Mplus model71latent 模型讲解

来自图书《MPlus中介调节模型》

使用Mplus构建复杂中介调节模型

• 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。 今天我们将学习如何使用Mplus构建一个非常复杂的模型：包含中介、调节和调节中介效应的模型。 这个教程并非一步步地讲解所有细节，而是以案例的方式呈现，方便大家查找需要的部分。

首先，我们会介绍这个复杂模型的理论模型，用清晰的图示来展现自变量、中介变量、调节变量以及因变量之间的关系，以及它们之间相互作用的方式。 这部分帮助大家理解模型的逻辑和假设。

接下来，我们将给出数学模型，用公式表达自变量、中介变量、调节变量以及因变量之间的关系。 这部分会比较简洁，主要关注模型的关键参数。

然后，我们会对模型进行数学推导，重点解释如何计算条件间接效应、条件直接效应和条件总效应，以及如何在不同调节变量水平下进行解读。 这部分需要一定的统计学基础。

最后，也是最重要的部分，我们将详细解读Mplus代码。 我们会逐行解释代码的含义，并提供可直接运行的代码，方便大家上手实践。 代码中包含详细的注释，即使您不熟悉Mplus，也能轻松理解。 教程中所有的模型都提供了可直接分析数据的Mplus代码。

希望本教程能够帮助大家更好地理解和应用Mplus进行复杂中介调节模型的构建和分析。 如有任何疑问，请随时提出。

理论模型

我们来看，这个图展示了一个比较复杂的模型。这里，X会影响M，M又会影响Y。同时，X也会直接影响Y。另外，W和V这两个变量会影响M到Y这条路，也会影响X直接到Y这条路。W和V之间也相互影响，而且这些影响同样会作用于M到Y的路径和X到Y的路径。简单来说，就是X通过M影响Y，然后W和V又会改变这种影响的大小。

数学模型

这张图展示的是一个复杂的模型，它研究了多个变量之间的相互影响。我们看到，自变量X，它通过a1，a2，a3这三条路径，影响着中介变量M。同时，X和调节变量W的交互作用（XW），也会影响M。中介变量M又通过路径b1影响着因变量Y。此外，M还会分别与调节变量W（MW），V（MV），以及W和V的交互作用（MWV）产生交互，从而间接地影响Y。另外，自变量X可以直接影响Y，我们用c1’表示。图中还显示了X、W、V之间的所有两两交互作用项（XW，XV，WV），以及三阶交互作用项XWV，它们分别通过路径c2’到c7’直接影响Y。通过分析这些路径的系数，我们能了解X对Y的直接和间接影响，以及W和V如何调节这些影响。

数学公式1

模型方程：

`Y = b0 + b1M + b2MW + b3MV + b4MWV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`

`M = a0 + a1X + a2W + a3XW`

首先，我们来看一下模型方程。这里，Y是因变量，M是中介变量，X是自变量，W和V是调节变量。第一个方程描述了Y如何被M，W，V以及它们的交互项和X及其交互项所影响。第二个方程描述了M如何被X、W以及它们的交互项所影响。我们的目标是分析X对Y的间接效应和直接效应。

数学公式2

模型方程：

`Y = b0 + b1M + b2MW + b3MV + b4MWV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`

`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) + b2(a0 + a1X + a2W + a3XW)W + b3(a0 + a1X + a2W + a3XW)V + b4(a0 + a1X + a2W + a3XW)WV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`

接下来，我们将中介变量M的表达式代入到Y的表达式中，这样我们就可以直接看到X如何通过M影响Y。这个步骤是通过替换来合并两个方程。

数学公式3

模型方程：

`Y = b0 + b1M + b2MW + b3MV + b4MWV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`

`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) + b2(a0 + a1X + a2W + a3XW)W + b3(a0 + a1X + a2W + a3XW)V + b4(a0 + a1X + a2W + a3XW)WV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`
展开括号：

`Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + a0b2W + a1b2XW + a2b2WW + a3b2XWW + a0b3V + a1b3XV + a2b3WV + a3b3XWV + a0b4WV + a1b4XWV + a2b4WWV + a3b4XWWV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`

