Mplus model19latent 模型讲解

Mplus中构建复杂调节中介模型的教程

理论模型
数学模型
数学推导
代码解读

大家好，欢迎学习本教程！本教程将手把手教大家如何在Mplus软件中构建一个复杂的调节中介模型。这个模型包含一个或多个中介变量、两个调节变量，并且考虑了中介-因变量路径和自变量-因变量路径的调节作用，甚至可以评估二阶交互作用。我们将从理论模型开始，逐步讲解其数学模型和推导过程，最后通过Mplus代码的详细解读，帮助大家理解如何操作。本教程会使用一个包含潜变量的实际案例进行演示，所有潜变量都由连续性观察变量测量。我们会学习如何计算并绘制在不同调节变量值下的条件间接效应、直接效应和总效应。相信通过本教程的学习，大家能够快速掌握如何在Mplus中构建和分析这种复杂的模型，并且可以将其作为参考，在需要时快速查阅相关信息。

理论模型

数学模型

这张图展示的是一个复杂的调节中介模型。我们用X表示自变量，M表示中介变量，Y表示因变量，V和Q是两个调节变量。

X直接影响M（路径a1），M直接影响Y（路径b1）。

关键在于，V和Q以及它们的交互作用（VQ）调节着M对Y的影响，分别对应路径b2、b3和b4。

同时，X和V、X和Q、V和Q，以及X和VQ的交互作用也会直接影响Y，分别对应路径c2’、c3’、c4’、c5’、c6’、c7’。

所以，X对Y的影响，既包含直接效应，也包含间接效应。直接效应包括路径c1’以及V、Q和VQ对Y的调节作用；间接效应则是X通过M影响Y，而这个影响还会受到V和Q的调节。这张图完整地展现了这个模型中各个变量之间的关系以及它们如何相互作用。

数学公式1

Y = b0 + b1M + b2MV + b3MQ + b4MVQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ

数学公式2

Y = b0 + b1M + b2MV + b3MQ + b4MVQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ
M = a0 + a1X

数学公式3

Y = b0 + b1M + b2MV + b3MQ + b4MVQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ
M = a0 + a1X
Y = b0 + b1(a0 + a1X) + b2(a0 + a1X)V + b3(a0 + a1X)Q + b4(a0 + a1X)VQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ

数学公式4

Y = b0 + b1M + b2MV + b3MQ + b4MVQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ
M = a0 + a1X
Y = b0 + b1(a0 + a1X) + b2(a0 + a1X)V + b3(a0 + a1X)Q + b4(a0 + a1X)VQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ
Y = b0 + a0b1 + a1b1X + a0b2V + a1b2XV + a0b3Q + a1b3XQ + a0b4VQ + a1b4XVQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ

数学公式5

Y = b0 + b1M + b2MV + b3MQ + b4MVQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ
M = a0 + a1X
Y = b0 + b1(a0 + a1X) + b2(a0 + a1X)V + b3(a0 + a1X)Q + b4(a0 + a1X)VQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ
Y = b0 + a0b1 + a1b1X + a0b2V + a1b2XV + a0b3Q + a1b3XQ + a0b4VQ + a1b4XVQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ
Y = (b0 + a0b1 + a0b2V + a0b3Q + a0b4VQ + c2'V + c3'Q + c6'VQ) + (a1b1 + a1b2V + a1b3Q + a1b4VQ + c1' + c4'V + c5'Q + c7'VQ)X

数学公式6

Y = b0 + b1M + b2MV + b3MQ + b4MVQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ
M = a0 + a1X
Y = b0 + b1(a0 + a1X) + b2(a0 + a1X)V + b3(a0 + a1X)Q + b4(a0 + a1X)VQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ
Y = b0 + a0b1 + a1b1X + a0b2V + a1b2XV + a0b3Q + a1b3XQ + a0b4VQ + a1b4XVQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ
Y = (b0 + a0b1 + a0b2V + a0b3Q + a0b4VQ + c2'V + c3'Q + c6'VQ) + (a1b1 + a1b2V + a1b3Q + a1b4VQ + c1' + c4'V + c5'Q + c7'VQ)X
a1(b1 + b2V + b3Q + b4VQ)

数学公式7

Y = b0 + b1M + b2MV + b3MQ + b4MVQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ
M = a0 + a1X
Y = b0 + b1(a0 + a1X) + b2(a0 + a1X)V + b3(a0 + a1X)Q + b4(a0 + a1X)VQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ
Y = b0 + a0b1 + a1b1X + a0b2V + a1b2XV + a0b3Q + a1b3XQ + a0b4VQ + a1b4XVQ + c1'X + c2'V + c3'Q + c4'XV + c5'XQ + c6'VQ + c7'XVQ
Y = (b0 + a0b1 + a0b2V + a0b3Q + a0b4VQ + c2'V + c3'Q + c6'VQ) + (a1b1 + a1b2V + a1b3Q + a1b4VQ + c1' + c4'V + c5'Q + c7'VQ)X
a1(b1 + b2V + b3Q + b4VQ)
c1' + c4'V + c5'Q + c7'VQ

