Mplus model13latent 模型讲解

来自图书《MPlus中介调节模型》

复杂模型的Mplus代码详解：包含中介、调节与调节中介效应

• 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构建一个复杂的模型，这个模型包含中介效应、调节效应，以及两者共同作用的调节中介效应。 本教程会涵盖模型的各个方面，从理论基础到实际操作。

首先，我们会讲解模型的理论框架，帮助大家理解模型中各个变量之间的关系。然后，我们会深入探讨模型的数学模型，以及相关的公式和推导过程。 这部分内容会对模型的原理进行详细阐述，让大家对模型有更深刻的认识。

接下来，我们将逐步拆解Mplus代码，讲解每一段代码的功能和作用，让大家能够轻松上手。最后，我们会演示如何利用Mplus的模型约束功能来计算和绘制图表，直观地展现不同调节变量水平下，条件间接效应的变化情况。

本教程旨在提供一个快速参考，方便大家查找和使用相关的Mplus代码。如果您需要更深入的统计咨询，请随时联系Data Sense。谢谢大家！

理论模型

我们来看这个模型图，它展示了一个复杂的关系网络。X是自变量，Y是因变量，M是中介变量，W和Z是调节变量。

X会影响Y，但这种影响一部分是通过M间接实现的，这就是中介效应。 同时，W和Z会改变X对M的影响，这就是调节效应。 而且，W还会直接影响X对Y的影响。 图中还考虑了各个变量间的交互作用，例如XW、XZ、WZ和XWZ，这让我们能够更全面地分析不同情况下的效应变化。箭头表示变量间的影响方向。

数学模型

这张图展示的是一个复杂的统计模型，它包含了自变量X、中介变量M、因变量Y，以及两个调节变量W和Z。

X会直接影响M（路径a1），W和Z也会分别直接影响M（路径a2和a3）。 X和W的交互作用（XW）、X和Z的交互作用（XZ）、W和Z的交互作用（WZ），以及X、W和Z的三重交互作用（XWZ）都会影响M（路径a4、a5、a6和a7）。

M会直接影响Y（路径b），X也会直接影响Y（路径c1’），W也会直接影响Y（路径c2’），X和W的交互作用（XW）也会直接影响Y（路径c3’）。

这个模型展示了X对Y的直接和间接影响（通过M），以及W和Z如何调节这种影响，从而形成调节中介效应。 箭头表示影响的方向，字母代表路径系数，我们会在后续的代码讲解中详细分析这些系数。

数学公式1

Y = b0 + b1M + c1'X + c2'W + c3'XW

这是我们的初始模型，Y是因变量，M是中介变量，X是自变量，W是控制变量

数学公式2

Y = b0 + b1M + c1'X + c2'W + c3'XW
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ

这是中介变量M的模型，它受X，W，Z以及它们的交互作用影响。

数学公式3

Y = b0 + b1M + c1'X + c2'W + c3'XW
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'XW

将M的公式代入Y的公式。

数学公式4

Y = b0 + b1M + c1'X + c2'W + c3'XW
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'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c1'X + c2'W + c3'XW

展开括号，得到Y关于X, W, Z的表达式。

数学公式5

Y = b0 + b1M + c1'X + c2'W + c3'XW
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'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + c2'W) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + c1' + c3'W)X

将公式整理成Y = a + bX的形式，其中a和b是X,W,Z的函数。

数学公式6

Y = b0 + b1M + c1'X + c2'W + c3'XW
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'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + c2'W) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + c1' + c3'W)X
条件于W, Z的X对Y的间接效应：
a1b1 + a4b1W + a5b1Z + a7b1WZ = (a1 + a4W + a5Z + a7WZ)b1

这是X对Y的间接效应，通过中介变量M实现，并且受W和Z的影响。

数学公式7

Y = b0 + b1M + c1'X + c2'W + c3'XW
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'XW
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + c2'W) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + c1' + c3'W)X
条件于W, Z的X对Y的间接效应：
a1b1 + a4b1W + a5b1Z + a7b1WZ = (a1 + a4W + a5Z + a7WZ)b1
条件于W的X对Y的直接效应：
c1' + c3'W

