Mplus model24latent 模型讲解

来自图书《MPlus中介调节模型》

Mplus复杂模型构建：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构建一个复杂的潜在变量模型，它包含了中介效应、调节效应以及调节中介效应。 这个模型相当复杂，包含一个潜在预测变量、一个潜在中介变量和三个潜在调节变量。 本教程会循序渐进地讲解，首先我们会从理论模型出发，清晰地阐述模型的各个组成部分以及它们之间的关系。然后，我们会建立相应的数学模型，用数学公式来精确描述这些关系。接下来，我们会对关键的数学推导过程进行讲解，帮助大家理解模型背后的逻辑。最后，我们会详细解读Mplus代码，展示如何用代码实现这个复杂的模型，并解释代码中每个参数的含义。通过本教程的学习，大家能够掌握构建和分析这类复杂模型的方法，并将其应用到自己的研究中。 如有任何问题，欢迎随时提出！

理论模型

我们来看这张图，它展示了我们今天要讨论的复杂模型。 这是一个包含中介效应和调节效应的模型。 X是我们的自变量，Y是因变量，M是中介变量，负责传递X对Y的影响。 W、Z、V是三个调节变量，它们会改变X、M、Y之间的关系。 具体来说，W和Z调节X对M的影响，V调节M对Y的影响，W和Z还调节X对Y的直接影响。 箭头表示变量之间的影响方向，可以看到X不仅通过M间接影响Y，也直接影响Y。 接下来我们将深入探讨这个模型的数学模型和Mplus代码实现。

数学模型

这张图展示了我们研究的复杂模型。模型中，X是我们的自变量，Y是因变量，M是中介变量，W、Z和V是调节变量。 X会直接影响M（a1），同时X与W、Z的交互作用也会影响M（a4, a5）。W和Z也会分别直接影响M（a2, a3）。M会直接影响Y（b1），M与V的交互作用也会影响Y（b3），V也会直接影响Y（b2）。此外，X还会直接影响Y（c1’），X与W、Z的交互作用也会直接影响Y（c4’, c5’），W和Z也会分别直接影响Y（c2’, c3’）。 这个模型涵盖了X对Y的直接和间接效应（通过M），以及W、Z、V对这些效应的调节作用，非常全面。

数学公式1

Y = b0 + b1M + b2V + b3MV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ

这是我们的初始模型，其中Y是因变量，M、V是自变量，X、W、Z是调节变量。b0到b3以及c1’到c5’是待估计的参数。

数学公式2

Y = b0 + b1M + b2V + b3MV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ

这是M的表达式，它体现了X、W、Z对M的影响。

数学公式3

Y = b0 + b1M + b2V + b3MV + 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) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ

将M的表达式代入Y的表达式，这是关键的一步，为后续计算间接效应做准备。

数学公式4

Y = b0 + b1M + b2V + b3MV + 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) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + a0b3V + a1b3XV + a2b3VW + a3b3ZV + a4b3XVW + a5b3XZV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ

展开括号，得到一个更复杂的表达式。

数学公式5

Y = b0 + b1M + b2V + b3MV + 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) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + a0b3V + a1b3XV + a2b3VW + a3b3ZV + a4b3XVW + a5b3XZV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = (b0 + a0b1 + a2b1W + a3b1Z + b2V + a0b3V + a2b3VW + a3b3ZV + c2'W + c3'Z) + (a1b1 + a4b1W + a5b1Z + a1b3V + a4b3VW + a5b3ZV + c1' + c4'W + c5'Z)X

将公式整理成Y = a + bX的形式，以便区分直接效应和间接效应。

数学公式6

Y = b0 + b1M + b2V + b3MV + 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) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + a0b3V + a1b3XV + a2b3VW + a3b3ZV + a4b3XVW + a5b3XZV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = (b0 + a0b1 + a2b1W + a3b1Z + b2V + a0b3V + a2b3VW + a3b3ZV + c2'W + c3'Z) + (a1b1 + a4b1W + a5b1Z + a1b3V + a4b3VW + a5b3ZV + c1' + c4'W + c5'Z)X
X对Y的间接效应 (在W, Z, V条件下)：a1b1 + a4b1W + a5b1Z + a1b3V + a4b3VW + a5b3ZV = (a1 + a4W + a5Z)(b1 + b3V)

