Mplus model13 模型讲解
来自图书《MPlus中介调节模型》
包含中介、调节和调节中介效应的Mplus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
数学公式5
Y = b0 + b1M + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + c2'W) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + c1' + c3'W)X数学公式6
Y = b0 + b1M + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + c2'W) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + c1' + c3'W)X
X 对 Y 的间接效应（条件于 W, Z）： a1b1 + a4b1W + a5b1Z + a7b1WZ = (a1 + a4W + a5Z + a7WZ)b1数学公式7
Y = b0 + b1M + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + c2'W) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + c1' + c3'W)X
X 对 Y 的间接效应（条件于 W, Z）： a1b1 + a4b1W + a5b1Z + a7b1WZ = (a1 + a4W + a5Z + a7WZ)b1
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 WZ XWZ;
DEFINE:
XW = X*W;
XZ = X*Z;
WZ = W*Z;
XWZ = X*W*Z;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
Y ON M (b1);
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);
M ON WZ (a6);
M ON XWZ (a7);代码解读5
USEVARIABLES = X M W Z Y XW XZ WZ XWZ;
DEFINE:
XW = X*W;
XZ = X*Z;
WZ = W*Z;
XWZ = X*W*Z;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
Y ON M (b1);
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);
M ON WZ (a6);
M ON XWZ (a7);
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 + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z; ...
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 WZ XWZ;
DEFINE:
XW = X*W;
XZ = X*Z;
WZ = W*Z;
XWZ = X*W*Z;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
Y ON M (b1);
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);
M ON WZ (a6);
M ON XWZ (a7);
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 + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z; ...
DIR_LOWW = cdash1 + cdash3*LOW_W; ...
TLOW_LOZ = ILOW_LOZ + DIR_LOWW; ...
PLOT(PLOW_LOZ PMEW_LOZ PHIW_LOZ ...);
LOOP(XVAL,1,5,0.1);
PLOW_LOZ = ILOW_LOZ*XVAL; ...
PLOT: TYPE = plot2;代码解读7
USEVARIABLES = X M W Z Y XW XZ WZ XWZ;
DEFINE:
XW = X*W;
XZ = X*Z;
WZ = W*Z;
XWZ = X*W*Z;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
BOOTSTRAP = 10000;
MODEL:
[Y] (b0);
Y ON M (b1);
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);
M ON WZ (a6);
M ON XWZ (a7);
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 + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z; ...
DIR_LOWW = cdash1 + cdash3*LOW_W; ...
TLOW_LOZ = ILOW_LOZ + DIR_LOWW; ...
PLOT(PLOW_LOZ PMEW_LOZ PHIW_LOZ ...);
LOOP(XVAL,1,5,0.1);
PLOW_LOZ = ILOW_LOZ*XVAL; ...
PLOT: TYPE = plot2;
OUTPUT:
STAND CINT(bcbootstrap);