现在，我们将上一步得到的表达式中的所有括号展开，这使得我们更容易观察各个变量之间的复杂关系。这是一个代数展开步骤。

数学公式4

模型方程：

`Y = b0 + b1M + b2MW + b3MV + b4MWV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`

`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) + b2(a0 + a1X + a2W + a3XW)W + b3(a0 + a1X + a2W + a3XW)V + b4(a0 + a1X + a2W + a3XW)WV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`
展开括号：

`Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + a0b2W + a1b2XW + a2b2WW + a3b2XWW + a0b3V + a1b3XV + a2b3WV + a3b3XWV + a0b4WV + a1b4XWV + a2b4WWV + a3b4XWWV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`
合并同类项，整理成`Y = a + bX`的形式：

`Y = (b0 + a0b1 + a2b1W + a0b2W + a2b2WW + a0b3V + a2b3WV + a0b4WV + a2b4WWV + c2'W + c3'V + c6'WV) + (a1b1 + a3b1W + a1b2W + a3b2WW + a1b3V + a3b3WV + a1b4WV + a3b4WWV + c1' + c4'W + c5'V + c7'WV)X`

然后，我们将所有不包含X的项放在一起，并提取出所有包含X的项。这将我们整理成Y = a + bX 的形式，其中a代表截距，b代表斜率。这一步是为下一步分离直接效应和间接效应做准备。

数学公式5

模型方程：

`Y = b0 + b1M + b2MW + b3MV + b4MWV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`

`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) + b2(a0 + a1X + a2W + a3XW)W + b3(a0 + a1X + a2W + a3XW)V + b4(a0 + a1X + a2W + a3XW)WV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`
展开括号：

`Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + a0b2W + a1b2XW + a2b2WW + a3b2XWW + a0b3V + a1b3XV + a2b3WV + a3b3XWV + a0b4WV + a1b4XWV + a2b4WWV + a3b4XWWV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`
合并同类项，整理成`Y = a + bX`的形式：

`Y = (b0 + a0b1 + a2b1W + a0b2W + a2b2WW + a0b3V + a2b3WV + a0b4WV + a2b4WWV + c2'W + c3'V + c6'WV) + (a1b1 + a3b1W + a1b2W + a3b2WW + a1b3V + a3b3WV + a1b4WV + a3b4WWV + c1' + c4'W + c5'V + c7'WV)X`
X对Y的间接效应（在W，V条件下）：

`(a1 + a3W)(b1 + b2W + b3V + b4WV)`

通过对上一步的结果进行分析，我们得到了X对Y的间接效应，这部分效应是通过中介变量M传递的。具体而言，我们提取了X前面的系数，并将其分解为两个部分：(a1 + a3W) 表示X对M的影响，(b1 + b2W + b3V + b4WV) 表示M对Y的影响，它们相乘的结果就是间接效应。W 和 V 会调节 X 对 M 的影响, 以及 M 对 Y 的影响。所以间接效应是W和V的函数。

数学公式6

模型方程：

`Y = b0 + b1M + b2MW + b3MV + b4MWV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`

`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) + b2(a0 + a1X + a2W + a3XW)W + b3(a0 + a1X + a2W + a3XW)V + b4(a0 + a1X + a2W + a3XW)WV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`
展开括号：

`Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + a0b2W + a1b2XW + a2b2WW + a3b2XWW + a0b3V + a1b3XV + a2b3WV + a3b3XWV + a0b4WV + a1b4XWV + a2b4WWV + a3b4XWWV + c1'X + c2'W + c3'V + c4'XW + c5'XV + c6'WV + c7'XWV`
合并同类项，整理成`Y = a + bX`的形式：

`Y = (b0 + a0b1 + a2b1W + a0b2W + a2b2WW + a0b3V + a2b3WV + a0b4WV + a2b4WWV + c2'W + c3'V + c6'WV) + (a1b1 + a3b1W + a1b2W + a3b2WW + a1b3V + a3b3WV + a1b4WV + a3b4WWV + c1' + c4'W + c5'V + c7'WV)X`
X对Y的间接效应（在W，V条件下）：

