Mplus model69latent 模型讲解

来自图书《MPlus中介调节模型》

使用Mplus进行复杂模型分析：中介、调节与调节中介模型

• 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。这个PPT页面概述了我们今天要学习的内容。 首先，我们会讲解模型的理论基础，解释中介、调节和调节中介效应的概念，以及它们在研究中的应用。 然后，我们将建立相应的数学模型，用公式清晰地表达模型中变量之间的关系。 接着，我们会逐步推导模型中的各种效应，例如直接效应、间接效应以及条件间接效应，为Mplus代码的理解打下基础。 最后，我们将详细解读Mplus代码，解释每一行代码的功能，以及如何使用Mplus软件拟合模型并进行结果解读。 通过本教程，您将掌握使用Mplus分析复杂模型的完整流程。

理论模型

我们来看这张图，它展示了一个复杂的调节中介模型。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。 可以看到，X直接影响M，M直接影响Y，X也直接影响Y。 更重要的是，W和Z分别调节X对M的影响，以及X对Y的直接影响。 而且，W和Z之间还有交互作用，它们与X一起，共同调节X对M和X对Y的影响。 箭头表示变量之间的因果关系，箭头的粗细不代表影响力的大小。 接下来，我们将用数学模型来更精确地描述这些关系。

数学模型

这张图展示的是一个比较复杂的模型，用来分析变量之间相互影响的关系。 我们来看一下图中都有哪些变量：X代表自变量，Y代表因变量，M是中介变量，W和Z是调节变量。

X对M有直接影响，同时X与W和Z的组合也会影响M。 M对Y也有直接影响，而且M与W的组合也会影响Y。 X对Y也有直接影响，X与W和Z的组合同样会影响Y。

这个模型考虑了各种可能性，包括X、W、Z对M和Y的直接和间接影响，以及它们之间的交互作用，能够帮助我们更全面地了解变量之间的关系，分析各种效应。

数学公式1

Y = b0 + b1M + b2MW + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ

这是我们的基本模型方程。Y是因变量，M是中介变量，X是自变量，W和Z是调节变量。第一个方程描述了Y如何受到M、X、W和Z的影响，第二个方程描述了M如何受到X、W和Z的影响。

数学公式2

Y = b0 + b1M + b2MW + 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) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)W + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ

将第二个方程代入第一个方程，以便我们能够分析X对Y的总效应。

数学公式3

Y = b0 + b1M + b2MW + 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) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)W + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + a0b2W + a1b2XW + a2b2WW + a3b2ZW + a4b2XWW + a5b2XZW + a6b2WWZ + a7b2XWWZ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ

展开括号，使公式更容易理解和整理。

数学公式4

Y = b0 + b1M + b2MW + 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) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)W + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + a0b2W + a1b2XW + a2b2WW + a3b2ZW + a4b2XWW + a5b2XZW + a6b2WWZ + a7b2XWWZ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + a0b2W + a2b2WW + a3b2ZW + a6b2WWZ + c2'W + c3'Z + c6'WZ) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b2W + a4b2WW + a5b2ZW + a7b2WWZ + c1' + c4'W + c5'Z + c7'WZ)X

将公式整理成Y = a + bX的形式，其中a和b是包含W和Z的表达式。

数学公式5

Y = b0 + b1M + b2MW + 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) + b2(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)W + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + a0b2W + a1b2XW + a2b2WW + a3b2ZW + a4b2XWW + a5b2XZW + a6b2WWZ + a7b2XWWZ + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + a0b2W + a2b2WW + a3b2ZW + a6b2WWZ + c2'W + c3'Z + c6'WZ) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b2W + a4b2WW + a5b2ZW + a7b2WWZ + c1' + c4'W + c5'Z + c7'WZ)X
X对Y的一个间接效应（以W，Z为条件）：(a1 + a4W + a5Z + a7WZ)(b1 + b2W)
X对Y的一个直接效应（以W，Z为条件）：c1' + c4'W + c5'Z + c7'WZ

最终结果：X对Y的间接效应和直接效应。间接效应表示X通过M对Y的影响，直接效应表示X对Y的直接影响，两者都受到W和Z的调节。

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，我们定义一下要使用的变量。X1到X4，M1到M4，依次类推，这些都是我们观测到的变量，它们对应着五个潜变量：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;

接下来是分析设定。我们选择一般随机效应模型，使用最大似然法进行估计，并用积分法处理潜变量。

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;

这里是模型的定义。我们把观测变量与对应的潜变量关联起来，例如X1到X4对应潜变量X。注意，W1和Z1前面有个星号，表示它们的因子载荷固定为1，用于标准化潜变量W和Z。

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;

这一步固定W和Z的方差为1，完成标准化。

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;
WZ | W XWITH Z;
XWZ | X XWITH WZ;

我们定义潜变量之间的交互作用项。例如，MW表示M和W的交互作用，XWITH表示生成交互项。这里考虑了多种潜变量间的交互作用。

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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1); ... Y ON XWZ (cdash7);

这是Y的回归方程，展示了Y与其他潜变量及其交互作用之间的关系。b1, cdash1等代表路径系数。

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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1); ... Y ON XWZ (cdash7);
M ON X (a1); ... M ON XWZ (a7);

这是M的回归方程，展示了M与其他潜变量及其交互作用之间的关系。a1到a7代表路径系数。

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;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1); ... Y ON XWZ (cdash7);
M ON X (a1); ... 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; ...

这里我们开始定义模型约束，主要是为了计算条件间接效应。我们定义了W和Z的低、中、高三个水平，并用数字表示。

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;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1); ... Y ON XWZ (cdash7);
M ON X (a1); ... 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 + ...; ... IHIW_HIZ = ...;

接下来，根据模型，我们计算不同调节变量组合下的条件间接效应。这些公式根据模型计算出间接效应。

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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1); ... Y ON XWZ (cdash7);
M ON X (a1); ... 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 + ...; ... IHIW_HIZ = ...;
DLOW_LOZ = ...; ... DHIW_HIZ = ...;
TLOW_LOZ = ...; ... THIW_HIZ = ...;

同理，我们计算条件直接效应和条件总效应。

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;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1); ... Y ON XWZ (cdash7);
M ON X (a1); ... 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 + ...; ... IHIW_HIZ = ...;
DLOW_LOZ = ...; ... DHIW_HIZ = ...;
TLOW_LOZ = ...; ... THIW_HIZ = ...;
PLOT(...);
LOOP(XVAL,-3,3,0.1); ...

最后，我们指定要绘制的变量，并设置循环，以便画出条件间接效应的图形。

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;
MW | M XWITH W;
XW | X XWITH W;
XZ | X XWITH Z;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1); ... Y ON XWZ (cdash7);
M ON X (a1); ... 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 + ...; ... IHIW_HIZ = ...;
DLOW_LOZ = ...; ... DHIW_HIZ = ...;
TLOW_LOZ = ...; ... THIW_HIZ = ...;
PLOT(...);
LOOP(XVAL,-3,3,0.1); ...
PLOT: TYPE = plot2;
OUTPUT: CINT;

指定绘图类型和输出置信区间。

资源汇总

• 本视频讲义地址: https://mlln.cn/mplus-model-templates/model69latent.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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