Mplus model53latent 模型讲解

来自图书《MPlus中介调节模型》

Mplus中介、调节与调节中介效应模型构建教程

• 理论模型
• 数学模型
• 数学推导
• Mplus代码解读

大家好，欢迎收看Data Sense提供的Mplus中介、调节与调节中介效应模型构建教程。本教程将带你一步步构建一个包含中介、调节和调节中介效应的复杂模型，并提供详细的Mplus代码和解读。 我们将从理论模型出发，逐步讲解数学模型，并进行详细的数学推导，最后，通过对Mplus代码的逐行解读，让你轻松掌握这个复杂模型的构建方法。 本教程结构清晰，方便大家查阅，即使你没有Mplus经验也不用担心，只需根据需要查看对应部分即可。 现在，让我们开始学习吧！首先，我们将介绍模型的理论基础……之后会讲解数学模型的构建……再深入探讨模型的数学推导过程……最后，我们将对Mplus代码进行详细解读，帮助大家理解代码的每一部分以及它们背后的统计学原理。 如有任何疑问，欢迎随时联系Data Sense，我们提供专业的统计咨询服务。

理论模型

我们来看，这是一个比较复杂的模型。X 可以影响 M，M 又会影响 Y。所以，X 不仅可以直接影响 Y，也会通过 M 来间接影响 Y。 同时，W 和 Z 会影响 X 对 M 的影响大小，也会影响 X 对 Y 的直接影响。 此外，V 和 Q 会影响 M 对 Y 的影响大小。这里还有很多交互作用，比如 W 和 X 之间，Z 和 X 之间，V 和 Q 之间， 以及 V，M和Q之间的交互作用，这些都表示调节变量之间的影响不是简单的叠加，而是有更复杂的相互作用。

数学模型

这张图展示的是我们模型的数学结构。大家可以看到，这里有几个关键变量。首先，X是我们关注的起点，它通过a1到a5这几条路径，影响着中介变量M。M接着通过b1这条路径影响着最终结果Y。同时，X还直接通过c1’到c5’这几条路径影响Y。除了X和M，还有一些调节变量，像是W、Z、V和Q。W和Z会调节X对M和Y的影响，而V和Q则调节M对Y的影响。还有一些交互项，比如XW、XZ、MV、MQ、VQ和MVQ，它们分别表示X和W、X和Z、M和V、M和Q、V和Q以及M和VQ之间的相互作用。箭头上的字母，像a1、b1、c1’这些，表示路径的系数，可以理解成影响的强度。

数学公式1

模型方程:

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ

M = a0 + a1X + a2W + a3Z + a4XW + a5XZ

首先，我们有两个模型方程。第一个方程，Y 等于一系列变量的加权和，包括中介变量M，调节变量V和Q，以及自变量X,W,Z的直接效应。第二个方程，中介变量M 是自变量X，W，Z，以及它们的交互项的函数。我们的目标是分析X对Y的间接效应，这需要将M的表达式代入Y的表达式。

数学公式2

模型方程:

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ

M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
将M的表达式代入Y:

Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2V + b3Q + b4(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + b5(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Q + b6VQ + b7(a0 + a1X + a2W + a3Z + a4XW + a5XZ)VQ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ

这是将M的表达式代入Y的方程后得到的展开式。我们现在需要整理这个表达式，以便区分直接效应和间接效应。

数学公式3

模型方程:

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ

M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
将M的表达式代入Y:

Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2V + b3Q + b4(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + b5(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Q + b6VQ + b7(a0 + a1X + a2W + a3Z + a4XW + a5XZ)VQ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
展开括号:

Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + b3Q + a0b4V + a1b4XV + a2b4WV + a3b4ZV + a4b4XWV + a5b4XZV + a0b5Q + a1b5XQ + a2b5WQ + a3b5ZQ + a4b5XWQ + a5b5XZQ + b6VQ + a0b7VQ + a1b7XVQ + a2b7WVQ + a3b7ZVQ + a4b7XWVQ + a5b7XZVQ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ

这一步我们展开所有括号，得到一个更长的方程，方便我们进一步提取系数。

数学公式4

模型方程:

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ

M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
将M的表达式代入Y:

Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2V + b3Q + b4(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + b5(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Q + b6VQ + b7(a0 + a1X + a2W + a3Z + a4XW + a5XZ)VQ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
展开括号:

Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + b3Q + a0b4V + a1b4XV + a2b4WV + a3b4ZV + a4b4XWV + a5b4XZV + a0b5Q + a1b5XQ + a2b5WQ + a3b5ZQ + a4b5XWQ + a5b5XZQ + b6VQ + a0b7VQ + a1b7XVQ + a2b7WVQ + a3b7ZVQ + a4b7XWVQ + a5b7XZVQ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
整理成 Y = a + bX 的形式:

Y = (b0 + a0b1 + a2b1W + a3b1Z + b2V + b3Q + a0b4V + a2b4WV + a3b4ZV + a0b5Q + a2b5WQ + a3b5ZQ + b6VQ + a0b7VQ + a2b7WVQ + a3b7ZVQ + c2'W + c3'Z) + (a1b1 + a4b1W + a5b1Z + a1b4V + a4b4WV + a5b4ZV + a1b5Q + a4b5WQ + a5b5ZQ + a1b7VQ + a4b7WVQ + a5b7ZVQ + c1' + c4'W + c5'Z)X

我们将方程整理为 Y = a + bX 的形式，其中 a 代表所有不含 X 的项，b 代表 X 的系数。这样，我们就可以清晰地看到X的系数，也就是X对Y的总效应。

数学公式5

模型方程:

Y = b0 + b1M + b2V + b3Q + b4MV + b5MQ + b6VQ + b7MVQ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ

M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
将M的表达式代入Y:

Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2V + b3Q + b4(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + b5(a0 + a1X + a2W + a3Z + a4XW + a5XZ)Q + b6VQ + b7(a0 + a1X + a2W + a3Z + a4XW + a5XZ)VQ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
展开括号:

Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + b3Q + a0b4V + a1b4XV + a2b4WV + a3b4ZV + a4b4XWV + a5b4XZV + a0b5Q + a1b5XQ + a2b5WQ + a3b5ZQ + a4b5XWQ + a5b5XZQ + b6VQ + a0b7VQ + a1b7XVQ + a2b7WVQ + a3b7ZVQ + a4b7XWVQ + a5b7XZVQ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
整理成 Y = a + bX 的形式:

Y = (b0 + a0b1 + a2b1W + a3b1Z + b2V + b3Q + a0b4V + a2b4WV + a3b4ZV + a0b5Q + a2b5WQ + a3b5ZQ + b6VQ + a0b7VQ + a2b7WVQ + a3b7ZVQ + c2'W + c3'Z) + (a1b1 + a4b1W + a5b1Z + a1b4V + a4b4WV + a5b4ZV + a1b5Q + a4b5WQ + a5b5ZQ + a1b7VQ + a4b7WVQ + a5b7ZVQ + c1' + c4'W + c5'Z)X
X 对 Y 的间接效应 (在 W, Z, V, Q 的条件下):

(a1 + a4W + a5Z)(b1 + b4V + b5Q + b7VQ)

X 对 Y 的直接效应 (在 W, Z 的条件下):

c1' + c4'W + c5'Z

最后，我们提取出 X 对 Y 的间接效应的公式，它是 (a1 + a4W + a5Z) 乘以 (b1 + b4V + b5Q + b7VQ)。同时，我们还得到了 X 对 Y 的直接效应的公式，它是 c1’ + c4’W + c5’Z。这些公式帮助我们量化X通过M对Y产生的效应，以及X直接对Y产生的影响。

代码解读1

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4 Q1 Q2 Q3 Q4
Y1 Y2 Y3 Y4;

第一步，定义分析中使用的变量。这里包括了测量潜在自变量X的四个指标变量X1到X4，测量潜在中介变量M的四个指标变量M1到M4，以及分别测量四个潜在调节变量W、Z、V、Q的指标变量W1到W4、Z1到Z4、V1到V4和Q1到Q4。最后，还有测量因变量Y的四个指标变量Y1到Y4。

代码解读2

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4 Q1 Q2 Q3 Q4
Y1 Y2 Y3 Y4;
ANALYSIS:
 TYPE = GENERAL RANDOM;
 ESTIMATOR = ML;
 ALGORITHM = INTEGRATION;

