Mplus model35latent 模型讲解

来自图书《MPlus中介调节模型》

使用Mplus分析复杂的中介、调节和调节中介效应模型

• 理论模型
• 数学模型
• 数学推导
• 代码解读

大家好，欢迎来到本教程。本页概述了我们今天将要学习的内容。首先，我们会讲解这个复杂模型的理论基础，建立清晰的理论模型框架。然后，我们将把理论模型转化为数学模型，用数学公式精确地表达变量之间的关系。接下来，我们将进行必要的数学推导，为Mplus代码的编写和结果解读提供理论支撑。最后，我们将详细解读Mplus代码，包括模型语句的含义、参数设置以及结果的解释。通过这四个步骤，我们将逐步掌握如何使用Mplus分析包含中介、调节和调节中介效应的复杂模型。 希望大家有所收获！

理论模型

我们来看这张图，它展示了一个比较复杂的模型。简单来说，这个模型里，X会影响M，M又会影响Y。同时，X可以直接影响Y。 这就是基本的关系。但这个模型更复杂的地方在于，W会影响X和M之间的关系，也就是说，W可以调节X对M的影响。同样，V和Q会调节M对Y的影响，意味着M对Y的影响会随着V和Q的变化而变化。同时，W,V,Q本身也会影响模型中的其他变量。 这张图就清晰地展现了这些变量之间是如何互相影响的。

数学模型

这张图展示了一个比较复杂的模型，它研究了变量之间的相互影响。我们来看一下，这里有几个核心的变量：X，可以理解为起始原因；Y，表示最终结果；M，它像一个中间桥梁，连接X和Y。除了这些，还有一些变量会影响它们之间的关系。W、V和Q都是调节变量，可以理解为影响关系的因素。还有两个特殊的变量，XW、MV和MQ，它们是交互项，代表两个变量共同作用的结果。具体来说，X通过a1这条路影响M；W通过a2这条路调节X对M的影响；XW通过a3这条路调节X对M的影响。M通过b1这条路影响Y，V通过b2这条路直接影响Y；Q通过b3这条路直接影响Y；MV通过b4这条路调节M对Y的影响；MQ通过b5这条路调节M对Y的影响。另外，X还会通过c’这条路直接影响Y。这个模型就是要研究，X是怎么通过M影响Y的，以及W、V和Q这些因素又是如何影响这种关系的。

数学公式1

模型方程如下：

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

M = a0 + a1X + a2W + a3XW

首先，我们来看一下模型方程。Y是因变量，M是中介变量，X是自变量，V、W和Q是调节变量。这里给出了两个方程，第一个是Y关于M、V、Q、MV、MQ和X的回归方程；第二个是M关于X和W的回归方程，并且包含了交互项XW。

数学公式2

模型方程如下：

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

M = a0 + a1X + a2W + a3XW
将第二个方程代入第一个方程，得到：

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

接下来，我们将第二个方程，也就是M的表达式，代入到第一个方程中，这样我们就得到了一个只包含X、W、V、Q的关于Y的方程。

数学公式3

模型方程如下：

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

M = a0 + a1X + a2W + a3XW
将第二个方程代入第一个方程，得到：

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

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

现在，我们把上一步得到的方程中的括号展开，这样可以更清楚地看到每一项的组成部分。

数学公式4

模型方程如下：

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

M = a0 + a1X + a2W + a3XW
将第二个方程代入第一个方程，得到：

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

Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2V + b3Q + a0b4V + a1b4XV + a2b4WV + a3b4XWV + a0b5Q + a1b5XQ + a2b5WQ + a3b5XWQ + c'X
将含有X的项合并，整理成 `Y = a + bX` 的形式：

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

为了更清晰地分析X对Y的影响，我们把所有包含X的项提取出来，把公式整理成类似 Y=a+bX 的形式，其中a是截距项，b是斜率，也就是总效应。这样更方便我们区分直接效应和间接效应。