代码解读1

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
V1 V2 V3 V4 Q1 Q2 Q3 Q4
Y1 Y2 Y3 Y4;

代码解读2

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
V1 V2 V3 V4 Q1 Q2 Q3 Q4
Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;

代码解读3

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
V1 V2 V3 V4 Q1 Q2 Q3 Q4
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;
V BY V1* V2 V3 V4;
Q BY Q1* Q2 Q3 Q4;
Y BY Y1 Y2 Y3 Y4;

代码解读4

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
V1 V2 V3 V4 Q1 Q2 Q3 Q4
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;
V BY V1* V2 V3 V4;
Q BY Q1* Q2 Q3 Q4;
Y BY Y1 Y2 Y3 Y4;
V@1;  Q@1;

代码解读5

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
V1 V2 V3 V4 Q1 Q2 Q3 Q4
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;
V BY V1* V2 V3 V4;
Q BY Q1* Q2 Q3 Q4;
Y BY Y1 Y2 Y3 Y4;
V@1;  Q@1;
MV | M XWITH V;
MQ | M XWITH Q;
XV | X XWITH V;
XQ | X XWITH Q;
VQ | V XWITH Q;
MVQ | M XWITH VQ;
XVQ | X XWITH VQ;

代码解读6

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
V1 V2 V3 V4 Q1 Q2 Q3 Q4
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;
V BY V1* V2 V3 V4;
Q BY Q1* Q2 Q3 Q4;
Y BY Y1 Y2 Y3 Y4;
V@1;  Q@1;
MV | M XWITH V;
MQ | M XWITH Q;
XV | X XWITH V;
XQ | X XWITH Q;
VQ | V XWITH Q;
MVQ | M XWITH VQ;
XVQ | X XWITH VQ;
Y ON M (b1);
Y ON MV (b2);
Y ON MQ (b3);
Y ON MVQ (b4);
Y ON X (cdash1);
Y ON V (cdash2);
Y ON Q (cdash3);
Y ON XV (cdash4);
Y ON XQ (cdash5);
Y ON VQ (cdash6);
Y ON XVQ (cdash7);

代码解读7

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
V1 V2 V3 V4 Q1 Q2 Q3 Q4
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;
V BY V1* V2 V3 V4;
Q BY Q1* Q2 Q3 Q4;
Y BY Y1 Y2 Y3 Y4;
V@1;  Q@1;
MV | M XWITH V;
MQ | M XWITH Q;
XV | X XWITH V;
XQ | X XWITH Q;
VQ | V XWITH Q;
MVQ | M XWITH VQ;
XVQ | X XWITH VQ;
Y ON M (b1);
Y ON MV (b2);
Y ON MQ (b3);
Y ON MVQ (b4);
Y ON X (cdash1);
Y ON V (cdash2);
Y ON Q (cdash3);
Y ON XV (cdash4);
Y ON XQ (cdash5);
Y ON VQ (cdash6);
Y ON XVQ (cdash7);
M ON X (a1);

代码解读8

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
V1 V2 V3 V4 Q1 Q2 Q3 Q4
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;
V BY V1* V2 V3 V4;
Q BY Q1* Q2 Q3 Q4;
Y BY Y1 Y2 Y3 Y4;
V@1;  Q@1;
MV | M XWITH V;
MQ | M XWITH Q;
XV | X XWITH V;
XQ | X XWITH Q;
VQ | V XWITH Q;
MVQ | M XWITH VQ;
XVQ | X XWITH VQ;
Y ON M (b1);
Y ON MV (b2);
Y ON MQ (b3);
Y ON MVQ (b4);
Y ON X (cdash1);
Y ON V (cdash2);
Y ON Q (cdash3);
Y ON XV (cdash4);
Y ON XQ (cdash5);
Y ON VQ (cdash6);
Y ON XVQ (cdash7);
M ON X (a1);
MODEL CONSTRAINT:
NEW(LOW_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q ...);
LOW_V = -1; MED_V = 0; HIGH_V = 1; ...

