Mplus model63latent 模型讲解

来自图书《MPlus中介调节模型》

调节中介模型（含双调节变量）的Mplus实现

• 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。本节课我们将学习如何使用Mplus构建一个复杂的调节中介模型。这个模型包含一个或多个中介变量，以及两个调节变量，这两个调节变量会同时影响自变量和中介变量之间的关系，以及自变量和因变量之间的直接关系。更进一步，其中一个调节变量还会影响中介变量和因变量之间的关系。 我们将从理论模型开始，逐步讲解模型的数学表达，推导关键公式，并最终通过Mplus代码实现模型的构建和参数估计。 我们会详细解释代码的每一部分，并展示如何计算和可视化条件间接效应、条件直接效应以及条件总效应。 本教程的代码可以直接复制粘贴到Mplus中运行，但是请务必根据您自己的数据修改变量名称和数量。 让我们一起开始学习吧！

理论模型

我们来看这张图，它展示了我们今天要讨论的调节中介模型。 模型中，X是自变量，Y是因变量，M是中介变量，W和Z是两个调节变量。箭头代表变量之间的影响关系。比如，X会直接影响M，也会直接影响Y；M会影响Y；而W和Z则分别调节X对M、X对Y以及M对Y的影响。 这个模型比较复杂，因为它不仅包含中介效应，还考虑了两个调节变量对各个路径的调节作用，我们将逐步讲解如何用Mplus来分析它。

数学模型

这张图展示了一个比较复杂的模型，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，而W和Z会调节X对M的影响。 X和W的交互项XW，以及X和Z的交互项XZ，也会进一步影响M。

M会直接影响Y，W也会直接影响Y，并且M和W的交互项MW也会影响Y。

此外，X也会直接影响Y，W和Z也会直接影响Y，XW和XZ也会直接影响Y。

总而言之，这个模型展示了X对Y的影响是如何通过M进行中介的，并且这个过程同时受到W和Z的调节。 模型中包含了直接效应、间接效应以及多种调节效应。

数学公式1

Y = b0 + b1M + b2MW + c1'X + c2'W + c3'Z + c4'XW + c5'XZ

这是我们的初始模型方程，其中Y是因变量，X是自变量，M, W, Z是中介变量和调节变量。

数学公式2

Y = b0 + b1M + b2MW + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ

这是中介变量M的方程，它受到自变量X以及其他变量W和Z的影响。

数学公式3

Y = b0 + b1M + b2MW + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + c1'X + c2'W + c3'Z + c4'XW + c5'XZ

将第二个方程代入第一个方程，得到一个包含X,W,Z的复合方程。

数学公式4

Y = b0 + b1M + b2MW + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2W + a1b2XW + a2b2WW + a3b2ZW + a4b2XWW + a5b2XZW + c1'X + c2'W + c3'Z + c4'XW + c5'XZ

展开括号，得到一个更复杂的方程。

数学公式5

Y = b0 + b1M + b2MW + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2W + a1b2XW + a2b2WW + a3b2ZW + a4b2XWW + a5b2XZW + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = (b0 + a0b1 + a2b1W + a3b1Z + a0b2W + a2b2WW + a3b2ZW + c2'W + c3'Z) + (a1b1 + a4b1W + a5b1Z + a1b2W + a4b2WW + a5b2ZW + c1' + c4'W + c5'Z)X

整理合并同类项，使方程符合Y = a + bX的形式，以便分析X对Y的影响。

数学公式6

Y = b0 + b1M + b2MW + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2W + a1b2XW + a2b2WW + a3b2ZW + a4b2XWW + a5b2XZW + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = (b0 + a0b1 + a2b1W + a3b1Z + a0b2W + a2b2WW + a3b2ZW + c2'W + c3'Z) + (a1b1 + a4b1W + a5b1Z + a1b2W + a4b2WW + a5b2ZW + c1' + c4'W + c5'Z)X
(a1 + a4W + a5Z)(b1 + b2W)