数学公式5

模型方程如下：

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

M = a0 + a1X + a2W + a3XW
将第二个方程代入第一个方程，得到：

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

Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2V + b3Q + a0b4V + a1b4XV + a2b4WV + a3b4XWV + a0b5Q + a1b5XQ + a2b5WQ + a3b5XWQ + c'X
将含有X的项合并，整理成 `Y = a + bX` 的形式：

Y = (b0 + a0b1 + a2b1W + b2V + b3Q + a0b4V + a2b4WV + a0b5Q + a2b5WQ) + (a1b1 + a3b1W + a1b4V + a3b4WV + a1b5Q + a3b5WQ + c')X
因此，我们可以得到：

间接效应 (X对Y的间接效应，在W, V, Q的条件下)：

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

直接效应 (X对Y的直接效应)：

c'

最后，我们根据上一步的结果，可以明确地得出间接效应和直接效应的表达式。间接效应是X通过M影响Y的效应，它受到调节变量W、V和Q的影响，而直接效应是X直接影响Y的效应，用c’表示。

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;

首先，我们使用 USEVARIABLES 命令来声明本次分析中需要用到的所有变量。这里包括了：四个用来测量潜在自变量X的指标变量X1到X4，四个用来测量潜在中介变量M的指标变量M1到M4，四个测量调节变量W的指标变量W1到W4，四个测量调节变量V的指标变量V1到V4，四个测量调节变量Q的指标变量Q1到Q4，以及最后，四个用来测量潜在因变量Y的指标变量Y1到Y4。

代码解读2

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

接下来，我们使用 ANALYSIS 命令来设置分析的参数。TYPE = GENERAL RANDOM 表示我们使用一般随机效应模型。ESTIMATOR = ML 表示我们使用极大似然估计法来进行参数估计。ALGORITHM = INTEGRATION 表示我们使用积分算法来处理潜在变量模型。

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;

然后，我们开始构建模型。首先定义测量模型，使用 BY 关键字将潜在变量与它们的观测指标变量联系起来。例如，X BY X1 X2 X3 X4 表示潜在变量X由它的四个观测指标X1到X4测量。注意到W1，V1，Q1*，表示将W，V，Q的方差固定为1，进行标准化。最后，我们将W，V，Q的方差固定为1，这也起到了标准化的效果。

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;

现在，我们定义潜在的交互项。 MV | M XWITH V 表示建立中介变量M与调节变量V的交互作用，用 MV 表示。MQ | M XWITH Q 表示建立中介变量M与调节变量Q的交互作用，用 MQ 表示。XW | X XWITH W 表示建立自变量X与调节变量W的交互作用，用 XW 表示。

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;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 Y ON X (cdash);

接下来，我们定义结构模型中，因变量Y和其他变量的关系。Y ON M (b1) 表示中介变量M对Y的影响，系数为b1。Y ON V (b2) 表示调节变量V对Y的影响，系数为b2。Y ON Q (b3) 表示调节变量Q对Y的影响，系数为b3。Y ON MV (b4) 表示交互项MV对Y的影响，系数为b4。Y ON MQ (b5) 表示交互项MQ对Y的影响，系数为b5。最后，Y ON X (cdash) 表示自变量X对Y的直接影响，系数为cdash。

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;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 Y ON X (cdash);
M ON X (a1);
 M ON W (a2);
 M ON XW (a3);

然后，我们定义结构模型中，中介变量M和其他变量的关系。M ON X (a1) 表示自变量X对中介变量M的影响，系数为a1。M ON W (a2) 表示调节变量W对中介变量M的影响，系数为a2。M ON XW (a3) 表示交互项XW对中介变量M的影响，系数为a3。

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;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 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
 TLWLVLQ TMWLVLQ THWLVLQ TLWMVLQ TMWMVLQ THWMVLQ
 TLWHVLQ TMWHVLQ THWHVLQ
 TLWLVMQ TMWLVMQ THWLVMQ TLWMVMQ TMWMVMQ THWMVMQ
 TLWHVMQ TMWHVMQ THWHVMQ
 TLWLVHQ TMWLVHQ THWLVHQ TLWMVHQ TMWMVHQ THWMVHQ
 TLWHVHQ TMWHVHQ THWHVHQ);

