Mplus model23latent 模型讲解

来自图书《MPlus中介调节模型》

Mplus中介、调节和调节中介效应模型构建教程

• 理论模型
• 数学模型
• 数学推导
• Mplus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构建复杂的包含中介、调节和调节中介效应的模型。 我们会以一个包含一个潜在自变量、一个潜在中介变量和三个潜在调节变量的复杂模型为例，进行详细讲解。 我们会逐步讲解理论模型、数学模型，以及关键的数学推导过程，让你彻底理解模型背后的逻辑。 当然，教程的重点是Mplus代码的解读，我会逐行解释代码的含义，帮助大家理解参数的设置和结果的解读。 最后，我们会展示如何计算在不同调节变量组合下的条件间接效应和总效应，并利用Mplus的绘图功能直观地展现结果。 这个教程就像一个Mplus建模的速查手册，你可以根据自己的需要直接查阅相关部分。 希望这个教程能帮助大家更好地运用Mplus进行数据分析。如有任何问题，欢迎联系Data Sense寻求帮助。

理论模型

我们来看这个模型图。它展示了一个比较复杂的调节中介模型。 X是自变量，Y是因变量，M是中介变量，W、Z、V是调节变量。 箭头表示变量之间的关系，比如X影响M，M影响Y，X也直接影响Y。 更重要的是，W、Z会调节X对M的影响，V会调节M对Y的影响，模型会分析X对Y的总效应和间接效应，以及这些调节变量对效应的影响。 接下来，我们将深入讲解这个模型的数学模型和Mplus代码。

数学模型

这张图展示了我们今天要分析的模型，它包含了中介效应和调节效应。 X是我们的自变量，Y是因变量，M是中介变量，它连接了X和Y。 W、Z和V是我们的调节变量，它们分别会影响X对M的影响，以及M对Y的影响。 XW、XZ和MV是交互项，它们也影响着M对Y的影响。 简单来说，这个模型研究的是X如何通过M影响Y，以及W、Z、V这三个调节变量是如何改变这种影响的。

数学公式1

Y = b0 + b1M + b2V + b3MV + c'X

这是我们的模型方程，其中Y是因变量，M和V是自变量，X是另一个影响M的变量，c’X代表X对Y的直接效应。

数学公式2

Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ

这是M的表达式，它受到X, W, Z的影响。

数学公式3

Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c'X

将M的表达式代入Y的表达式。

数学公式4

Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + a0b3V + a1b3XV + a2b3VW + a3b3ZV + a4b3XVW + a5b3XZV + c'X

展开括号。

数学公式5

Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + a0b3V + a1b3XV + a2b3VW + a3b3ZV + a4b3XVW + a5b3XZV + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + b2V + a0b3V + a2b3VW + a3b3ZV) + (a1b1 + a4b1W + a5b1Z + a1b3V + a4b3VW + a5b3ZV + c')X

合并同类项，整理成Y = a + bX的形式。

数学公式6

Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + a0b3V + a1b3XV + a2b3VW + a3b3ZV + a4b3XVW + a5b3XZV + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + b2V + a0b3V + a2b3VW + a3b3ZV) + (a1b1 + a4b1W + a5b1Z + a1b3V + a4b3VW + a5b3ZV + c')X
X 对 Y 的间接效应（在 W，Z，V 条件下）：(a1 + a4W + a5Z)(b1 + b3V)

这是X对Y的间接效应，它通过M间接影响Y。

数学公式7

Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ
Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + a0b3V + a1b3XV + a2b3VW + a3b3ZV + a4b3XVW + a5b3XZV + c'X
Y = (b0 + a0b1 + a2b1W + a3b1Z + b2V + a0b3V + a2b3VW + a3b3ZV) + (a1b1 + a4b1W + a5b1Z + a1b3V + a4b3VW + a5b3ZV + c')X
X 对 Y 的间接效应（在 W，Z，V 条件下）：(a1 + a4W + a5Z)(b1 + b3V)
X 对 Y 的直接效应：c'

这是X对Y的直接效应。

代码解读1

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
Y1 Y2 Y3 Y4;

首先，我们定义了要使用的变量。X1到X4是自变量X的指标变量，M1到M4是中介变量M的指标变量，W1到W4、Z1到Z4、V1到V4分别对应三个调节变量W、Z、V的指标变量，Y1到Y4是因变量Y的指标变量。