第二步，进行分析设置。首先，TYPE设置为GENERAL RANDOM，表示使用广义随机效应模型，这适用于包含潜在变量的模型。其次，ESTIMATOR设置为ML，表示使用最大似然估计方法进行参数估计。最后，ALGORITHM设置为INTEGRATION，表示使用数值积分算法来处理潜在变量的模型。

代码解读3

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
 Z BY Z1* Z2 Z3 Z4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;  V@1;  Q@1;

第三步，定义模型。首先，定义测量模型。例如，X BY X1 X2 X3 X4，表示潜在变量X由X1到X4这四个指标变量测量。星号*表示将W1、Z1、V1和Q1的载荷固定为1，对相应的潜在变量进行标准化。然后，W@1; Z@1; V@1; Q@1; 表示将调节变量W、Z、V、Q的方差都固定为1，也是为了标准化它们。

代码解读4

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
 Z BY Z1* Z2 Z3 Z4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 XZ | X XWITH Z;
 VQ | V XWITH Q;
 MVQ | M XWITH VQ;

第四步，定义潜在交互项。例如，MV | M XWITH V; 表示创建了中介变量M和调节变量V的交互项，其他类似。这些交互项将在模型中作为新的预测变量使用。

代码解读5

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
 Z BY Z1* Z2 Z3 Z4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 XZ | X XWITH Z;
 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 (cdash1);
 Y ON W (cdash2);
 Y ON Z (cdash3);
 Y ON XW (cdash4);
 Y ON XZ (cdash5);
 M ON X (a1);
 M ON W (a2);
 M ON Z (a3);
 M ON XW (a4);
 M ON XZ (a5);

第五步，定义结构模型，指定潜在变量之间的回归关系。例如，Y ON M (b1) 表示因变量Y对中介变量M的回归系数为b1。其他类似，例如M ON X (a1) 表示中介变量M对自变量X的回归系数为a1。括号中的b1，a1等都是参数名称。

代码解读6

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
 Z BY Z1* Z2 Z3 Z4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 XZ | X XWITH Z;
 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 (cdash1);
 Y ON W (cdash2);
 Y ON Z (cdash3);
 Y ON XW (cdash4);
 Y ON XZ (cdash5);
 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_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q
 ILLLL IMLLL IHLLL ILMLL IMMLL IHMLL ILHLL IMHLL IHHLL
 ILLML IMLML IHLML ILMML IMMML IHMML ILHML IMHML IHHML
 ILLHL IMLHL IHLHL ILMHL IMMHL IHMHL ILHHL IMHHL IHHHL
 ILLLM IMLLM IHLLM ILMLM IMMLM IHMLM ILHLM IMHLM IHHLM
 ILLMM IMLMM IHLMM ILMMM IMMMM IHMMM ILHMM IMHMM IHHMM
 ILLHM IMLHM IHLHM ILMHM IMMHM IHMHM ILHHM IMHHM IHHHM
 ILLLH IMLLH IHLLH ILMLH IMMLH IHMLH ILHLH IMHLH IHHLH
 ILLMH IMLMH IHLMH ILMMH IMMMH IHMMH ILHMH IMHMH IHHMH
 ILLHH IMLHH IHLHH ILMHH IMMHH IHMHH ILHHH IMHHH IHHHH
 DLOW_LOZ DMEW_LOZ DHIW_LOZ DLOW_MEZ DMEW_MEZ DHIW_MEZ
 DLOW_HIZ DMEW_HIZ DHIW_HIZ
 TLLLL TMLLL THLLL TLMLL TMMLL THMLL TLHLL TMHLL THHLL
 TLLML TMLML THLML TLMML TMMML THMML TLHML TMHML THHML
 TLLHL TMLHL THLHL TLMHL TMMHL THMHL TLHHL TMHHL THHHL
 TLLLM TMLLM THLLM TLMLM TMMLM THMLM TLHLM TMHLM THHLM
 TLLMM TMLMM THLMM TLMMM TMMMM THMMM TLHMM TMHMM THHMM
 TLLHM TMLHM THLHM TLMHM TMMHM THMHM TLHHM TMHHM THHHM
 TLLLH TMLLH THLLH TLMLH TMMLH THMLH TLHLH TMHLH THHLH
 TLLMH TMLMH THLMH TLMMH TMMMH THMMH TLHMH TMHMH THHMH
 TLLHH TMLHH THLHH TLMHH TMMHH THMHH TLHHH TMHHH THHHH);