接下来，我们使用 MODEL CONSTRAINT 命令来定义模型约束，从而计算不同调节变量水平下的条件间接效应和条件总效应。首先，我们使用 NEW 命令来定义一系列新的参数，这些参数包括调节变量W，V，Q的低、中、高三种水平，以及在不同调节变量水平下对应的条件间接效应（以IL开头）和条件总效应（以TL开头）。

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;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 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
 TLWLVLQ TMWLVLQ THWLVLQ TLWMVLQ TMWMVLQ THWMVLQ
 TLWHVLQ TMWHVLQ THWHVLQ
 TLWLVMQ TMWLVMQ THWLVMQ TLWMVMQ TMWMVMQ THWMVMQ
 TLWHVMQ TMWHVMQ THWHVMQ
 TLWLVHQ TMWLVHQ THWLVHQ TLWMVHQ TMWMVHQ THWMVHQ
 TLWHVHQ TMWHVHQ THWHVHQ);
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;

然后，我们给调节变量W，V，Q的低、中、高三个水平赋值，分别设置为-1，0和1。这些值通常代表调节变量标准差的-1倍，0倍和1倍。

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;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 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
 TLWLVLQ TMWLVLQ THWLVLQ TLWMVLQ TMWMVLQ THWMVLQ
 TLWHVLQ TMWHVLQ THWHVLQ
 TLWLVMQ TMWLVMQ THWLVMQ TLWMVMQ TMWMVMQ THWMVMQ
 TLWHVMQ TMWHVMQ THWHVMQ
 TLWLVHQ TMWLVHQ THWLVHQ TLWMVHQ TMWMVHQ THWMVHQ
 TLWHVHQ TMWHVHQ THWHVHQ);
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;
 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;
 IHWLVLQ = a1*b1 + a3*b1*HIGH_W + a1*b4*LOW_V + a3*b4*HIGH_W*LOW_V +
 a1*b5*LOW_Q + a3*b5*HIGH_W*LOW_Q;
 ...

现在，我们开始计算在不同调节变量水平下的条件间接效应。这里展示的是 ILWLVLQ， IMWLVLQ 和 IHWLVLQ 的计算公式，以W的低、中、高水平为例，V和Q均处于低水平。这些公式是基于模型参数推导出来的，代表在不同调节变量水平下，自变量X通过中介变量M对因变量Y产生的间接影响。后面的公式定义了所有调节变量水平组合下的条件间接效应。

代码解读10

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;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 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
 TLWLVLQ TMWLVLQ THWLVLQ TLWMVLQ TMWMVLQ THWMVLQ
 TLWHVLQ TMWHVLQ THWHVLQ
 TLWLVMQ TMWLVMQ THWLVMQ TLWMVMQ TMWMVMQ THWMVMQ
 TLWHVMQ TMWHVMQ THWHVMQ
 TLWLVHQ TMWLVHQ THWLVHQ TLWMVHQ TMWMVHQ THWMVHQ
 TLWHVHQ TMWHVHQ THWHVHQ);
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;
 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;
 IHWLVLQ = a1*b1 + a3*b1*HIGH_W + a1*b4*LOW_V + a3*b4*HIGH_W*LOW_V +
 a1*b5*LOW_Q + a3*b5*HIGH_W*LOW_Q;
 ...
TLWLVLQ = ILWLVLQ + cdash;
 TMWLVLQ = IMWLVLQ + cdash;
 THWLVLQ = IHWLVLQ + cdash;
 ...

接下来，我们计算在不同调节变量水平下的条件总效应。条件总效应等于对应的条件间接效应加上直接效应cdash。这里展示了TLWLVLQ，TMWLVLQ和THWLVLQ的计算公式，即在V和Q处于低水平时，W处于低中高水平时的条件总效应。后面的公式定义了所有调节变量水平组合下的条件总效应。