这是X对Y的直接效应，不受中介变量M的影响，但受W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;

第一步，我们先定义要用到的变量。X1到X4，M1到M4，W1到W4，Z1到Z4，以及Y1到Y4，这些都是我们观察到的变量，它们分别对应着我们模型中的五个潜在变量：X，M，W，Z和Y。

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;

第二步，设置分析类型。我们使用一般随机效应模型，估计方法采用最大似然估计，并使用数值积分算法，这是因为我们的模型包含了潜在变量。

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;

第三步，定义测量模型。这里我们指定了每个潜在变量是如何通过其对应的观察变量来测量的。注意，W1和Z1前面加了星号，表示它们的方差被固定为1，这是一种标准化潜在变量的方法。

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;

这里进一步明确固定W和Z的方差为1，确保模型识别。

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;

第五步，创建潜在变量的交互项。XWITH运算符用于创建交互项，例如XW代表X和W的交互作用。我们这里包含了X和W，X和Z，W和Z，以及X,W,Z的三阶交互作用。

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 W (cdash2); Y ON XW (cdash3);

第六步，定义Y的回归方程。Y受M，X，W以及X和W的交互项XW的影响。括号里的b1, cdash1, cdash2, cdash3是路径系数的名称。

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 W (cdash2); Y ON XW (cdash3);
M ON X (a1); M ON W (a2); M ON Z (a3); M ON XW (a4); M ON XZ (a5); M ON WZ (a6); M ON XWZ (a7);

第七步，定义M的回归方程。M受X，W，Z以及它们的各种交互项的影响。 a1到a7是路径系数的名称。

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 W (cdash2); Y ON XW (cdash3);
M ON X (a1); M ON W (a2); M ON Z (a3); M ON XW (a4); M ON XZ (a5); M ON WZ (a6); 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; ...

第八步，开始定义模型约束。我们定义了一系列新的参数，用于存储之后计算得到的不同条件下的间接效应和直接效应。

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 W (cdash2); Y ON XW (cdash3);
M ON X (a1); M ON W (a2); M ON Z (a3); M ON XW (a4); M ON XZ (a5); M ON WZ (a6); 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; ...

第九步，计算在不同调节变量水平下的条件间接效应。这些公式是根据我们模型的结构推导出来的。

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 W (cdash2); Y ON XW (cdash3);
M ON X (a1); M ON W (a2); M ON Z (a3); M ON XW (a4); M ON XZ (a5); M ON WZ (a6); 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; ...
DIR_LOWW = cdash1 + cdash3*LOW_W; ...; TLOW_LOZ = ILOW_LOZ + DIR_LOWW; ...

第十步，计算条件直接效应和条件总效应。条件总效应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 W (cdash2); Y ON XW (cdash3);
M ON X (a1); M ON W (a2); M ON Z (a3); M ON XW (a4); M ON XZ (a5); M ON WZ (a6); 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; ...
DIR_LOWW = cdash1 + cdash3*LOW_W; ...; TLOW_LOZ = ILOW_LOZ + DIR_LOWW; ...
PLOT(PLOW_LOZ PMEW_LOZ PHIW_LOZ ...); LOOP(XVAL,-3,3,0.1); PLOW_LOZ = ILOW_LOZ*XVAL; ...

第十一步，定义绘图。我们将绘制条件间接效应随自变量X变化的曲线图，并在不同调节变量水平下分别显示。

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 W (cdash2); Y ON XW (cdash3);
M ON X (a1); M ON W (a2); M ON Z (a3); M ON XW (a4); M ON XZ (a5); M ON WZ (a6); 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; ...
DIR_LOWW = cdash1 + cdash3*LOW_W; ...; TLOW_LOZ = ILOW_LOZ + DIR_LOWW; ...
PLOT(PLOW_LOZ PMEW_LOZ PHIW_LOZ ...); LOOP(XVAL,-3,3,0.1); PLOW_LOZ = ILOW_LOZ*XVAL; ...
PLOT: TYPE = plot2; OUTPUT: CINT;

最后一步，指定绘图类型为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/model13latent.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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