`(a1 + a3W)(b1 + b2W + b3V + b4WV)`
X对Y的直接效应（在W，V条件下）：

`c1' + c4'W + c5'V + c7'WV`

最后，我们得到了X对Y的直接效应，这部分效应不通过中介变量M。它直接反映了X对Y的影响。与间接效应相似，直接效应也受W和V的调节，也是W和V的函数。

代码解读1

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 V1 V2 V3 V4
Y1 Y2 Y3 Y4;

首先，我们使用USEVARIABLES命令来声明分析中要用到的所有变量。这里包括自变量X的四个指标X1到X4，中介变量M的四个指标M1到M4，两个调节变量W和V，它们各自也有四个指标，分别是W1到W4和V1到V4，最后是因变量Y的四个指标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
Y1 Y2 Y3 Y4;
ANALYSIS:
 TYPE = GENERAL RANDOM;
 ESTIMATOR = ML;
 ALGORITHM = INTEGRATION;

接下来是分析设置部分，我们使用ANALYSIS命令。TYPE = GENERAL RANDOM指定了分析类型为一般随机效应模型，这可以处理潜变量；ESTIMATOR = ML表示使用最大似然估计方法来估计模型参数；ALGORITHM = INTEGRATION表示使用积分算法来处理潜变量的估计。

代码解读3

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

在模型部分，我们首先定义潜变量的测量模型。例如，X BY X1 X2 X3 X4表示潜变量X由X1到X4这四个指标测量。类似地，定义了M,W,V和Y的测量模型。注意，W和V的指标前有星号，意味着它们是标准化的。W@1和V@1表示将W和V的方差固定为1，这也是为了标准化。

代码解读4

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 V1 V2 V3 V4
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;
 Y BY Y1 Y2 Y3 Y4;
 W@1;  V@1;
MW | M XWITH W;
 MV | M XWITH V;
 XW | X XWITH W;
 XV | X XWITH V;
 WV | W XWITH V;
 MWV | M XWITH WV;
 XWV | X XWITH WV;

接下来，我们创建了潜变量之间的交互项。例如，MW表示M与W的交互作用，它是通过M XWITH W定义的。其他交互项，如MV, XW, XV, WV, MWV和XWV的定义方式类似，涵盖了所有二阶和三阶的交互作用。

代码解读5

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 V1 V2 V3 V4
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;
 Y BY Y1 Y2 Y3 Y4;
 W@1;  V@1;
MW | M XWITH W;
 MV | M XWITH V;
 XW | X XWITH W;
 XV | X XWITH V;
 WV | W XWITH V;
 MWV | M XWITH WV;
 XWV | X XWITH WV;
Y ON M (b1);
 Y ON MW (b2);
 Y ON MV (b3);
 Y ON MWV (b4);
 Y ON X(cdash1);
 Y ON W (cdash2);
 Y ON V (cdash3);
 Y ON XW (cdash4);
 Y ON XV (cdash5);
 Y ON WV (cdash6);
 Y ON XWV (cdash7);

现在，我们定义因变量Y的回归方程。Y ON M (b1)表示Y对中介变量M的回归系数为b1。类似地，Y 对其他所有变量和交互项都有回归系数。例如，Y ON MW (b2)表示Y对M和W交互项的回归系数为b2，以此类推，直到Y ON XWV (cdash7)，表示Y对X，W，V的三阶交互项的回归系数为cdash7。这些括号里的参数名，后面都会用到。

代码解读6

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 V1 V2 V3 V4
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;
 Y BY Y1 Y2 Y3 Y4;
 W@1;  V@1;
MW | M XWITH W;
 MV | M XWITH V;
 XW | X XWITH W;
 XV | X XWITH V;
 WV | W XWITH V;
 MWV | M XWITH WV;
 XWV | X XWITH WV;
Y ON M (b1);
 Y ON MW (b2);
 Y ON MV (b3);
 Y ON MWV (b4);
 Y ON X(cdash1);
 Y ON W (cdash2);
 Y ON V (cdash3);
 Y ON XW (cdash4);
 Y ON XV (cdash5);
 Y ON WV (cdash6);
 Y ON XWV (cdash7);
M ON X (a1);
 M ON W (a2);
 M ON XW (a3);