代码解读11

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;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 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
 TLWLVLQ TMWLVLQ THWLVLQ TLWMVLQ TMWMVLQ THWMVLQ
 TLWHVLQ TMWHVLQ THWHVLQ
 TLWLVMQ TMWLVMQ THWLVMQ TLWMVMQ TMWMVMQ THWMVMQ
 TLWHVMQ TMWHVMQ THWHVMQ
 TLWLVHQ TMWLVHQ THWLVHQ TLWMVHQ TMWMVHQ THWMVHQ
 TLWHVHQ TMWHVHQ THWHVHQ);
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;
 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;
 IHWLVLQ = a1*b1 + a3*b1*HIGH_W + a1*b4*LOW_V + a3*b4*HIGH_W*LOW_V +
 a1*b5*LOW_Q + a3*b5*HIGH_W*LOW_Q;
 ...
TLWLVLQ = ILWLVLQ + cdash;
 TMWLVLQ = IMWLVLQ + cdash;
 THWLVLQ = IHWLVLQ + cdash;
 ...
PLOT(PLWLVLQ PMWLVLQ PHWLVLQ PLWMVLQ PMWMVLQ PHWMVLQ
 PLWHVLQ PMWHVLQ PHWHVLQ
 PLWLVMQ PMWLVMQ PHWLVMQ PLWMVMQ PMWMVMQ PHWMVMQ
 PLWHVMQ PMWHVMQ PHWHVMQ
 PLWLVHQ PMWLVHQ PHWLVHQ PLWMVHQ PMWMVHQ PHWMVHQ
 PLWHVHQ PMWHVHQ PHWHVHQ);

然后，我们使用 PLOT 命令来指定需要绘制的变量，这里定义了一系列以PL、PM、PH开头的变量用于绘制不同调节水平下的条件间接效应。

代码解读12

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;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 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
 TLWLVLQ TMWLVLQ THWLVLQ TLWMVLQ TMWMVLQ THWMVLQ
 TLWHVLQ TMWHVLQ THWHVLQ
 TLWLVMQ TMWLVMQ THWLVMQ TLWMVMQ TMWMVMQ THWMVMQ
 TLWHVMQ TMWHVMQ THWHVMQ
 TLWLVHQ TMWLVHQ THWLVHQ TLWMVHQ TMWMVHQ THWMVHQ
 TLWHVHQ TMWHVHQ THWHVHQ);
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;
 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;
 IHWLVLQ = a1*b1 + a3*b1*HIGH_W + a1*b4*LOW_V + a3*b4*HIGH_W*LOW_V +
 a1*b5*LOW_Q + a3*b5*HIGH_W*LOW_Q;
 ...
TLWLVLQ = ILWLVLQ + cdash;
 TMWLVLQ = IMWLVLQ + cdash;
 THWLVLQ = IHWLVLQ + cdash;
 ...
PLOT(PLWLVLQ PMWLVLQ PHWLVLQ PLWMVLQ PMWMVLQ PHWMVLQ
 PLWHVLQ PMWHVLQ PHWHVLQ
 PLWLVMQ PMWLVMQ PHWLVMQ PLWMVMQ PMWMVMQ PHWMVMQ
 PLWHVMQ PMWHVMQ PHWHVMQ
 PLWLVHQ PMWLVHQ PHWLVHQ PLWMVHQ PMWMVHQ PHWMVHQ
 PLWHVHQ PMWHVHQ PHWHVHQ);
LOOP(XVAL,-3,3,0.1);
 PLWLVLQ = ILWLVLQ*XVAL;
 PMWLVLQ = IMWLVLQ*XVAL;
 PHWLVLQ = IHWLVLQ*XVAL;
 ...

接下来，我们使用 LOOP 命令来设置一个循环。循环变量 XVAL 从-3变化到3，步长为0.1。在循环内部，我们将不同调节变量水平下的条件间接效应与XVAL相乘，并将结果赋值给对应的以PL、PM、PH开头的变量。这些变量将在后续的绘图中使用，用于展示条件间接效应随自变量X的变化情况。