第六步，开始模型约束部分。这里定义了新的参数，代表不同调节变量组合下的间接效应、直接效应和总效应。例如ILLLL代表所有调节变量都取最低值时的间接效应。

代码解读7

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
 Z BY Z1* Z2 Z3 Z4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 XZ | X XWITH Z;
 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 (cdash1);
 Y ON W (cdash2);
 Y ON Z (cdash3);
 Y ON XW (cdash4);
 Y ON XZ (cdash5);
 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_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q
 ILLLL IMLLL IHLLL ILMLL IMMLL IHMLL ILHLL IMHLL IHHLL
 ILLML IMLML IHLML ILMML IMMML IHMML ILHML IMHML IHHML
 ILLHL IMLHL IHLHL ILMHL IMMHL IHMHL ILHHL IMHHL IHHHL
 ILLLM IMLLM IHLLM ILMLM IMMLM IHMLM ILHLM IMHLM IHHLM
 ILLMM IMLMM IHLMM ILMMM IMMMM IHMMM ILHMM IMHMM IHHMM
 ILLHM IMLHM IHLHM ILMHM IMMHM IHMHM ILHHM IMHHM IHHHM
 ILLLH IMLLH IHLLH ILMLH IMMLH IHMLH ILHLH IMHLH IHHLH
 ILLMH IMLMH IHLMH ILMMH IMMMH IHMMH ILHMH IMHMH IHHMH
 ILLHH IMLHH IHLHH ILMHH IMMHH IHMHH ILHHH IMHHH IHHHH
 DLOW_LOZ DMEW_LOZ DHIW_LOZ DLOW_MEZ DMEW_MEZ DHIW_MEZ
 DLOW_HIZ DMEW_HIZ DHIW_HIZ
 TLLLL TMLLL THLLL TLMLL TMMLL THMLL TLHLL TMHLL THHLL
 TLLML TMLML THLML TLMML TMMML THMML TLHML TMHML THHML
 TLLHL TMLHL THLHL TLMHL TMMHL THMHL TLHHL TMHHL THHHL
 TLLLM TMLLM THLLM TLMLM TMMLM THMLM TLHLM TMHLM THHLM
 TLLMM TMLMM THLMM TLMMM TMMMM THMMM TLHMM TMHMM THHMM
 TLLHM TMLHM THLHM TLMHM TMMHM THMHM TLHHM TMHHM THHHM
 TLLLH TMLLH THLLH TLMLH TMMLH THMLH TLHLH TMHLH THHLH
 TLLMH TMLMH THLMH TLMMH TMMMH THMMH TLHMH TMHMH THHMH
 TLLHH TMLHH THLHH TLMHH TMMHH THMHH TLHHH TMHHH THHHH);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_Z = -1;
 MED_Z = 0;
 HIGH_Z = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;
 LOW_Q = -1;
 MED_Q = 0;
 HIGH_Q = 1;

