Mplus model37latent 模型讲解

Mplus复杂模型构建：中介、调节与调节中介效应

理论模型
数学模型
数学推导
Mplus代码解读

大家好，欢迎来到本教程。今天我们将学习如何使用Mplus构建一个包含中介、调节和调节中介效应的复杂模型。这个模型包含一个潜变量自变量，一个潜变量中介变量和三个潜变量调节变量，非常复杂。本教程将循序渐进地讲解，首先我们从理论模型开始，明确模型中各个变量之间的关系。然后，我们将建立相应的数学模型，用公式来精确表达这些关系。接下来，我们将进行数学推导，解释模型中各个参数的含义以及如何计算它们。最后，我们将详细解读Mplus代码，展示如何用Mplus软件来拟合这个模型，并解释代码中各个参数的设置。本教程虽然涵盖了理论、模型和代码，但它更像是一个速查工具，您可以根据需要选择性地阅读。如有任何疑问，欢迎联系Data Sense，我们提供专业的统计咨询服务。

理论模型

数学模型

数学公式1

模型方程:

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c'X

M = a0 + a1X + a2W + a3XW

数学公式2

模型方程:

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c'X

M = a0 + a1X + a2W + a3XW
将M的表达式代入Y的表达式中:

Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2V + b3Q + b4(a0 + a1X + a2W + a3XW)V + b5(a0 + a1X + a2W + a3XW)Q + b6VQ + b7(a0 + a1X + a2W + a3XW)VQ + c'X

数学公式3

模型方程:

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c'X

M = a0 + a1X + a2W + a3XW
将M的表达式代入Y的表达式中:

Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2V + b3Q + b4(a0 + a1X + a2W + a3XW)V + b5(a0 + a1X + a2W + a3XW)Q + b6VQ + b7(a0 + a1X + a2W + a3XW)VQ + c'X
展开括号:

Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2V + b3Q + a0b4V + a1b4XV + a2b4WV + a3b4XWV + a0b5Q + a1b5XQ + a2b5WQ + a3b5XWQ + b6VQ + a0b7VQ + a1b7XVQ + a2b7WVQ + a3b7XWVQ + c'X

数学公式4

模型方程:

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c'X

M = a0 + a1X + a2W + a3XW
将M的表达式代入Y的表达式中:

Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2V + b3Q + b4(a0 + a1X + a2W + a3XW)V + b5(a0 + a1X + a2W + a3XW)Q + b6VQ + b7(a0 + a1X + a2W + a3XW)VQ + c'X
展开括号:

Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2V + b3Q + a0b4V + a1b4XV + a2b4WV + a3b4XWV + a0b5Q + a1b5XQ + a2b5WQ + a3b5XWQ + b6VQ + a0b7VQ + a1b7XVQ + a2b7WVQ + a3b7XWVQ + c'X
整理成Y = a + bX的形式:

Y = (b0 + a0b1 + a2b1W + b2V + b3Q + a0b4V + a2b4WV + a0b5Q + a2b5WQ + b6VQ + a0b7VQ + a2b7WVQ) + (a1b1 + a3b1W + a1b4V + a3b4WV + a1b5Q + a3b5WQ + a1b7VQ + a3b7WVQ + c')X

数学公式5

模型方程:

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c'X

M = a0 + a1X + a2W + a3XW
将M的表达式代入Y的表达式中:

Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2V + b3Q + b4(a0 + a1X + a2W + a3XW)V + b5(a0 + a1X + a2W + a3XW)Q + b6VQ + b7(a0 + a1X + a2W + a3XW)VQ + c'X
展开括号:

Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2V + b3Q + a0b4V + a1b4XV + a2b4WV + a3b4XWV + a0b5Q + a1b5XQ + a2b5WQ + a3b5XWQ + b6VQ + a0b7VQ + a1b7XVQ + a2b7WVQ + a3b7XWVQ + c'X
整理成Y = a + bX的形式:

Y = (b0 + a0b1 + a2b1W + b2V + b3Q + a0b4V + a2b4WV + a0b5Q + a2b5WQ + b6VQ + a0b7VQ + a2b7WVQ) + (a1b1 + a3b1W + a1b4V + a3b4WV + a1b5Q + a3b5WQ + a1b7VQ + a3b7WVQ + c')X
X对Y的间接效应(在W, V, Q条件下):

(a1 + a3W)(b1 + b4V + b5Q + b7VQ)

数学公式6

模型方程:

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c'X

M = a0 + a1X + a2W + a3XW
将M的表达式代入Y的表达式中:

Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2V + b3Q + b4(a0 + a1X + a2W + a3XW)V + b5(a0 + a1X + a2W + a3XW)Q + b6VQ + b7(a0 + a1X + a2W + a3XW)VQ + c'X
展开括号:

Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2V + b3Q + a0b4V + a1b4XV + a2b4WV + a3b4XWV + a0b5Q + a1b5XQ + a2b5WQ + a3b5XWQ + b6VQ + a0b7VQ + a1b7XVQ + a2b7WVQ + a3b7XWVQ + c'X
整理成Y = a + bX的形式:

Y = (b0 + a0b1 + a2b1W + b2V + b3Q + a0b4V + a2b4WV + a0b5Q + a2b5WQ + b6VQ + a0b7VQ + a2b7WVQ) + (a1b1 + a3b1W + a1b4V + a3b4WV + a1b5Q + a3b5WQ + a1b7VQ + a3b7WVQ + c')X
X对Y的间接效应(在W, V, Q条件下):

(a1 + a3W)(b1 + b4V + b5Q + b7VQ)
X对Y的直接效应:

c'

代码解读1

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 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
W1 W2 W3 W4 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
W1 W2 W3 W4 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;
 W BY W1* W2 W3 W4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  V@1;  Q@1;

代码解读4

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 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;
 W BY W1* W2 W3 W4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 VQ | V XWITH Q;
 MVQ | M XWITH VQ;

代码解读5

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 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;
 W BY W1* W2 W3 W4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 VQ | V XWITH Q;
 MVQ | M XWITH VQ;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 Y ON VQ (b6);
 Y ON MVQ (b7);
 Y ON X (cdash);
 M ON X (a1);
 M ON W (a2);
 M ON XW (a3);

代码解读6

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 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;
 W BY W1* W2 W3 W4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 VQ | V XWITH Q;
 MVQ | M XWITH VQ;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 Y ON VQ (b6);
 Y ON MVQ (b7);
 Y ON X (cdash);
 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_Q MED_Q HIGH_Q
 ILWLVLQ IMWLVLQ IHWLVLQ ILWMVLQ IMWMVLQ IHWMVLQ
 ILWHVLQ IMWHVLQ IHWHVLQ
 ILWLVMQ IMWLVMQ IHWLVMQ ILWMVMQ IMWMVMQ IHWMVMQ
 ILWHVMQ IMWHVMQ IHWHVMQ
 ILWLVHQ IMWLVHQ IHWLVHQ ILWMVHQ IMWMVHQ IHWMVHQ
 ILWHVHQ IMWHVHQ IHWHVHQ);

代码解读7

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 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;
 W BY W1* W2 W3 W4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 VQ | V XWITH Q;
 MVQ | M XWITH VQ;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 Y ON VQ (b6);
 Y ON MVQ (b7);
 Y ON X (cdash);
 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_Q MED_Q HIGH_Q
 ILWLVLQ IMWLVLQ IHWLVLQ ILWMVLQ IMWMVLQ IHWMVLQ
 ILWHVLQ IMWHVLQ IHWHVLQ
 ILWLVMQ IMWLVMQ IHWLVMQ ILWMVMQ IMWMVMQ IHWMVMQ
 ILWHVMQ IMWHVMQ IHWHVMQ
 ILWLVHQ IMWLVHQ IHWLVHQ ILWMVHQ IMWMVHQ IHWMVHQ
 ILWHVHQ IMWHVHQ IHWHVHQ);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;
 LOW_Q = -1;
 MED_Q = 0;
 HIGH_Q = 1;