代码解读13

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;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 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
 TLWLVLQ TMWLVLQ THWLVLQ TLWMVLQ TMWMVLQ THWMVLQ
 TLWHVLQ TMWHVLQ THWHVLQ
 TLWLVMQ TMWLVMQ THWLVMQ TLWMVMQ TMWMVMQ THWMVMQ
 TLWHVMQ TMWHVMQ THWHVMQ
 TLWLVHQ TMWLVHQ THWLVHQ TLWMVHQ TMWMVHQ THWMVHQ
 TLWHVHQ TMWHVHQ THWHVHQ);
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;
 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;
 IHWLVLQ = a1*b1 + a3*b1*HIGH_W + a1*b4*LOW_V + a3*b4*HIGH_W*LOW_V +
 a1*b5*LOW_Q + a3*b5*HIGH_W*LOW_Q;
 ...
TLWLVLQ = ILWLVLQ + cdash;
 TMWLVLQ = IMWLVLQ + cdash;
 THWLVLQ = IHWLVLQ + cdash;
 ...
PLOT(PLWLVLQ PMWLVLQ PHWLVLQ PLWMVLQ PMWMVLQ PHWMVLQ
 PLWHVLQ PMWHVLQ PHWHVLQ
 PLWLVMQ PMWLVMQ PHWLVMQ PLWMVMQ PMWMVMQ PHWMVMQ
 PLWHVMQ PMWHVMQ PHWHVMQ
 PLWLVHQ PMWLVHQ PHWLVHQ PLWMVHQ PMWMVHQ PHWMVHQ
 PLWHVHQ PMWHVHQ PHWHVHQ);
LOOP(XVAL,-3,3,0.1);
 PLWLVLQ = ILWLVLQ*XVAL;
 PMWLVLQ = IMWLVLQ*XVAL;
 PHWLVLQ = IHWLVLQ*XVAL;
 ...
PLOT:
 TYPE = plot2;

现在，我们使用 PLOT 命令来设置绘图类型为 plot2，这将绘制出我们之前定义的散点图。

代码解读14

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;
Y ON M (b1);
 Y ON V (b2);
 Y ON Q (b3);
 Y ON MV (b4);
 Y ON MQ (b5);
 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
 TLWLVLQ TMWLVLQ THWLVLQ TLWMVLQ TMWMVLQ THWMVLQ
 TLWHVLQ TMWHVLQ THWHVLQ
 TLWLVMQ TMWLVMQ THWLVMQ TLWMVMQ TMWMVMQ THWMVMQ
 TLWHVMQ TMWHVMQ THWHVMQ
 TLWLVHQ TMWLVHQ THWLVHQ TLWMVHQ TMWMVHQ THWMVHQ
 TLWHVHQ TMWHVHQ THWHVHQ);
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;
 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;
 IHWLVLQ = a1*b1 + a3*b1*HIGH_W + a1*b4*LOW_V + a3*b4*HIGH_W*LOW_V +
 a1*b5*LOW_Q + a3*b5*HIGH_W*LOW_Q;
 ...
TLWLVLQ = ILWLVLQ + cdash;
 TMWLVLQ = IMWLVLQ + cdash;
 THWLVLQ = IHWLVLQ + cdash;
 ...
PLOT(PLWLVLQ PMWLVLQ PHWLVLQ PLWMVLQ PMWMVLQ PHWMVLQ
 PLWHVLQ PMWHVLQ PHWHVLQ
 PLWLVMQ PMWLVMQ PHWLVMQ PLWMVMQ PMWMVMQ PHWMVMQ
 PLWHVMQ PMWHVMQ PHWHVMQ
 PLWLVHQ PMWLVHQ PHWLVHQ PLWMVHQ PMWMVHQ PHWMVHQ
 PLWHVHQ PMWHVHQ PHWHVHQ);
LOOP(XVAL,-3,3,0.1);
 PLWLVLQ = ILWLVLQ*XVAL;
 PMWLVLQ = IMWLVLQ*XVAL;
 PHWLVLQ = IHWLVLQ*XVAL;
 ...
PLOT:
 TYPE = plot2;
OUTPUT:
 CINT;

最后，我们使用 OUTPUT 命令来要求输出置信区间，这将提供参数估计的不确定性信息。

资源汇总

• 本视频讲义地址: https://mlln.cn/mplus-model-templates/model35latent.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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