第七步，定义调节变量的低、中、高三个水平的值，通常为标准差的-1倍、0倍和1倍。

代码解读8

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
 Z BY Z1* Z2 Z3 Z4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 XZ | X XWITH Z;
 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 (cdash1);
 Y ON W (cdash2);
 Y ON Z (cdash3);
 Y ON XW (cdash4);
 Y ON XZ (cdash5);
 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_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q
 ILLLL IMLLL IHLLL ILMLL IMMLL IHMLL ILHLL IMHLL IHHLL
 ILLML IMLML IHLML ILMML IMMML IHMML ILHML IMHML IHHML
 ILLHL IMLHL IHLHL ILMHL IMMHL IHMHL ILHHL IMHHL IHHHL
 ILLLM IMLLM IHLLM ILMLM IMMLM IHMLM ILHLM IMHLM IHHLM
 ILLMM IMLMM IHLMM ILMMM IMMMM IHMMM ILHMM IMHMM IHHMM
 ILLHM IMLHM IHLHM ILMHM IMMHM IHMHM ILHHM IMHHM IHHHM
 ILLLH IMLLH IHLLH ILMLH IMMLH IHMLH ILHLH IMHLH IHHLH
 ILLMH IMLMH IHLMH ILMMH IMMMH IHMMH ILHMH IMHMH IHHMH
 ILLHH IMLHH IHLHH ILMHH IMMHH IHMHH ILHHH IMHHH IHHHH
 DLOW_LOZ DMEW_LOZ DHIW_LOZ DLOW_MEZ DMEW_MEZ DHIW_MEZ
 DLOW_HIZ DMEW_HIZ DHIW_HIZ
 TLLLL TMLLL THLLL TLMLL TMMLL THMLL TLHLL TMHLL THHLL
 TLLML TMLML THLML TLMML TMMML THMML TLHML TMHML THHML
 TLLHL TMLHL THLHL TLMHL TMMHL THMHL TLHHL TMHHL THHHL
 TLLLM TMLLM THLLM TLMLM TMMLM THMLM TLHLM TMHLM THHLM
 TLLMM TMLMM THLMM TLMMM TMMMM THMMM TLHMM TMHMM THHMM
 TLLHM TMLHM THLHM TLMHM TMMHM THMHM TLHHM TMHHM THHHM
 TLLLH TMLLH THLLH TLMLH TMMLH THMLH TLHLH TMHLH THHLH
 TLLMH TMLMH THLMH TLMMH TMMMH THMMH TLHMH TMHMH THHMH
 TLLHH TMLHH THLHH TLMHH TMMHH THMHH TLHHH TMHHH THHHH);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_Z = -1;
 MED_Z = 0;
 HIGH_Z = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;
 LOW_Q = -1;
 MED_Q = 0;
 HIGH_Q = 1;
ILLLL = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b4*LOW_V +
 a4*b4*LOW_W*LOW_V + a5*b4*LOW_Z*LOW_V + a1*b5*LOW_Q +
 a4*b5*LOW_W*LOW_Q + a5*b5*LOW_Z*LOW_Q + a1*b7*LOW_V*LOW_Q +
 a4*b7*LOW_W*LOW_V*LOW_Q + a5*b7*LOW_Z*LOW_V*LOW_Q;