代码解读8

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 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;
 W BY W1* W2 W3 W4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 VQ | V XWITH Q;
 MVQ | M XWITH VQ;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 Y ON VQ (b6);
 Y ON MVQ (b7);
 Y ON X (cdash);
 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_Q MED_Q HIGH_Q
 ILWLVLQ IMWLVLQ IHWLVLQ ILWMVLQ IMWMVLQ IHWMVLQ
 ILWHVLQ IMWHVLQ IHWHVLQ
 ILWLVMQ IMWLVMQ IHWLVMQ ILWMVMQ IMWMVMQ IHWMVMQ
 ILWHVMQ IMWHVMQ IHWHVMQ
 ILWLVHQ IMWLVHQ IHWLVHQ ILWMVHQ IMWMVHQ IHWMVHQ
 ILWHVHQ IMWHVHQ IHWHVHQ);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;
 LOW_Q = -1;
 MED_Q = 0;
 HIGH_Q = 1;
ILWLVLQ = a1*b1 + a3*b1*LOW_W + a1*b4*LOW_V + a3*b4*LOW_W*LOW_V +
 a1*b5*LOW_Q + a3*b5*LOW_W*LOW_Q + a1*b7*LOW_V*LOW_Q +
 a3*b7*LOW_W*LOW_V*LOW_Q;
 IMWLVLQ = a1*b1 + a3*b1*MED_W + a1*b4*LOW_V + a3*b4*MED_W*LOW_V +
 a1*b5*LOW_Q + a3*b5*MED_W*LOW_Q + a1*b7*LOW_V*LOW_Q +
 a3*b7*MED_W*LOW_V*LOW_Q;
 ...
 IHWHVHQ = a1*b1 + a3*b1*HIGH_W + a1*b4*HIGH_V + a3*b4*HIGH_W*HIGH_V +
 a1*b5*HIGH_Q + a3*b5*HIGH_W*HIGH_Q + a1*b7*HIGH_V*HIGH_Q +
 a3*b7*HIGH_W*HIGH_V*HIGH_Q;

代码解读9

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 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;
 W BY W1* W2 W3 W4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 VQ | V XWITH Q;
 MVQ | M XWITH VQ;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 Y ON VQ (b6);
 Y ON MVQ (b7);
 Y ON X (cdash);
 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_Q MED_Q HIGH_Q
 ILWLVLQ IMWLVLQ IHWLVLQ ILWMVLQ IMWMVLQ IHWMVLQ
 ILWHVLQ IMWHVLQ IHWHVLQ
 ILWLVMQ IMWLVMQ IHWLVMQ ILWMVMQ IMWMVMQ IHWMVMQ
 ILWHVMQ IMWHVMQ IHWHVMQ
 ILWLVHQ IMWLVHQ IHWLVHQ ILWMVHQ IMWMVHQ IHWMVHQ
 ILWHVHQ IMWHVHQ IHWHVHQ);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;
 LOW_Q = -1;
 MED_Q = 0;
 HIGH_Q = 1;
ILWLVLQ = a1*b1 + a3*b1*LOW_W + a1*b4*LOW_V + a3*b4*LOW_W*LOW_V +
 a1*b5*LOW_Q + a3*b5*LOW_W*LOW_Q + a1*b7*LOW_V*LOW_Q +
 a3*b7*LOW_W*LOW_V*LOW_Q;
 IMWLVLQ = a1*b1 + a3*b1*MED_W + a1*b4*LOW_V + a3*b4*MED_W*LOW_V +
 a1*b5*LOW_Q + a3*b5*MED_W*LOW_Q + a1*b7*LOW_V*LOW_Q +
 a3*b7*MED_W*LOW_V*LOW_Q;
 ...
 IHWHVHQ = a1*b1 + a3*b1*HIGH_W + a1*b4*HIGH_V + a3*b4*HIGH_W*HIGH_V +
 a1*b5*HIGH_Q + a3*b5*HIGH_W*HIGH_Q + a1*b7*HIGH_V*HIGH_Q +
 a3*b7*HIGH_W*HIGH_V*HIGH_Q;
OUTPUT: CINT;

资源汇总

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