Mplus model65 模型讲解

来自图书《MPlus中介调节模型》

Mplus中调节中介模型构建教程

  • 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

Y = b0 + b1M + b2V + b3MW + b4MV + c1'X + c2'W + c3'XW

数学公式2

Y = b0 + b1M + b2V + b3MW + b4MV + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3XW

数学公式3

Y = b0 + b1M + b2V + b3MW + b4MV + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2V + b3(a0 + a1X + a2W + a3XW)W + b4(a0 + a1X + a2W + a3XW)V + c1'X + c2'W + c3'XW

数学公式4

Y = b0 + b1M + b2V + b3MW + b4MV + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2V + b3(a0 + a1X + a2W + a3XW)W + b4(a0 + a1X + a2W + a3XW)V + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2V + a0b3W + a1b3XW + a2b3WW + a3b3XWW + a0b4V + a1b4XV + a2b4WV + a3b4XWV + c1'X + c2'W + c3'XW

数学公式5

Y = b0 + b1M + b2V + b3MW + b4MV + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2V + b3(a0 + a1X + a2W + a3XW)W + b4(a0 + a1X + a2W + a3XW)V + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2V + a0b3W + a1b3XW + a2b3WW + a3b3XWW + a0b4V + a1b4XV + a2b4WV + a3b4XWV + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + a2b1W + b2V + a0b3W + a2b3WW + a0b4V + a2b4W + c2'W) + (a1b1 + a3b1W + a1b3W + a3b3WW + a1b4V + a3b4WV + c1' + c3'W)X

数学公式6

Y = b0 + b1M + b2V + b3MW + b4MV + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2V + b3(a0 + a1X + a2W + a3XW)W + b4(a0 + a1X + a2W + a3XW)V + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2V + a0b3W + a1b3XW + a2b3WW + a3b3XWW + a0b4V + a1b4XV + a2b4WV + a3b4XWV + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + a2b1W + b2V + a0b3W + a2b3WW + a0b4V + a2b4W + c2'W) + (a1b1 + a3b1W + a1b3W + a3b3WW + a1b4V + a3b4WV + c1' + c3'W)X
(a1 + a3W)(b1 + b3W + b4V)

数学公式7

Y = b0 + b1M + b2V + b3MW + b4MV + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2V + b3(a0 + a1X + a2W + a3XW)W + b4(a0 + a1X + a2W + a3XW)V + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2V + a0b3W + a1b3XW + a2b3WW + a3b3XWW + a0b4V + a1b4XV + a2b4WV + a3b4XWV + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + a2b1W + b2V + a0b3W + a2b3WW + a0b4V + a2b4W + c2'W) + (a1b1 + a3b1W + a1b3W + a3b3WW + a1b4V + a3b4WV + c1' + c3'W)X
(a1 + a3W)(b1 + b3W + b4V)
c1' + c3'W

代码解读1

USEVARIABLES = X M W V Y XW MW MV;

代码解读2

USEVARIABLES = X M W V Y XW MW MV;
DEFINE:
 MW = M*W;
 MV = M*V;
 XW = X*W;

代码解读3

USEVARIABLES = X M W V Y XW MW MV;
DEFINE:
 MW = M*W;
 MV = M*V;
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;

代码解读4

USEVARIABLES = X M W V Y XW MW MV;
DEFINE:
 MW = M*W;
 MV = M*V;
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON MW (b3);
 Y ON MV (b4);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);

代码解读5

USEVARIABLES = X M W V Y XW MW MV;
DEFINE:
 MW = M*W;
 MV = M*V;
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON MW (b3);
 Y ON MV (b4);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
MODEL:
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON XW (a3);

代码解读6

USEVARIABLES = X M W V Y XW MW MV;
DEFINE:
 MW = M*W;
 MV = M*V;
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON MW (b3);
 Y ON MV (b4);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
MODEL:
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON XW (a3);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_V MED_V HIGH_V ...);
 LOW_W = #LOWW;
 MED_W = #MEDW;
 HIGH_W = #HIGHW; ...

代码解读7

USEVARIABLES = X M W V Y XW MW MV;
DEFINE:
 MW = M*W;
 MV = M*V;
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON MW (b3);
 Y ON MV (b4);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
MODEL:
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON XW (a3);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_V MED_V HIGH_V ...);
 LOW_W = #LOWW;
 MED_W = #MEDW;
 HIGH_W = #HIGHW; ...
ILOW_LOV = a1*b1 + a3*b1*LOW_W + ...
 DIR_LOWW = cdash1 + cdash3*LOW_W; ...
 TLOW_LOV = ILOW_LOV + DIR_LOWW; ...

代码解读8

USEVARIABLES = X M W V Y XW MW MV;
DEFINE:
 MW = M*W;
 MV = M*V;
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON MW (b3);
 Y ON MV (b4);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
MODEL:
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON XW (a3);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_V MED_V HIGH_V ...);
 LOW_W = #LOWW;
 MED_W = #MEDW;
 HIGH_W = #HIGHW; ...
ILOW_LOV = a1*b1 + a3*b1*LOW_W + ...
 DIR_LOWW = cdash1 + cdash3*LOW_W; ...
 TLOW_LOV = ILOW_LOV + DIR_LOWW; ...
PLOT(...);
 LOOP(XVAL,1,5,0.1);
 PLOW_LOV = ILOW_LOV*XVAL; ...
 PLOT: TYPE = plot2;

代码解读9

USEVARIABLES = X M W V Y XW MW MV;
DEFINE:
 MW = M*W;
 MV = M*V;
 XW = X*W;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON V (b2);
 Y ON MW (b3);
 Y ON MV (b4);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
MODEL:
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON XW (a3);
MODEL CONSTRAINT:
 NEW(LOW_W MED_W HIGH_W LOW_V MED_V HIGH_V ...);
 LOW_W = #LOWW;
 MED_W = #MEDW;
 HIGH_W = #HIGHW; ...
ILOW_LOV = a1*b1 + a3*b1*LOW_W + ...
 DIR_LOWW = cdash1 + cdash3*LOW_W; ...
 TLOW_LOV = ILOW_LOV + DIR_LOWW; ...
PLOT(...);
 LOOP(XVAL,1,5,0.1);
 PLOW_LOV = ILOW_LOV*XVAL; ...
 PLOT: TYPE = plot2;
OUTPUT: STAND CINT(bcbootstrap);

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