Mplus model12latent 模型讲解

来自图书《MPlus中介调节模型》

Mplus中介调节模型分析教程

• 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软件构建和分析包含中介变量和调节变量的复杂模型。本教程将系统地讲解这个模型，帮助大家掌握Mplus的高级统计分析技巧。

首先，我们将从理论模型入手，理解中介效应和调节效应的定义以及它们在该模型中的相互作用。 然后，我们会深入探讨模型的数学表达形式，用公式清晰地展现自变量、中介变量、调节变量和因变量之间的关系。

接下来，我们将逐步推导模型的数学公式，帮助大家理解模型的逻辑和计算过程。 这部分会比较细致，大家可以根据自身需要选择性地学习。

最后，我们将重点讲解Mplus的代码，并逐行解释代码的含义。 通过代码示例，大家可以快速上手，并应用到自己的研究中。

希望通过本教程的学习，大家能够熟练掌握Mplus在中介调节模型分析中的应用。如有任何问题，欢迎随时与我联系。谢谢！

理论模型

我们来看这张图，它展示了一个比较复杂的模型。这里面，X是我们的自变量，Y是因变量，M是中介变量，W和Z是调节变量。 X不仅直接影响Y，还通过M间接影响Y。 同时，W和Z会影响X对M的影响，以及X对Y的直接影响。 箭头表示变量之间的因果关系，例如，X指向M表示X影响M。这个模型考虑了各种交互作用，例如X和W的交互作用，X和Z的交互作用，甚至还有X、W和Z的三重交互作用。 我们接下来会一步步地解释这个模型的数学表达和Mplus代码。

数学模型

这张图展示的是一个比较复杂的模型，它包含了几个关键变量。

首先，X是我们的自变量，它会影响到中介变量M。

M是中介变量，它在X和Y之间起桥梁作用。

Y是我们的因变量，我们想要研究X对Y的影响。

W和Z是两个调节变量，它们会影响X对M和Y的影响。

图中箭头表示变量之间的关系，箭头旁的字母代表具体的路径系数，也就是影响的大小和方向。

这个模型能够帮助我们分析X对Y的总效应，以及X对Y的直接和间接效应（通过M）。更重要的是，它还能考察W和Z对X影响M和Y的调节作用。

数学公式1

Y = b0 + b1M + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ

这是我们的模型方程式，Y是因变量，M是中介变量，X是自变量，W和Z是调节变量。 b0, b1, c1’, c2’, c3’, c4’, c5’, c6’, c7’ 都是待估计的系数。

数学公式2

Y = b0 + b1M + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ

这是中介变量M的表达式，它由自变量X和调节变量W, Z及其交互项决定。 a0, a1, a2, a3, a4, a5, a6, a7 都是待估计的系数。

数学公式3

Y = b0 + b1M + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ

将M的表达式代入Y的表达式，这是将中介变量整合到模型中的关键步骤。

数学公式4

Y = b0 + b1M + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ

展开括号，以便后续合并同类项。

数学公式5

Y = b0 + b1M + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + c2'W + c3'Z + c6'WZ) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + c1' + c4'W + c5'Z + c7'WZ)X

合并同类项，将公式整理成Y = a + bX的形式，以便更清晰地分析X对Y的影响。

数学公式6

Y = b0 + b1M + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + c2'W + c3'Z + c6'WZ) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + c1' + c4'W + c5'Z + c7'WZ)X
(a1 + a4W + a5Z + a7WZ)b1

这是X对Y的条件间接效应，它受到W和Z的调节。 注意，这个效应的大小取决于W和Z的值。

数学公式7

Y = b0 + b1M + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + c2'W + c3'Z + c6'WZ) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + c1' + c4'W + c5'Z + c7'WZ)X
(a1 + a4W + a5Z + a7WZ)b1
c1' + c4'W + c5'Z + c7'WZ

这是X对Y的条件直接效应，同样也受到W和Z的调节。 这部分效应不受中介变量M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 Y1 Y2 Y3 Y4;

首先，我们用USEVARIABLES语句声明所有要分析的变量。X1到X4、M1到M4、W1到W4、Z1到Z4以及Y1到Y4分别代表五个潜变量X、M、W、Z和Y的测量指标。这些变量是我们模型的基础。

代码解读2

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

接下来，进入分析设置部分。我们选择广义随机效应模型（TYPE = GENERAL RANDOM），使用极大似然估计法（ESTIMATOR = ML），并采用积分算法（ALGORITHM = INTEGRATION）进行计算。

代码解读3

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;

现在，我们定义模型。这里定义了五个潜变量X、M、W、Z和Y的测量模型。’BY’语句指定了每个潜变量对应的测量指标。其中，W和Z的方差被固定为1，表示标准化处理。

代码解读4

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;
XW | X XWITH W;
XZ | X XWITH Z;
WZ | W XWITH Z;
XWZ | X XWITH WZ;

