Mplus model25latent 模型讲解
来自图书《MPlus中介调节模型》
Mplus复杂模型构建：包含中介、调节和调节中介效应
- 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
数学公式2
数学公式3
数学公式4
Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)V + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + b2V + a0b3V + a1b3XV + a2b3WV + a3b3ZV + a4b3XWV + a5b3XZV + a6b3WZV + a7b3XWZV + c'X数学公式5
Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)V + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + b2V + a0b3V + a1b3XV + a2b3WV + a3b3ZV + a4b3XWV + a5b3XZV + a6b3WZV + a7b3XWZV + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + b2V + a0b3V + a2b3WV + a3b3ZV + a6b3WZV) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b3V + a4b3WV + a5b3ZV + a7b3WZV + c')X数学公式6
Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)V + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + b2V + a0b3V + a1b3XV + a2b3WV + a3b3ZV + a4b3XWV + a5b3XZV + a6b3WZV + a7b3XWZV + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + b2V + a0b3V + a2b3WV + a3b3ZV + a6b3WZV) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b3V + a4b3WV + a5b3ZV + a7b3WZV + c')X
X对Y的间接效应（在W, Z, V条件下）：(a1 + a4W + a5Z + a7WZ)(b1 + b3V)数学公式7
Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)V + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + b2V + a0b3V + a1b3XV + a2b3WV + a3b3ZV + a4b3XWV + a5b3XZV + a6b3WZV + a7b3XWZV + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + b2V + a0b3V + a2b3WV + a3b3ZV + a6b3WZV) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b3V + a4b3WV + a5b3ZV + a7b3WZV + c')X
X对Y的间接效应（在W, Z, V条件下）：(a1 + a4W + a5Z + a7WZ)(b1 + b3V)
X对Y的直接效应：c'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;
WZ | W XWITH Z;
XWZ | X XWITH WZ;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;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON V (b2);
Y ON MV (b3);
Y ON X (cdash);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
M ON WZ (a6);
M ON XWZ (a7);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;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON V (b2);
Y ON MV (b3);
Y ON X (cdash);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
M ON WZ (a6);
M ON XWZ (a7);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z LOW_V MED_V HIGH_V ...);
LOW_W = -1; MED_W = 0; HIGH_W = 1; ...
ILWLZLV = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z + a1*b3*LOW_V + a4*b3*LOW_W*LOW_V + a5*b3*LOW_Z*LOW_V + a7*b3*LOW_W*LOW_Z*LOW_V;
... (其余IL, IM, IH 计算类似，此处省略)...
TLWLZLV = ILWLZLV + cdash; ... (其余TL, TM, TH 计算类似，此处省略)...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;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON V (b2);
Y ON MV (b3);
Y ON X (cdash);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);
M ON WZ (a6);
M ON XWZ (a7);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z LOW_V MED_V HIGH_V ...);
LOW_W = -1; MED_W = 0; HIGH_W = 1; ...
ILWLZLV = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z + a1*b3*LOW_V + a4*b3*LOW_W*LOW_V + a5*b3*LOW_Z*LOW_V + a7*b3*LOW_W*LOW_Z*LOW_V;
... (其余IL, IM, IH 计算类似，此处省略)...
TLWLZLV = ILWLZLV + cdash; ... (其余TL, TM, TH 计算类似，此处省略)...
PLOT(PLWLZLV PMWLZLV PHWLZLV ...);
LOOP(XVAL,-3,3,0.1);
PLWLZLV = ILWLZLV*XVAL; ... (其余PL 计算类似，此处省略)...
PLOT: TYPE = plot2;
OUTPUT: CINT;