Mplus model31 模型讲解
来自图书《MPlus中介调节模型》
Mplus 中介、调节和调节中介效应模型构建教程
- 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
条件间接效应 (X 对 Y 的间接效应，在给定 W, Z, V 的条件下)：
a1b1 + a4b1W + a5b1Z + a1b2V + a4b2WV + a5b2ZV = (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
条件间接效应 (X 对 Y 的间接效应，在给定 W, Z, V 的条件下)：
a1b1 + a4b1W + a5b1Z + a1b2V + a4b2WV + a5b2ZV = (a1 + a4W + a5Z)(b1 + b2V)
条件直接效应 (X 对 Y 的直接效应，在给定 W, Z, V 的条件下)：
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 = X M W Z V Y XW XZ XV MV;
DEFINE:
MV = M*V;
XW = X*W;
XZ = X*Z;
XV = X*V;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
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] (a0);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);代码解读5
USEVARIABLES = X M W Z V Y XW XZ XV MV;
DEFINE:
MV = M*V;
XW = X*W;
XZ = X*Z;
XV = X*V;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
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] (a0);
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 = #LOWW;
...
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6
USEVARIABLES = X M W Z V Y XW XZ XV MV;
DEFINE:
MV = M*V;
XW = X*W;
XZ = X*Z;
XV = X*V;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
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] (a0);
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 = #LOWW;
...
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;
...
LOOP(XVAL,1,5,0.1);
PLWLZLV = ILWLZLV*XVAL;
...代码解读7
USEVARIABLES = X M W Z V Y XW XZ XV MV;
DEFINE:
MV = M*V;
XW = X*W;
XZ = X*Z;
XV = X*V;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
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] (a0);
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 = #LOWW;
...
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;
...
LOOP(XVAL,1,5,0.1);
PLWLZLV = ILWLZLV*XVAL;
...
PLOT:
TYPE = plot2;代码解读8
USEVARIABLES = X M W Z V Y XW XZ XV MV;
DEFINE:
MV = M*V;
XW = X*W;
XZ = X*Z;
XV = X*V;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
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] (a0);
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 = #LOWW;
...
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;
...
LOOP(XVAL,1,5,0.1);
PLWLZLV = ILWLZLV*XVAL;
...
PLOT:
TYPE = plot2;
OUTPUT:
STAND CINT(bcbootstrap);