这一部分定义了潜变量之间的交互作用。’XWITH’表示两个潜变量之间的交互作用，例如XW表示X和W的交互作用，XWZ表示X、W和Z的交互作用。

代码解读5

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;
XW | X XWITH W;
XZ | X XWITH Z;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON X (cdash1); ... Y ON XWZ (cdash7);

这里定义了结果变量Y与其他变量的关系。例如，’Y ON M (b1)’表示Y受M的影响，b1是路径系数。后面类似地定义了Y与其他变量及其交互项的关系。

代码解读6

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;
XW | X XWITH W;
XZ | X XWITH Z;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON X (cdash1); ... Y ON XWZ (cdash7);
M ON X (a1);
M ON W (a2); ... M ON XWZ (a7);

同样，这里定义了中介变量M与其他变量及其交互项的关系。例如，’M ON X (a1)’表示M受X的影响，a1是路径系数。

代码解读7

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;
XW | X XWITH W;
XZ | X XWITH Z;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON X (cdash1); ... Y ON XWZ (cdash7);
M ON X (a1);
M ON W (a2); ... M ON XWZ (a7);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z ...);
LOW_W = -1; MED_W = 0; HIGH_W = 1; ...

接下来，我们进行模型约束，计算条件间接效应。首先，定义新的参数，代表调节变量W和Z的不同水平（例如，低、中、高）。

代码解读8

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;
XW | X XWITH W;
XZ | X XWITH Z;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON X (cdash1); ... Y ON XWZ (cdash7);
M ON X (a1);
M ON W (a2); ... M ON XWZ (a7);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z ...);
LOW_W = -1; MED_W = 0; HIGH_W = 1; ...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z; ...

这一部分计算不同条件下的条件间接效应。例如，’ILOW_LOZ’计算的是在W和Z都处于低水平时的条件间接效应，它通过将结构方程中的路径系数代入计算得到。

代码解读9

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;
XW | X XWITH W;
XZ | X XWITH Z;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON X (cdash1); ... Y ON XWZ (cdash7);
M ON X (a1);
M ON W (a2); ... M ON XWZ (a7);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z ...);
LOW_W = -1; MED_W = 0; HIGH_W = 1; ...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z; ...
DLOW_LOZ = cdash1 + cdash4*LOW_W + cdash5*LOW_Z + cdash7*LOW_W*LOW_Z; ...

类似地，这里计算不同条件下的条件直接效应。

代码解读10

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;
XW | X XWITH W;
XZ | X XWITH Z;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON X (cdash1); ... Y ON XWZ (cdash7);
M ON X (a1);
M ON W (a2); ... M ON XWZ (a7);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z ...);
LOW_W = -1; MED_W = 0; HIGH_W = 1; ...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z; ...
DLOW_LOZ = cdash1 + cdash4*LOW_W + cdash5*LOW_Z + cdash7*LOW_W*LOW_Z; ...
TLOW_LOZ = ILOW_LOZ + DLOW_LOZ; ...

这里计算不同条件下的条件总效应，它是条件间接效应和条件直接效应的总和。

代码解读11

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;
XW | X XWITH W;
XZ | X XWITH Z;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON X (cdash1); ... Y ON XWZ (cdash7);
M ON X (a1);
M ON W (a2); ... M ON XWZ (a7);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z ...);
LOW_W = -1; MED_W = 0; HIGH_W = 1; ...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z; ...
DLOW_LOZ = cdash1 + cdash4*LOW_W + cdash5*LOW_Z + cdash7*LOW_W*LOW_Z; ...
TLOW_LOZ = ILOW_LOZ + DLOW_LOZ; ...
PLOT(...);
LOOP(XVAL,-3,3,0.1);
PLOW_LOZ = ILOW_LOZ*XVAL; ...

最后，我们定义绘图部分，通过循环计算不同X值下不同条件的间接效应，并绘制图形来展示结果。

代码解读12

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;
XW | X XWITH W;
XZ | X XWITH Z;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON X (cdash1); ... Y ON XWZ (cdash7);
M ON X (a1);
M ON W (a2); ... M ON XWZ (a7);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z ...);
LOW_W = -1; MED_W = 0; HIGH_W = 1; ...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z; ...
DLOW_LOZ = cdash1 + cdash4*LOW_W + cdash5*LOW_Z + cdash7*LOW_W*LOW_Z; ...
TLOW_LOZ = ILOW_LOZ + DLOW_LOZ; ...
PLOT(...);
LOOP(XVAL,-3,3,0.1);
PLOW_LOZ = ILOW_LOZ*XVAL; ...
PLOT: TYPE = plot2;
OUTPUT: CINT;

设置绘图类型为plot2，并输出置信区间。

资源汇总

• 本视频讲义地址: https://mlln.cn/mplus-model-templates/model12latent.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

感谢大家的收看！ 本节课的资源已全部提供，请大家点击页面上的链接下载或查看。 希望这份资料对大家的学习有所帮助，也欢迎大家点赞收藏，方便日后查阅！