接下来，我们定义中介变量M的回归方程。M ON X (a1)表示M对X的回归系数为a1，M ON W (a2)表示M对W的回归系数为a2，M ON XW (a3)表示M对X和W交互项的回归系数为a3。 这些系数将用于计算间接效应。

代码解读7

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 V1 V2 V3 V4
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;
 Y BY Y1 Y2 Y3 Y4;
 W@1;  V@1;
MW | M XWITH W;
 MV | M XWITH V;
 XW | X XWITH W;
 XV | X XWITH V;
 WV | W XWITH V;
 MWV | M XWITH WV;
 XWV | X XWITH WV;
Y ON M (b1);
 Y ON MW (b2);
 Y ON MV (b3);
 Y ON MWV (b4);
 Y ON X(cdash1);
 Y ON W (cdash2);
 Y ON V (cdash3);
 Y ON XW (cdash4);
 Y ON XV (cdash5);
 Y ON WV (cdash6);
 Y ON XWV (cdash7);
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
 ILOW_LOV IMEW_LOV IHIW_LOV ILOW_MEV IMEW_MEV IHIW_MEV
 ILOW_HIV IMEW_HIV IHIW_HIV
 DLOW_LOV DMEW_LOV DHIW_LOV DLOW_MEV DMEW_MEV DHIW_MEV
 DLOW_HIV DMEW_HIV DHIW_HIV
 TLOW_LOV TMEW_LOV THIW_LOV TLOW_MEV TMEW_MEV THIW_MEV
 TLOW_HIV TMEW_HIV THIW_HIV);

现在我们进入模型约束部分，这是最复杂的部分。首先，我们使用NEW命令声明新的参数来存储计算结果。这些参数分为几类，包括调节变量W和V的低、中、高水平，不同调节水平下的间接效应，直接效应以及总效应。它们的名字都很有规律，方便我们理解它们各自代表的意义。

代码解读8

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 V1 V2 V3 V4
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;
 Y BY Y1 Y2 Y3 Y4;
 W@1;  V@1;
MW | M XWITH W;
 MV | M XWITH V;
 XW | X XWITH W;
 XV | X XWITH V;
 WV | W XWITH V;
 MWV | M XWITH WV;
 XWV | X XWITH WV;
Y ON M (b1);
 Y ON MW (b2);
 Y ON MV (b3);
 Y ON MWV (b4);
 Y ON X(cdash1);
 Y ON W (cdash2);
 Y ON V (cdash3);
 Y ON XW (cdash4);
 Y ON XV (cdash5);
 Y ON WV (cdash6);
 Y ON XWV (cdash7);
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
 ILOW_LOV IMEW_LOV IHIW_LOV ILOW_MEV IMEW_MEV IHIW_MEV
 ILOW_HIV IMEW_HIV IHIW_HIV
 DLOW_LOV DMEW_LOV DHIW_LOV DLOW_MEV DMEW_MEV DHIW_MEV
 DLOW_HIV DMEW_HIV DHIW_HIV
 TLOW_LOV TMEW_LOV THIW_LOV TLOW_MEV TMEW_MEV THIW_MEV
 TLOW_HIV TMEW_HIV THIW_HIV);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;