第八步，计算在所有调节变量都取最低值时的间接效应（ILLLL）。公式基于前面定义的模型方程推导而来。这里是简化版本，其他参数的计算方式类似，这里为了简洁省略。

代码解读9

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
 Z BY Z1* Z2 Z3 Z4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 XZ | X XWITH Z;
 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 (cdash1);
 Y ON W (cdash2);
 Y ON Z (cdash3);
 Y ON XW (cdash4);
 Y ON XZ (cdash5);
 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_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q
 ILLLL IMLLL IHLLL ILMLL IMMLL IHMLL ILHLL IMHLL IHHLL
 ILLML IMLML IHLML ILMML IMMML IHMML ILHML IMHML IHHML
 ILLHL IMLHL IHLHL ILMHL IMMHL IHMHL ILHHL IMHHL IHHHL
 ILLLM IMLLM IHLLM ILMLM IMMLM IHMLM ILHLM IMHLM IHHLM
 ILLMM IMLMM IHLMM ILMMM IMMMM IHMMM ILHMM IMHMM IHHMM
 ILLHM IMLHM IHLHM ILMHM IMMHM IHMHM ILHHM IMHHM IHHHM
 ILLLH IMLLH IHLLH ILMLH IMMLH IHMLH ILHLH IMHLH IHHLH
 ILLMH IMLMH IHLMH ILMMH IMMMH IHMMH ILHMH IMHMH IHHMH
 ILLHH IMLHH IHLHH ILMHH IMMHH IHMHH ILHHH IMHHH IHHHH
 DLOW_LOZ DMEW_LOZ DHIW_LOZ DLOW_MEZ DMEW_MEZ DHIW_MEZ
 DLOW_HIZ DMEW_HIZ DHIW_HIZ
 TLLLL TMLLL THLLL TLMLL TMMLL THMLL TLHLL TMHLL THHLL
 TLLML TMLML THLML TLMML TMMML THMML TLHML TMHML THHML
 TLLHL TMLHL THLHL TLMHL TMMHL THMHL TLHHL TMHHL THHHL
 TLLLM TMLLM THLLM TLMLM TMMLM THMLM TLHLM TMHLM THHLM
 TLLMM TMLMM THLMM TLMMM TMMMM THMMM TLHMM TMHMM THHMM
 TLLHM TMLHM THLHM TLMHM TMMHM THMHM TLHHM TMHHM THHHM
 TLLLH TMLLH THLLH TLMLH TMMLH THMLH TLHLH TMHLH THHLH
 TLLMH TMLMH THLMH TLMMH TMMMH THMMH TLHMH TMHMH THHMH
 TLLHH TMLHH THLHH TLMHH TMMHH THMHH TLHHH TMHHH THHHH);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_Z = -1;
 MED_Z = 0;
 HIGH_Z = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;
 LOW_Q = -1;
 MED_Q = 0;
 HIGH_Q = 1;
ILLLL = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b4*LOW_V +
 a4*b4*LOW_W*LOW_V + a5*b4*LOW_Z*LOW_V + a1*b5*LOW_Q +
 a4*b5*LOW_W*LOW_Q + a5*b5*LOW_Z*LOW_Q + a1*b7*LOW_V*LOW_Q +
 a4*b7*LOW_W*LOW_V*LOW_Q + a5*b7*LOW_Z*LOW_V*LOW_Q;
PLOT(PLLLL PMLLL PHLLL PLMLL PMMLL PHMLL PLHLL PMHLL PHHLL
 PLLML PMLML PHLML PLMML PMMML PHMML PLHML PMHML PHHML
 PLLHL PMLHL PHLHL PLMHL PMMHL PHMHL PLHHL PMHHL PHHHL
 PLLLM PMLLM PHLLM PLMLM PMMLM PHMLM PLHLM PMHLM PHHLM
 PLLMM PMLMM PHLMM PLMMM PMMMM PHMMM PLHMM PMHMM PHHMM
 PLLHM PMLHM PHLHM PLMHM PMMHM PHMHM PLHHM PMHHM PHHHM
 PLLLH PMLLH PHLLH PLMLH PMMLH PHMLH PLHLH PMHLH PHHLH
 PLLMH PMLMH PHLMH PLMMH PMMMH PHMMH PLHMH PMHMH PHHMH
 PLLHH PMLHH PHLHH PLMHH PMMHH PHMHH PLHHH PMHHH PHHHH);

