Mplus model11latent 模型讲解

来自图书《MPlus中介调节模型》

Mplus中介、调节和调节中介模型构建教程

• 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。本教程将手把手教你如何用Mplus构建包含中介、调节和调节中介效应的复杂模型。 我们会一步步讲解，从模型的理论基础开始，到数学公式的推导，再到Mplus代码的编写和结果解读。 本教程的结构非常清晰，首先我们会介绍模型的理论框架，让你理解这个模型在做什么，以及它背后的逻辑。 然后，我们会给出模型的数学表达式，让你了解模型的具体计算方法。接下来，我们会对关键的数学推导步骤进行讲解，帮助你理解模型的运行机制。最后，也是最重要的部分，我们会详细讲解Mplus代码的编写，并对代码中的每一行进行注释，让你能够轻松理解和修改代码。 本教程的代码是基于Hayes的PROCESS宏改编而来，并调整为Mplus的语法，方便大家使用。 请注意，本教程假设你已经具备一定的潜变量建模基础知识。 好了，让我们开始吧！

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对Y的影响，一部分是直接的，一部分是通过M间接实现的，这就是中介效应。

更复杂的是，W和Z会同时调节X对M的影响，也就是说，W和Z会改变X对M的影响强度。 它们不仅单独影响，还会互相影响，共同调节X对M的路径。

接下来，我们将一步步讲解如何用Mplus构建并分析这个模型。

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关系。

首先，我们有X，它是一个预测因子；Y，它是我们的结果变量；M，它是中介变量，X会影响M，而M又会影响Y。

此外，我们还有两个调节变量，W和Z。它们会影响X对M的影响，以及X对Y的间接影响。也就是说，W和Z会改变X影响M和Y的程度。

图中显示了X、W、Z如何直接影响M，以及它们之间的交互作用如何进一步影响M。X也直接影响Y。

最终，这个模型的目标就是分析W和Z对X影响M和Y的调节作用。 简单来说，就是看看W和Z是如何改变X对M和Y的影响的。

数学公式1

Y = b0 + b1M + c'X

这是我们的初始模型方程。Y是因变量，X是自变量，M是中介变量，b0, b1, c’是系数。

数学公式2

Y = b0 + b1M + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ

这是中介变量M的方程，其中X, W, Z是自变量，a0, a1, a2, a3, a4, a5, a6, a7是系数。

数学公式3

Y = b0 + b1M + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + c'X

将M的方程代入Y的方程。

数学公式4

Y = b0 + b1M + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c'X

展开括号，得到Y关于X, W, Z的表达式。

数学公式5

Y = b0 + b1M + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + c')X

整理成Y = a + bX的形式，方便分析X对Y的影响。

数学公式6

Y = b0 + b1M + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + c')X
X 对 Y 的间接效应 (在 W, Z 条件下)： a1b1 + a4b1W + a5b1Z + a7b1WZ = (a1 + a4W + a5Z + a7WZ)b1

这就是X对Y的间接效应，它通过中介变量M发挥作用，并且受到W和Z的影响。

数学公式7

Y = b0 + b1M + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + c')X
X 对 Y 的间接效应 (在 W, Z 条件下)： a1b1 + a4b1W + a5b1Z + a7b1WZ = (a1 + a4W + a5Z + a7WZ)b1
X 对 Y 的直接效应： c'

这是X对Y的直接效应，不经过中介变量M。

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，我们定义了分析中用到的所有变量。X1到X4是自变量X的四个指标，M1到M4是中介变量M的指标，以此类推，Y是因变量。

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。我们使用一般随机效应模型，采用最大似然估计法，并用数值积分算法处理潜在变量。

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;

这里定义了测量模型，将潜在变量X、M、W、Z、Y与它们的观测指标连接起来。注意，W1和Z1后面加了星号，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;

这一步再次明确固定W和Z的方差为1，确保它们是标准化的。

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;

我们定义了潜在变量之间的交互项，例如XW表示X和W的交互作用，这体现了调节效应。

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

这是结构模型部分，定义了潜在变量之间的回归关系。例如，Y对M的回归系数命名为b1，X对Y的直接效应命名为cdash。

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 (cdash); 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; ...

接下来是模型约束。我们定义了新的参数，代表调节变量W和Z的不同水平（低、中、高），分别赋值为-1, 0, 1。

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 (cdash); 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; ...

这一部分计算在不同调节变量水平下的条件间接效应。公式中包含了各个路径系数和调节变量的取值。

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 (cdash); 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; ...
TLOW_LOZ = ILOW_LOZ + cdash; ...

这里计算条件总效应，它是条件间接效应和直接效应的总和。

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 (cdash); 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; ...
TLOW_LOZ = ILOW_LOZ + cdash; ...
PLOT(PLOW_LOZ PMEW_LOZ PHIW_LOZ ...); LOOP(XVAL,-3,3,0.1); PLOW_LOZ = ILOW_LOZ*XVAL; ... PLOT: TYPE = plot2;

最后，我们定义了要绘制的图形，并通过循环计算不同X值下的条件间接效应，最后指定绘图类型为plot2。

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 (cdash); 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; ...
TLOW_LOZ = ILOW_LOZ + cdash; ...
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，我们要求Mplus输出置信区间。

资源汇总

• 本视频讲义地址: https://mlln.cn/mplus-model-templates/model11latent.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！