这里我们指定调节变量W和V的低、中、高水平值，分别设置为-1, 0 和 1，相当于取一个标准差， 方便理解。

代码解读9

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 V1 V2 V3 V4
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;
 Y BY Y1 Y2 Y3 Y4;
 W@1;  V@1;
MW | M XWITH W;
 MV | M XWITH V;
 XW | X XWITH W;
 XV | X XWITH V;
 WV | W XWITH V;
 MWV | M XWITH WV;
 XWV | X XWITH WV;
Y ON M (b1);
 Y ON MW (b2);
 Y ON MV (b3);
 Y ON MWV (b4);
 Y ON X(cdash1);
 Y ON W (cdash2);
 Y ON V (cdash3);
 Y ON XW (cdash4);
 Y ON XV (cdash5);
 Y ON WV (cdash6);
 Y ON XWV (cdash7);
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
 ILOW_LOV IMEW_LOV IHIW_LOV ILOW_MEV IMEW_MEV IHIW_MEV
 ILOW_HIV IMEW_HIV IHIW_HIV
 DLOW_LOV DMEW_LOV DHIW_LOV DLOW_MEV DMEW_MEV DHIW_MEV
 DLOW_HIV DMEW_HIV DHIW_HIV
 TLOW_LOV TMEW_LOV THIW_LOV TLOW_MEV TMEW_MEV THIW_MEV
 TLOW_HIV TMEW_HIV THIW_HIV);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;
ILOW_LOV = a1*b1 + a3*b1*LOW_W + a1*b2*LOW_W + a3*b2*LOW_W*LOW_W +
 a1*b3*LOW_V + a3*b3*LOW_W*LOW_V + a1*b4*LOW_W*LOW_V +
 a3*b4*LOW_W*LOW_W*LOW_V;
 IMEW_LOV = a1*b1 + a3*b1*MED_W + a1*b2*MED_W + a3*b2*MED_W*MED_W +
 a1*b3*LOW_V + a3*b3*MED_W*LOW_V + a1*b4*MED_W*LOW_V +
 a3*b4*MED_W*MED_W*LOW_V;
 IHIW_LOV = a1*b1 + a3*b1*HIGH_W + a1*b2*HIGH_W + a3*b2*HIGH_W*HIGH_W +
 a1*b3*LOW_V + a3*b3*HIGH_W*LOW_V + a1*b4*HIGH_W*LOW_V +
 a3*b4*HIGH_W*HIGH_W*LOW_V;
...

这里我们开始计算不同调节变量水平组合下的间接效应。例如，ILOW_LOV代表当W和V都处于低水平时的间接效应。计算公式基于前面定义的路径系数a1, a2, a3, b1, b2, b3和b4，以及W和V的低水平值。IMEW_LOV和IHIW_LOV分别计算当W处于中水平和高水平，而V处于低水平时的间接效应。这里只展示了三个，实际上，我们需要把所有W和V的组合都计算一遍，这里省略了中间的计算代码。

代码解读10

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 V1 V2 V3 V4
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;
 Y BY Y1 Y2 Y3 Y4;
 W@1;  V@1;
MW | M XWITH W;
 MV | M XWITH V;
 XW | X XWITH W;
 XV | X XWITH V;
 WV | W XWITH V;
 MWV | M XWITH WV;
 XWV | X XWITH WV;
Y ON M (b1);
 Y ON MW (b2);
 Y ON MV (b3);
 Y ON MWV (b4);
 Y ON X(cdash1);
 Y ON W (cdash2);
 Y ON V (cdash3);
 Y ON XW (cdash4);
 Y ON XV (cdash5);
 Y ON WV (cdash6);
 Y ON XWV (cdash7);
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
 ILOW_LOV IMEW_LOV IHIW_LOV ILOW_MEV IMEW_MEV IHIW_MEV
 ILOW_HIV IMEW_HIV IHIW_HIV
 DLOW_LOV DMEW_LOV DHIW_LOV DLOW_MEV DMEW_MEV DHIW_MEV
 DLOW_HIV DMEW_HIV DHIW_HIV
 TLOW_LOV TMEW_LOV THIW_LOV TLOW_MEV TMEW_MEV THIW_MEV
 TLOW_HIV TMEW_HIV THIW_HIV);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;
ILOW_LOV = a1*b1 + a3*b1*LOW_W + a1*b2*LOW_W + a3*b2*LOW_W*LOW_W +
 a1*b3*LOW_V + a3*b3*LOW_W*LOW_V + a1*b4*LOW_W*LOW_V +
 a3*b4*LOW_W*LOW_W*LOW_V;
 IMEW_LOV = a1*b1 + a3*b1*MED_W + a1*b2*MED_W + a3*b2*MED_W*MED_W +
 a1*b3*LOW_V + a3*b3*MED_W*LOW_V + a1*b4*MED_W*LOW_V +
 a3*b4*MED_W*MED_W*LOW_V;
 IHIW_LOV = a1*b1 + a3*b1*HIGH_W + a1*b2*HIGH_W + a3*b2*HIGH_W*HIGH_W +
 a1*b3*LOW_V + a3*b3*HIGH_W*LOW_V + a1*b4*HIGH_W*LOW_V +
 a3*b4*HIGH_W*HIGH_W*LOW_V;
...
DLOW_LOV = cdash1 + cdash4*LOW_W + cdash5*LOW_V + cdash7*LOW_W*LOW_V;
 DMEW_LOV = cdash1 + cdash4*MED_W + cdash5*LOW_V + cdash7*MED_W*LOW_V;
 DHIW_LOV = cdash1 + cdash4*HIGH_W + cdash5*LOW_V + cdash7*HIGH_W*LOW_V;
...