第九步，定义要绘制的图，这里指定了要绘制的曲线是不同调节变量组合下的间接效应随自变量变化的曲线。P开头的参数是随后循环里计算出来的点。

代码解读10

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
 Z BY Z1* Z2 Z3 Z4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 XZ | X XWITH Z;
 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 (cdash1);
 Y ON W (cdash2);
 Y ON Z (cdash3);
 Y ON XW (cdash4);
 Y ON XZ (cdash5);
 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_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q
 ILLLL IMLLL IHLLL ILMLL IMMLL IHMLL ILHLL IMHLL IHHLL
 ILLML IMLML IHLML ILMML IMMML IHMML ILHML IMHML IHHML
 ILLHL IMLHL IHLHL ILMHL IMMHL IHMHL ILHHL IMHHL IHHHL
 ILLLM IMLLM IHLLM ILMLM IMMLM IHMLM ILHLM IMHLM IHHLM
 ILLMM IMLMM IHLMM ILMMM IMMMM IHMMM ILHMM IMHMM IHHMM
 ILLHM IMLHM IHLHM ILMHM IMMHM IHMHM ILHHM IMHHM IHHHM
 ILLLH IMLLH IHLLH ILMLH IMMLH IHMLH ILHLH IMHLH IHHLH
 ILLMH IMLMH IHLMH ILMMH IMMMH IHMMH ILHMH IMHMH IHHMH
 ILLHH IMLHH IHLHH ILMHH IMMHH IHMHH ILHHH IMHHH IHHHH
 DLOW_LOZ DMEW_LOZ DHIW_LOZ DLOW_MEZ DMEW_MEZ DHIW_MEZ
 DLOW_HIZ DMEW_HIZ DHIW_HIZ
 TLLLL TMLLL THLLL TLMLL TMMLL THMLL TLHLL TMHLL THHLL
 TLLML TMLML THLML TLMML TMMML THMML TLHML TMHML THHML
 TLLHL TMLHL THLHL TLMHL TMMHL THMHL TLHHL TMHHL THHHL
 TLLLM TMLLM THLLM TLMLM TMMLM THMLM TLHLM TMHLM THHLM
 TLLMM TMLMM THLMM TLMMM TMMMM THMMM TLHMM TMHMM THHMM
 TLLHM TMLHM THLHM TLMHM TMMHM THMHM TLHHM TMHHM THHHM
 TLLLH TMLLH THLLH TLMLH TMMLH THMLH TLHLH TMHLH THHLH
 TLLMH TMLMH THLMH TLMMH TMMMH THMMH TLHMH TMHMH THHMH
 TLLHH TMLHH THLHH TLMHH TMMHH THMHH TLHHH TMHHH THHHH);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_Z = -1;
 MED_Z = 0;
 HIGH_Z = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;
 LOW_Q = -1;
 MED_Q = 0;
 HIGH_Q = 1;
ILLLL = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b4*LOW_V +
 a4*b4*LOW_W*LOW_V + a5*b4*LOW_Z*LOW_V + a1*b5*LOW_Q +
 a4*b5*LOW_W*LOW_Q + a5*b5*LOW_Z*LOW_Q + a1*b7*LOW_V*LOW_Q +
 a4*b7*LOW_W*LOW_V*LOW_Q + a5*b7*LOW_Z*LOW_V*LOW_Q;
PLOT(PLLLL PMLLL PHLLL PLMLL PMMLL PHMLL PLHLL PMHLL PHHLL
 PLLML PMLML PHLML PLMML PMMML PHMML PLHML PMHML PHHML
 PLLHL PMLHL PHLHL PLMHL PMMHL PHMHL PLHHL PMHHL PHHHL
 PLLLM PMLLM PHLLM PLMLM PMMLM PHMLM PLHLM PMHLM PHHLM
 PLLMM PMLMM PHLMM PLMMM PMMMM PHMMM PLHMM PMHMM PHHMM
 PLLHM PMLHM PHLHM PLMHM PMMHM PHMHM PLHHM PMHHM PHHHM
 PLLLH PMLLH PHLLH PLMLH PMMLH PHMLH PLHLH PMHLH PHHLH
 PLLMH PMLMH PHLMH PLMMH PMMMH PHMMH PLHMH PMHMH PHHMH
 PLLHH PMLHH PHLHH PLMHH PMMHH PHMHH PLHHH PMHHH PHHHH);
LOOP(XVAL,-3,3,0.1);
PLLLL = ILLLL*XVAL;

第十步，进行循环计算。自变量X从-3到3，步长为0.1。在循环中计算不同X值下的间接效应。PLLLL = ILLLL*XVAL，表示当所有调节变量都为低水平时，间接效应乘以X的当前取值，得到要绘制的曲线上的一点。其他参数的计算类似，此处省略以保持简洁。

