Mplus model61 模型讲解
来自图书《MPlus中介调节模型》
Mplus 中介调节效应模型构建教程
- 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
Y = b0 + b1M + b2MW + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2W + a1b2XW + a2b2W² + a3b2ZW + a4b2XW² + a5b2XZW + c1'X + c2'W + c3'XW数学公式4
Y = b0 + b1M + b2MW + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2W + a1b2XW + a2b2W² + a3b2ZW + a4b2XW² + a5b2XZW + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + a2b1W + a3b1Z + a0b2W + a2b2W² + a3b2ZW + c2'W) + (a1b1 + a4b1W + a5b1Z + a1b2W + a4b2W² + a5b2ZW + c1' + c3'W)X数学公式5
Y = b0 + b1M + b2MW + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2W + a1b2XW + a2b2W² + a3b2ZW + a4b2XW² + a5b2XZW + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + a2b1W + a3b1Z + a0b2W + a2b2W² + a3b2ZW + c2'W) + (a1b1 + a4b1W + a5b1Z + a1b2W + a4b2W² + a5b2ZW + c1' + c3'W)X
X对Y的间接效应（条件于W, Z）：(a1 + a4W + a5Z)(b1 + b2W)
X对Y的直接效应（条件于W）：c1' + c3'W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 Y XW XZ MW;
DEFINE:
MW = M*W;
XW = X*W;
XZ = X*Z;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
Y ON M (b1);
Y ON MW (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
[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 Y XW XZ MW;
DEFINE:
MW = M*W;
XW = X*W;
XZ = X*Z;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
Y ON M (b1);
Y ON MW (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
[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_W = #LOWW;
...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + ...;
...
DIR_LOWW = cdash1 + cdash3*LOW_W;
...
TLOW_LOZ = ILOW_LOZ + DIR_LOWW; ...代码解读6
USEVARIABLES = X M W Z Y XW XZ MW;
DEFINE:
MW = M*W;
XW = X*W;
XZ = X*Z;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
Y ON M (b1);
Y ON MW (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
[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_W = #LOWW;
...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + ...;
...
DIR_LOWW = cdash1 + cdash3*LOW_W;
...
TLOW_LOZ = ILOW_LOZ + DIR_LOWW; ...
PLOT(...); LOOP(...);代码解读7
USEVARIABLES = X M W Z Y XW XZ MW;
DEFINE:
MW = M*W;
XW = X*W;
XZ = X*Z;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
Y ON M (b1);
Y ON MW (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
[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_W = #LOWW;
...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + ...;
...
DIR_LOWW = cdash1 + cdash3*LOW_W;
...
TLOW_LOZ = ILOW_LOZ + DIR_LOWW; ...
PLOT(...); LOOP(...);
PLOT: TYPE = plot2;代码解读8
USEVARIABLES = X M W Z Y XW XZ MW;
DEFINE:
MW = M*W;
XW = X*W;
XZ = X*Z;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
Y ON M (b1);
Y ON MW (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON XW (cdash3);
[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_W = #LOWW;
...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + ...;
...
DIR_LOWW = cdash1 + cdash3*LOW_W;
...
TLOW_LOZ = ILOW_LOZ + DIR_LOWW; ...
PLOT(...); LOOP(...);
PLOT: TYPE = plot2;
OUTPUT: STAND CINT(bcbootstrap);