接下来，我们计算不同调节变量水平组合下的直接效应。例如，DLOW_LOV代表当W和V都处于低水平时的直接效应。计算公式基于前面定义的路径系数cdash1, cdash2, cdash3, cdash4, cdash5, cdash6, 和cdash7，以及W和V的低水平值。DMEW_LOV和DHIW_LOV分别计算当W处于中水平和高水平，而V处于低水平时的直接效应。同样，这里省略了中间的计算代码。

代码解读11

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 V1 V2 V3 V4
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;
 Y BY Y1 Y2 Y3 Y4;
 W@1;  V@1;
MW | M XWITH W;
 MV | M XWITH V;
 XW | X XWITH W;
 XV | X XWITH V;
 WV | W XWITH V;
 MWV | M XWITH WV;
 XWV | X XWITH WV;
Y ON M (b1);
 Y ON MW (b2);
 Y ON MV (b3);
 Y ON MWV (b4);
 Y ON X(cdash1);
 Y ON W (cdash2);
 Y ON V (cdash3);
 Y ON XW (cdash4);
 Y ON XV (cdash5);
 Y ON WV (cdash6);
 Y ON XWV (cdash7);
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
 ILOW_LOV IMEW_LOV IHIW_LOV ILOW_MEV IMEW_MEV IHIW_MEV
 ILOW_HIV IMEW_HIV IHIW_HIV
 DLOW_LOV DMEW_LOV DHIW_LOV DLOW_MEV DMEW_MEV DHIW_MEV
 DLOW_HIV DMEW_HIV DHIW_HIV
 TLOW_LOV TMEW_LOV THIW_LOV TLOW_MEV TMEW_MEV THIW_MEV
 TLOW_HIV TMEW_HIV THIW_HIV);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;
ILOW_LOV = a1*b1 + a3*b1*LOW_W + a1*b2*LOW_W + a3*b2*LOW_W*LOW_W +
 a1*b3*LOW_V + a3*b3*LOW_W*LOW_V + a1*b4*LOW_W*LOW_V +
 a3*b4*LOW_W*LOW_W*LOW_V;
 IMEW_LOV = a1*b1 + a3*b1*MED_W + a1*b2*MED_W + a3*b2*MED_W*MED_W +
 a1*b3*LOW_V + a3*b3*MED_W*LOW_V + a1*b4*MED_W*LOW_V +
 a3*b4*MED_W*MED_W*LOW_V;
 IHIW_LOV = a1*b1 + a3*b1*HIGH_W + a1*b2*HIGH_W + a3*b2*HIGH_W*HIGH_W +
 a1*b3*LOW_V + a3*b3*HIGH_W*LOW_V + a1*b4*HIGH_W*LOW_V +
 a3*b4*HIGH_W*HIGH_W*LOW_V;
...
DLOW_LOV = cdash1 + cdash4*LOW_W + cdash5*LOW_V + cdash7*LOW_W*LOW_V;
 DMEW_LOV = cdash1 + cdash4*MED_W + cdash5*LOW_V + cdash7*MED_W*LOW_V;
 DHIW_LOV = cdash1 + cdash4*HIGH_W + cdash5*LOW_V + cdash7*HIGH_W*LOW_V;
...
TLOW_LOV = ILOW_LOV + DLOW_LOV;
 TMEW_LOV = IMEW_LOV + DMEW_LOV;
 THIW_LOV = IHIW_LOV + DHIW_LOV;
...

