Mplus model31latent 模型讲解
来自图书《MPlus中介调节模型》
复杂潜变量中介调节模型的Mplus实现
- 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
数学公式2
数学公式3
数学公式4
Y = b0 + b1M + b2MV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'V + c7'XV
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'V + c7'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2V + a1b2XV + a2b2WV + a3b2ZV + a4b2XWV + a5b2XZV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'V + c7'XV数学公式5
Y = b0 + b1M + b2MV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'V + c7'XV
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'V + c7'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2V + a1b2XV + a2b2WV + a3b2ZV + a4b2XWV + a5b2XZV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'V + c7'XV
Y = (b0 + a0b1 + a2b1W + a3b1Z + a0b2V + a2b2WV + a3b2ZV + c2'W + c3'Z + c6'V) + (a1b1 + a4b1W + a5b1Z + a1b2V + a4b2WV + a5b2ZV + c1' + c4'W + c5'Z + c7'V)X数学公式6
Y = b0 + b1M + b2MV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'V + c7'XV
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'V + c7'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2V + a1b2XV + a2b2WV + a3b2ZV + a4b2XWV + a5b2XZV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'V + c7'XV
Y = (b0 + a0b1 + a2b1W + a3b1Z + a0b2V + a2b2WV + a3b2ZV + c2'W + c3'Z + c6'V) + (a1b1 + a4b1W + a5b1Z + a1b2V + a4b2WV + a5b2ZV + c1' + c4'W + c5'Z + c7'V)X
X对Y的一个间接效应（在W, Z, V条件下）：(a1 + a4W + a5Z)(b1 + b2V)数学公式7
Y = b0 + b1M + b2MV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'V + c7'XV
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'V + c7'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2V + a1b2XV + a2b2WV + a3b2ZV + a4b2XWV + a5b2XZV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'V + c7'XV
Y = (b0 + a0b1 + a2b1W + a3b1Z + a0b2V + a2b2WV + a3b2ZV + c2'W + c3'Z + c6'V) + (a1b1 + a4b1W + a5b1Z + a1b2V + a4b2WV + a5b2ZV + c1' + c4'W + c5'Z + c7'V)X
X对Y的一个间接效应（在W, Z, V条件下）：(a1 + a4W + a5Z)(b1 + b2V)
X对Y的一个直接效应（在W, Z, V条件下）：c1' + c4'W + c5'Z + c7'V代码解读1
代码解读2
代码解读3
代码解读4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1; V@1;
MV | M XWITH V;
XW | X XWITH W;
XZ | X XWITH Z;
XV | X XWITH V;代码解读5
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1; V@1;
MV | M XWITH V;
XW | X XWITH W;
XZ | X XWITH Z;
XV | X XWITH V;
Y ON M (b1);
Y ON MV (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
Y ON V (cdash6);
Y ON XV (cdash7);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);代码解读6
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1; V@1;
MV | M XWITH V;
XW | X XWITH W;
XZ | X XWITH Z;
XV | X XWITH V;
Y ON M (b1);
Y ON MV (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
Y ON V (cdash6);
Y ON XV (cdash7);
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_W = -1; ... HIGH_V = 1;
ILWLZLV = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b2*LOW_V + a4*b2*LOW_W*LOW_V + a5*b2*LOW_Z*LOW_V; ...代码解读7
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1; V@1;
MV | M XWITH V;
XW | X XWITH W;
XZ | X XWITH Z;
XV | X XWITH V;
Y ON M (b1);
Y ON MV (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
Y ON V (cdash6);
Y ON XV (cdash7);
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_W = -1; ... HIGH_V = 1;
ILWLZLV = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b2*LOW_V + a4*b2*LOW_W*LOW_V + a5*b2*LOW_Z*LOW_V; ...
PLOT(PLWLZLV PMWLZLV PHWLZLV ...);
LOOP(XVAL,-3,3,0.1);
PLWLZLV = ILWLZLV*XVAL; ...代码解读8
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
W BY W1* W2 W3 W4;
Z BY Z1* Z2 Z3 Z4;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1; Z@1; V@1;
MV | M XWITH V;
XW | X XWITH W;
XZ | X XWITH Z;
XV | X XWITH V;
Y ON M (b1);
Y ON MV (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
Y ON V (cdash6);
Y ON XV (cdash7);
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_W = -1; ... HIGH_V = 1;
ILWLZLV = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b2*LOW_V + a4*b2*LOW_W*LOW_V + a5*b2*LOW_Z*LOW_V; ...
PLOT(PLWLZLV PMWLZLV PHWLZLV ...);
LOOP(XVAL,-3,3,0.1);
PLWLZLV = ILWLZLV*XVAL; ...
PLOT: TYPE = plot2;
OUTPUT: CINT;