGORITHM = INTEGRATION;
MODEL: 
X BY X1 X2 X3 X4; 
M BY M1 M2 M3 M4; 
V BY V1* V2 V3 V4; 
Q BY Q1* Q2 Q3 Q4; 
Y BY Y1 Y2 Y3 Y4; 
V@1; Q@1;
MV | M XWITH V; 
MQ | M XWITH Q; 
XV | X XWITH V; 
VQ | V XWITH Q; 
MVQ | M XWITH VQ;
Y ON M (b1); 
Y ON Q (b2); 
Y ON MV (b3); 
Y ON MQ (b4); 
Y ON VQ (b5); 
Y ON MVQ (b6); 
Y ON X (cdash1); 
Y ON V (cdash2); 
Y ON XV (cdash3); 
M ON X (a1);
MODEL CONSTRAINT: 
NEW(LOW_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q ...); 
LOW_V = -1; MED_V = 0; HIGH_V = 1; ...
ILOV_LOQ = a1*b1 + a1*b3*LOW_V + a1*b4*LOW_Q + a1*b6*LOW_V*LOW_Q; ...
DIR_LOWV = cdash1 + cdash3*LOW_V; ... 
TLOV_LOQ = ILOV_LOQ + DIR_LOWV; ...
PLOT(PLOV_LOQ PMEV_LOQ PHIV_LOQ ...); 
LOOP(XVAL,-3,3,0.1); 
PLOV_LOQ = ILOV_LOQ*XVAL; ...
PLOT: TYPE = plot2; 
OUTPUT: CINT;

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