然后，我们计算总效应。总效应是间接效应和直接效应之和。例如，TLOW_LOV代表当W和V都处于低水平时的总效应，它是ILOW_LOV和DLOW_LOV之和。同样，这里省略了中间的计算代码。

代码解读12

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 V1 V2 V3 V4
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;
 Y BY Y1 Y2 Y3 Y4;
 W@1;  V@1;
MW | M XWITH W;
 MV | M XWITH V;
 XW | X XWITH W;
 XV | X XWITH V;
 WV | W XWITH V;
 MWV | M XWITH WV;
 XWV | X XWITH WV;
Y ON M (b1);
 Y ON MW (b2);
 Y ON MV (b3);
 Y ON MWV (b4);
 Y ON X(cdash1);
 Y ON W (cdash2);
 Y ON V (cdash3);
 Y ON XW (cdash4);
 Y ON XV (cdash5);
 Y ON WV (cdash6);
 Y ON XWV (cdash7);
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
 ILOW_LOV IMEW_LOV IHIW_LOV ILOW_MEV IMEW_MEV IHIW_MEV
 ILOW_HIV IMEW_HIV IHIW_HIV
 DLOW_LOV DMEW_LOV DHIW_LOV DLOW_MEV DMEW_MEV DHIW_MEV
 DLOW_HIV DMEW_HIV DHIW_HIV
 TLOW_LOV TMEW_LOV THIW_LOV TLOW_MEV TMEW_MEV THIW_MEV
 TLOW_HIV TMEW_HIV THIW_HIV);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;
ILOW_LOV = a1*b1 + a3*b1*LOW_W + a1*b2*LOW_W + a3*b2*LOW_W*LOW_W +
 a1*b3*LOW_V + a3*b3*LOW_W*LOW_V + a1*b4*LOW_W*LOW_V +
 a3*b4*LOW_W*LOW_W*LOW_V;
 IMEW_LOV = a1*b1 + a3*b1*MED_W + a1*b2*MED_W + a3*b2*MED_W*MED_W +
 a1*b3*LOW_V + a3*b3*MED_W*LOW_V + a1*b4*MED_W*LOW_V +
 a3*b4*MED_W*MED_W*LOW_V;
 IHIW_LOV = a1*b1 + a3*b1*HIGH_W + a1*b2*HIGH_W + a3*b2*HIGH_W*HIGH_W +
 a1*b3*LOW_V + a3*b3*HIGH_W*LOW_V + a1*b4*HIGH_W*LOW_V +
 a3*b4*HIGH_W*HIGH_W*LOW_V;
...
DLOW_LOV = cdash1 + cdash4*LOW_W + cdash5*LOW_V + cdash7*LOW_W*LOW_V;
 DMEW_LOV = cdash1 + cdash4*MED_W + cdash5*LOW_V + cdash7*MED_W*LOW_V;
 DHIW_LOV = cdash1 + cdash4*HIGH_W + cdash5*LOW_V + cdash7*HIGH_W*LOW_V;
...
TLOW_LOV = ILOW_LOV + DLOW_LOV;
 TMEW_LOV = IMEW_LOV + DMEW_LOV;
 THIW_LOV = IHIW_LOV + DHIW_LOV;
...
PLOT(PLOW_LOV PMEW_LOV PHIW_LOV PLOW_MEV PMEW_MEV PHIW_MEV
 PLOW_HIV PMEW_HIV PHIW_HIV);
 LOOP(XVAL,-3,3,0.1);
 PLOW_LOV = ILOW_LOV*XVAL;
 PMEW_LOV = IMEW_LOV*XVAL;
 PHIW_LOV = IHIW_LOV*XVAL;
...