这是X对Y的条件间接效应，它取决于W和Z的取值。

数学公式7

Y = b0 + b1M + b2MW + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ)W + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a0b2W + a1b2XW + a2b2WW + a3b2ZW + a4b2XWW + a5b2XZW + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = (b0 + a0b1 + a2b1W + a3b1Z + a0b2W + a2b2WW + a3b2ZW + c2'W + c3'Z) + (a1b1 + a4b1W + a5b1Z + a1b2W + a4b2WW + a5b2ZW + c1' + c4'W + c5'Z)X
(a1 + a4W + a5Z)(b1 + b2W)
c1' + c4'W + c5'Z

这是X对Y的条件直接效应，同样取决于W和Z的取值。

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，我们定义了模型中用到的所有变量。X1到X4测量潜在变量X，以此类推，Y1到Y4测量潜在变量Y。W和Z是调节变量。

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;

接下来是分析设置。我们使用广义随机效应模型，采用最大似然估计法，并使用数值积分来处理潜在变量。

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;

这里我们定义了测量模型，将观测变量与对应的潜在变量联系起来。注意，W和Z的第一个指标后有星号，表示它们的方差固定为1，也就是标准化。

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;

这一行再次明确固定W和Z的方差为1，保证它们是标准化变量。

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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;

这里定义了潜在变量的交互项，例如MW表示M和W的交互作用。这部分体现了调节效应。

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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON MW (b2);
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);

这是结构模型，描述了潜在变量之间的关系，并为路径参数命名，例如b1代表M对Y的直接效应。

代码解读7

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4
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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON MW (b2);
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_W = -1; MED_W = 0; HIGH_W = 1; ...

模型约束部分。我们定义了新的参数，用于存储计算结果，并设定调节变量W和Z的低、中、高三个水平。

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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON MW (b2);
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_W = -1; MED_W = 0; HIGH_W = 1; ...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + ...;
IMEW_LOZ = a1*b1 + a4*b1*MED_W + ...; ...

这一部分是关键，它根据模型计算在不同调节变量水平下的条件间接效应（ILOW_LOZ，IMEW_LOZ等等）。公式基于模型参数推导而来。

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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON MW (b2);
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_W = -1; MED_W = 0; HIGH_W = 1; ...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + ...;
IMEW_LOZ = a1*b1 + a4*b1*MED_W + ...; ...
DLOW_LOZ = ...; DMEW_LOZ = ...; ...
TLOW_LOZ = ...; TMEW_LOZ = ...; ...

类似地，我们计算条件直接效应（DLOW_LOZ等）和条件总效应（TLOW_LOZ等）。

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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON MW (b2);
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_W = -1; MED_W = 0; HIGH_W = 1; ...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + ...;
IMEW_LOZ = a1*b1 + a4*b1*MED_W + ...; ...
DLOW_LOZ = ...; DMEW_LOZ = ...; ...
TLOW_LOZ = ...; TMEW_LOZ = ...; ...
PLOT(PLOW_LOZ PMEW_LOZ PHIW_LOZ ...);
LOOP(XVAL,-3,3,0.1);
PLOW_LOZ = ILOW_LOZ*XVAL; ...

最后，我们指定绘图，并使用循环来计算不同X值下的条件间接效应，以便绘制曲线图。

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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON MW (b2);
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_W = -1; MED_W = 0; HIGH_W = 1; ...
ILOW_LOZ = a1*b1 + a4*b1*LOW_W + ...;
IMEW_LOZ = a1*b1 + a4*b1*MED_W + ...; ...
DLOW_LOZ = ...; DMEW_LOZ = ...; ...
TLOW_LOZ = ...; TMEW_LOZ = ...; ...
PLOT(PLOW_LOZ PMEW_LOZ PHIW_LOZ ...);
LOOP(XVAL,-3,3,0.1);
PLOW_LOZ = ILOW_LOZ*XVAL; ...
OUTPUT: CINT;

最后，我们要求输出置信区间。

资源汇总

• 本视频讲义地址: https://mlln.cn/mplus-model-templates/model63latent.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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