代码解读2

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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（TYPE = GENERAL RANDOM），最大似然估计法（ESTIMATOR = ML），并采用积分算法（ALGORITHM = INTEGRATION）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 V1 V2 V3 V4
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;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;

这里定义了测量模型。我们把每个潜在变量（X, M, W, Z, V, Y）与它们的观测指标联系起来。注意，W1, Z1, V1前面加了星号，表示我们固定了这些指标变量的载荷，使调节变量的方差为1，方便模型解读。

代码解读4

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;  V@1;

这一行代码将调节变量W, Z, V的方差固定为1，也就是对它们进行标准化处理。

代码解读5

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;  V@1;
MV | M XWITH V;
XW | X XWITH W;
XZ | X XWITH Z;

这里定义了潜在变量之间的交互作用项。MV表示M和V的交互作用，XW表示X和W的交互作用，XZ表示X和Z的交互作用，这些交互作用项体现了调节效应。

代码解读6

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;  V@1;
MV | M XWITH V;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON V (b2);
Y ON MV (b3);
Y ON X (cdash);

这是Y的回归方程，显示了M、V、MV和X对Y的影响。b1, b2, b3, cdash是待估计的参数。

代码解读7

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;  V@1;
MV | M XWITH V;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON V (b2);
Y ON MV (b3);
Y ON X (cdash);
M ON X (a1);
M ON W (a2);
M ON Z (a3);
M ON XW (a4);
M ON XZ (a5);

这是M的回归方程，显示了X、W、Z、XW和XZ对M的影响。a1到a5是待估计的参数。

代码解读8

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;  V@1;
MV | M XWITH V;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON V (b2);
Y ON MV (b3);
Y ON X (cdash);
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_V MED_V HIGH_V ... );
LOW_W = -1; MED_W = 0; HIGH_W = 1; ...

接下来是模型约束部分。我们定义了新的参数，代表调节变量在不同水平下的间接效应和总效应。这里将调节变量的低、中、高三个水平设定为-1，0，1，相当于标准差。

代码解读9

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;  V@1;
MV | M XWITH V;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON V (b2);
Y ON MV (b3);
Y ON X (cdash);
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_V MED_V HIGH_V ... );
LOW_W = -1; MED_W = 0; HIGH_W = 1; ...
ILWLZLV = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b3*LOW_V + ...;
...

这部分代码根据之前的模型计算在不同调节变量水平组合下的间接效应。例如，ILWLZLV表示在W低、Z低、V低水平下的间接效应，公式根据模型参数推导得出。

代码解读10

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;  V@1;
MV | M XWITH V;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON V (b2);
Y ON MV (b3);
Y ON X (cdash);
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_V MED_V HIGH_V ... );
LOW_W = -1; MED_W = 0; HIGH_W = 1; ...
ILWLZLV = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b3*LOW_V + ...;
...
TLWLZLV = ILWLZLV + cdash; ...

这部分代码计算在不同调节变量水平组合下的总效应，等于间接效应加上直接效应。

代码解读11

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;  V@1;
MV | M XWITH V;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON V (b2);
Y ON MV (b3);
Y ON X (cdash);
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_V MED_V HIGH_V ... );
LOW_W = -1; MED_W = 0; HIGH_W = 1; ...
ILWLZLV = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b3*LOW_V + ...;
...
TLWLZLV = ILWLZLV + cdash; ...
PLOT(...);
LOOP(XVAL,-3,3,0.1); ...

最后，我们定义了绘制条件间接效应图的代码，并使用循环计算不同X值下的条件间接效应，为绘图准备数据。

代码解读12

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 V1 V2 V3 V4
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;
V BY V1* V2 V3 V4;
Y BY Y1 Y2 Y3 Y4;
W@1;  Z@1;  V@1;
MV | M XWITH V;
XW | X XWITH W;
XZ | X XWITH Z;
Y ON M (b1);
Y ON V (b2);
Y ON MV (b3);
Y ON X (cdash);
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_V MED_V HIGH_V ... );
LOW_W = -1; MED_W = 0; HIGH_W = 1; ...
ILWLZLV = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a1*b3*LOW_V + ...;
...
TLWLZLV = ILWLZLV + cdash; ...
PLOT(...);
LOOP(XVAL,-3,3,0.1); ...
PLOT: TYPE = plot2;
OUTPUT: CINT;

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/model23latent.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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