接下来是绘图部分，我们使用PLOT命令来指定需要绘制的图。PLOT中列出的是要绘制的变量，这些变量将在后面计算。然后我们用LOOP命令定义一个循环，让自变量X的值从-3到3，每次增加0.1。接下来，我们计算在不同X值和不同调节变量水平下的间接效应，用于绘图。例如，PLOW_LOV代表当W和V都处于低水平时，不同X值下的间接效应，它是ILOW_LOV乘以XVAL得到的。这里省略了中间的计算代码，我们对所有的条件间接效应进行了类似的计算。

代码解读13

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 V1 V2 V3 V4
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;
 Y BY Y1 Y2 Y3 Y4;
 W@1;  V@1;
MW | M XWITH W;
 MV | M XWITH V;
 XW | X XWITH W;
 XV | X XWITH V;
 WV | W XWITH V;
 MWV | M XWITH WV;
 XWV | X XWITH WV;
Y ON M (b1);
 Y ON MW (b2);
 Y ON MV (b3);
 Y ON MWV (b4);
 Y ON X(cdash1);
 Y ON W (cdash2);
 Y ON V (cdash3);
 Y ON XW (cdash4);
 Y ON XV (cdash5);
 Y ON WV (cdash6);
 Y ON XWV (cdash7);
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
 ILOW_LOV IMEW_LOV IHIW_LOV ILOW_MEV IMEW_MEV IHIW_MEV
 ILOW_HIV IMEW_HIV IHIW_HIV
 DLOW_LOV DMEW_LOV DHIW_LOV DLOW_MEV DMEW_MEV DHIW_MEV
 DLOW_HIV DMEW_HIV DHIW_HIV
 TLOW_LOV TMEW_LOV THIW_LOV TLOW_MEV TMEW_MEV THIW_MEV
 TLOW_HIV TMEW_HIV THIW_HIV);
LOW_W = -1;
 MED_W = 0;
 HIGH_W = 1;
 LOW_V = -1;
 MED_V = 0;
 HIGH_V = 1;
ILOW_LOV = a1*b1 + a3*b1*LOW_W + a1*b2*LOW_W + a3*b2*LOW_W*LOW_W +
 a1*b3*LOW_V + a3*b3*LOW_W*LOW_V + a1*b4*LOW_W*LOW_V +
 a3*b4*LOW_W*LOW_W*LOW_V;
 IMEW_LOV = a1*b1 + a3*b1*MED_W + a1*b2*MED_W + a3*b2*MED_W*MED_W +
 a1*b3*LOW_V + a3*b3*MED_W*LOW_V + a1*b4*MED_W*LOW_V +
 a3*b4*MED_W*MED_W*LOW_V;
 IHIW_LOV = a1*b1 + a3*b1*HIGH_W + a1*b2*HIGH_W + a3*b2*HIGH_W*HIGH_W +
 a1*b3*LOW_V + a3*b3*HIGH_W*LOW_V + a1*b4*HIGH_W*LOW_V +
 a3*b4*HIGH_W*HIGH_W*LOW_V;
...
DLOW_LOV = cdash1 + cdash4*LOW_W + cdash5*LOW_V + cdash7*LOW_W*LOW_V;
 DMEW_LOV = cdash1 + cdash4*MED_W + cdash5*LOW_V + cdash7*MED_W*LOW_V;
 DHIW_LOV = cdash1 + cdash4*HIGH_W + cdash5*LOW_V + cdash7*HIGH_W*LOW_V;
...
TLOW_LOV = ILOW_LOV + DLOW_LOV;
 TMEW_LOV = IMEW_LOV + DMEW_LOV;
 THIW_LOV = IHIW_LOV + DHIW_LOV;
...
PLOT(PLOW_LOV PMEW_LOV PHIW_LOV PLOW_MEV PMEW_MEV PHIW_MEV
 PLOW_HIV PMEW_HIV PHIW_HIV);
 LOOP(XVAL,-3,3,0.1);
 PLOW_LOV = ILOW_LOV*XVAL;
 PMEW_LOV = IMEW_LOV*XVAL;
 PHIW_LOV = IHIW_LOV*XVAL;
...
PLOT:
 TYPE = plot2;
OUTPUT:
 CINT;

最后，我们指定绘图类型为plot2。OUTPUT: CINT命令表示输出置信区间。这就完成了整个Mplus代码的解读。

资源汇总

• 本视频讲义地址: https://mlln.cn/mplus-model-templates/model71latent.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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