代码解读11

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
 Z BY Z1* Z2 Z3 Z4;
 V BY V1* V2 V3 V4;
 Q BY Q1* Q2 Q3 Q4;
 Y BY Y1 Y2 Y3 Y4;
  W@1;  Z@1;  V@1;  Q@1;
MV | M XWITH V;
 MQ | M XWITH Q;
 XW | X XWITH W;
 XZ | X XWITH Z;
 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 (cdash1);
 Y ON W (cdash2);
 Y ON Z (cdash3);
 Y ON XW (cdash4);
 Y ON XZ (cdash5);
 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_V MED_V HIGH_V LOW_Q MED_Q HIGH_Q
 ILLLL IMLLL IHLLL ILMLL IMMLL IHMLL ILHLL IMHLL IHHLL
 ILLML IMLML IHLML ILMML IMMML IHMML ILHML IMHML IHHML
 ILLHL IMLHL IHLHL ILMHL IMMHL IHMHL ILHHL IMHHL IHHHL
 ILLLM IMLLM IHLLM ILMLM IMMLM IHMLM ILHLM IMHLM IHHLM
 ILLMM IMLMM IHLMM ILMMM IMMMM IHMMM ILHMM IMHMM IHHMM
 ILLHM IMLHM IHLHM ILMHM IMMHM IHMHM ILHHM IMHHM IHHHM
 ILLLH IMLLH IHLLH ILMLH IMMLH IHMLH ILHLH IMHLH IHHLH
 ILLMH IMLMH IHLMH ILMMH IMMMH IHMMH ILHMH IMHMH IHHMH
 ILLHH IMLHH IHLHH ILMHH IMMHH IHMHH ILHHH IMHHH IHHHH
 DLOW_LOZ DMEW_LOZ DHIW_LOZ DLOW_MEZ DMEW_MEZ DHIW_MEZ
 DLOW_HIZ DMEW_HIZ DHIW_HIZ
 TLLLL TMLLL THLLL TLMLL TMMLL THMLL TLHLL TMHLL THHLL
 TLLML TMLML THLML TLMML TMMML THMML TLHML TMHML THHML
 TLLHL TMLHL THLHL TLMHL TMMHL THMHL TLHHL TMHHL THHHL
 TLLLM TMLLM THLLM TLMLM TMMLM THMLM TLHLM TMHLM THHLM
 TLLMM TMLMM THLMM TLMMM TMMMM THMMM TLHMM TMHMM THHMM
 TLLHM TMLHM THLHM TLMHM TMMHM THMHM TLHHM TMHHM THHHM
 TLLLH TMLLH THLLH TLMLH TMMLH THMLH TLHLH TMHLH THHLH
 TLLMH TMLMH THLMH TLMMH TMMMH THMMH TLHMH TMHMH THHMH
 TLLHH TMLHH THLHH TLMHH TMMHH THMHH TLHHH TMHHH THHHH);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_Z = -1;
 MED_Z = 0;
 HIGH_Z = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;
 LOW_Q = -1;
 MED_Q = 0;
 HIGH_Q = 1;
ILLLL = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b4*LOW_V +
 a4*b4*LOW_W*LOW_V + a5*b4*LOW_Z*LOW_V + a1*b5*LOW_Q +
 a4*b5*LOW_W*LOW_Q + a5*b5*LOW_Z*LOW_Q + a1*b7*LOW_V*LOW_Q +
 a4*b7*LOW_W*LOW_V*LOW_Q + a5*b7*LOW_Z*LOW_V*LOW_Q;
PLOT(PLLLL PMLLL PHLLL PLMLL PMMLL PHMLL PLHLL PMHLL PHHLL
 PLLML PMLML PHLML PLMML PMMML PHMML PLHML PMHML PHHML
 PLLHL PMLHL PHLHL PLMHL PMMHL PHMHL PLHHL PMHHL PHHHL
 PLLLM PMLLM PHLLM PLMLM PMMLM PHMLM PLHLM PMHLM PHHLM
 PLLMM PMLMM PHLMM PLMMM PMMMM PHMMM PLHMM PMHMM PHHMM
 PLLHM PMLHM PHLHM PLMHM PMMHM PHMHM PLHHM PMHHM PHHHM
 PLLLH PMLLH PHLLH PLMLH PMMLH PHMLH PLHLH PMHLH PHHLH
 PLLMH PMLMH PHLMH PLMMH PMMMH PHMMH PLHMH PMHMH PHHMH
 PLLHH PMLHH PHLHH PLMHH PMMHH PHMHH PLHHH PMHHH PHHHH);
LOOP(XVAL,-3,3,0.1);
PLLLL = ILLLL*XVAL;
OUTPUT:
 CINT;

最后一步，输出置信区间。CINT表示输出置信区间，可以帮助评估模型参数估计的可靠性。

资源汇总

• 本视频讲义地址: https://mlln.cn/mplus-model-templates/model53latent.html
• 图书《MPlus中介调节模型》打包下载: 点击下载
• 图书《MPlus中介调节模型》在线看: 点击查看
• 视频教程: 点击这里打开视频
• Mplus 模型模板教程列表: https://mlln.cn/mplus-model-templates
• 统计咨询: https://wx.zsxq.com/group/88888188828842

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