代码解读9

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
V1 V2 V3 V4 Q1 Q2 Q3 Q4
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;
V BY V1* V2 V3 V4;
Q BY Q1* Q2 Q3 Q4;
Y BY Y1 Y2 Y3 Y4;
V@1;  Q@1;
MV | M XWITH V;
MQ | M XWITH Q;
XV | X XWITH V;
XQ | X XWITH Q;
VQ | V XWITH Q;
MVQ | M XWITH VQ;
XVQ | X XWITH VQ;
Y ON M (b1);
Y ON MV (b2);
Y ON MQ (b3);
Y ON MVQ (b4);
Y ON X (cdash1);
Y ON V (cdash2);
Y ON Q (cdash3);
Y ON XV (cdash4);
Y ON XQ (cdash5);
Y ON VQ (cdash6);
Y ON XVQ (cdash7);
M ON X (a1);
MODEL CONSTRAINT:
NEW(LOW_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q ...);
LOW_V = -1; MED_V = 0; HIGH_V = 1; ...
ILOV_LOQ = a1*b1 + a1*b2*LOW_V + a1*b3*LOW_Q + a1*b4*LOW_V*LOW_Q; ...

代码解读10

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
V1 V2 V3 V4 Q1 Q2 Q3 Q4
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;
V BY V1* V2 V3 V4;
Q BY Q1* Q2 Q3 Q4;
Y BY Y1 Y2 Y3 Y4;
V@1;  Q@1;
MV | M XWITH V;
MQ | M XWITH Q;
XV | X XWITH V;
XQ | X XWITH Q;
VQ | V XWITH Q;
MVQ | M XWITH VQ;
XVQ | X XWITH VQ;
Y ON M (b1);
Y ON MV (b2);
Y ON MQ (b3);
Y ON MVQ (b4);
Y ON X (cdash1);
Y ON V (cdash2);
Y ON Q (cdash3);
Y ON XV (cdash4);
Y ON XQ (cdash5);
Y ON VQ (cdash6);
Y ON XVQ (cdash7);
M ON X (a1);
MODEL CONSTRAINT:
NEW(LOW_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q ...);
LOW_V = -1; MED_V = 0; HIGH_V = 1; ...
ILOV_LOQ = a1*b1 + a1*b2*LOW_V + a1*b3*LOW_Q + a1*b4*LOW_V*LOW_Q; ...
DLOV_LOQ = ...; ...
TLOV_LOQ = ...; ...

代码解读11

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
V1 V2 V3 V4 Q1 Q2 Q3 Q4
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;
V BY V1* V2 V3 V4;
Q BY Q1* Q2 Q3 Q4;
Y BY Y1 Y2 Y3 Y4;
V@1;  Q@1;
MV | M XWITH V;
MQ | M XWITH Q;
XV | X XWITH V;
XQ | X XWITH Q;
VQ | V XWITH Q;
MVQ | M XWITH VQ;
XVQ | X XWITH VQ;
Y ON M (b1);
Y ON MV (b2);
Y ON MQ (b3);
Y ON MVQ (b4);
Y ON X (cdash1);
Y ON V (cdash2);
Y ON Q (cdash3);
Y ON XV (cdash4);
Y ON XQ (cdash5);
Y ON VQ (cdash6);
Y ON XVQ (cdash7);
M ON X (a1);
MODEL CONSTRAINT:
NEW(LOW_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q ...);
LOW_V = -1; MED_V = 0; HIGH_V = 1; ...
ILOV_LOQ = a1*b1 + a1*b2*LOW_V + a1*b3*LOW_Q + a1*b4*LOW_V*LOW_Q; ...
DLOV_LOQ = ...; ...
TLOV_LOQ = ...; ...
PLOT(...);
LOOP(XVAL,-3,3,0.1); ...
PLOT: TYPE = plot2;

代码解读12

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
V1 V2 V3 V4 Q1 Q2 Q3 Q4
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;
V BY V1* V2 V3 V4;
Q BY Q1* Q2 Q3 Q4;
Y BY Y1 Y2 Y3 Y4;
V@1;  Q@1;
MV | M XWITH V;
MQ | M XWITH Q;
XV | X XWITH V;
XQ | X XWITH Q;
VQ | V XWITH Q;
MVQ | M XWITH VQ;
XVQ | X XWITH VQ;
Y ON M (b1);
Y ON MV (b2);
Y ON MQ (b3);
Y ON MVQ (b4);
Y ON X (cdash1);
Y ON V (cdash2);
Y ON Q (cdash3);
Y ON XV (cdash4);
Y ON XQ (cdash5);
Y ON VQ (cdash6);
Y ON XVQ (cdash7);
M ON X (a1);
MODEL CONSTRAINT:
NEW(LOW_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q ...);
LOW_V = -1; MED_V = 0; HIGH_V = 1; ...
ILOV_LOQ = a1*b1 + a1*b2*LOW_V + a1*b3*LOW_Q + a1*b4*LOW_V*LOW_Q; ...
DLOV_LOQ = ...; ...
TLOV_LOQ = ...; ...
PLOT(...);
LOOP(XVAL,-3,3,0.1); ...
PLOT: TYPE = plot2;
OUTPUT: CINT;

资源汇总

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