这就是X对Y的间接效应，它包含了通过M对Y的影响。注意这里考虑了W, Z, V的调节作用。

数学公式7

Y = b0 + b1M + b2V + b3MV + 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) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + b2V + a0b3V + a1b3XV + a2b3VW + a3b3ZV + a4b3XVW + a5b3XZV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ
Y = (b0 + a0b1 + a2b1W + a3b1Z + b2V + a0b3V + a2b3VW + a3b3ZV + c2'W + c3'Z) + (a1b1 + a4b1W + a5b1Z + a1b3V + a4b3VW + a5b3ZV + c1' + c4'W + c5'Z)X
X对Y的间接效应 (在W, Z, V条件下)：a1b1 + a4b1W + a5b1Z + a1b3V + a4b3VW + a5b3ZV = (a1 + a4W + a5Z)(b1 + b3V)
X对Y的直接效应 (在W, Z条件下): c1' + c4'W + c5'Z

X对Y的直接效应，不通过M的路径。

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，我们定义了分析中用到的所有变量。X1到X4是X这个潜变量的四个指标；M1到M4是M潜变量的指标，以此类推。Y1到Y4是因变量Y的四个指标。

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。我们指定模型类型为一般随机模型，使用最大似然估计法，并选择积分算法来处理模型计算。

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;

这是模型的测量部分。我们定义了六个潜变量（X, M, W, Z, V, Y）及其对应的指标变量。注意，W1, Z1, V1后面带星号，表示它们的方差被固定为1，用于标准化潜变量。

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;

这里我们将W、Z、V潜变量的方差固定为1，使它们成为标准化变量。

代码解读5

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;

这一步定义了潜变量之间的交互项。例如，’MV | M XWITH V’表示M和V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 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 (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);

这是模型的结构部分。我们定义了潜变量之间的关系，并用括号中的参数表示路径系数。例如，’Y ON M (b1)’表示Y受M的影响，其路径系数为b1。

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 (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_V MED_V HIGH_V ...); 
LOW_W = -1; ... HIGH_V = 1;
ILWLZLV = a1*b1 + a4*b1*LOW_W + ...; ... IHWHZHV = ...;

接下来是模型约束，这部分比较复杂，用于计算在不同调节变量水平下的条件间接效应。我们定义了新的参数来表示这些效应，并根据模型公式计算它们。例如，ILWLZLV代表在W,Z,V都处于低水平时的间接效应。

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 (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_V MED_V HIGH_V ...); 
LOW_W = -1; ... HIGH_V = 1;
ILWLZLV = a1*b1 + a4*b1*LOW_W + ...; ... IHWHZHV = ...;
DLOW_LOZ = cdash1 + cdash4*LOW_W + cdash5*LOW_Z; ... DHIW_HIZ = ...;
TLWLZLV = ILWLZLV + DLOW_LOZ; ... THWHZHV = ...;

这里计算条件直接效应（DLOW_LOZ等）和条件总效应（TLWLZLV等）。总效应等于间接效应加上直接效应。

代码解读9

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 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 (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_V MED_V HIGH_V ...); 
LOW_W = -1; ... HIGH_V = 1;
ILWLZLV = a1*b1 + a4*b1*LOW_W + ...; ... IHWHZHV = ...;
DLOW_LOZ = cdash1 + cdash4*LOW_W + cdash5*LOW_Z; ... DHIW_HIZ = ...;
TLWLZLV = ILWLZLV + DLOW_LOZ; ... THWHZHV = ...;
PLOT(PLWLZLV PMWLZLV PHWLZLV ...);
LOOP(XVAL,-3,3,0.1);
PLWLZLV = ILWLZLV*XVAL; ... PHWHZHV = IHWHZHV*XVAL;

最后，我们定义绘图命令。程序会循环计算不同X值下各个条件效应，然后绘制出效应随X值变化的曲线图。

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 (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_V MED_V HIGH_V ...); 
LOW_W = -1; ... HIGH_V = 1;
ILWLZLV = a1*b1 + a4*b1*LOW_W + ...; ... IHWHZHV = ...;
DLOW_LOZ = cdash1 + cdash4*LOW_W + cdash5*LOW_Z; ... DHIW_HIZ = ...;
TLWLZLV = ILWLZLV + DLOW_LOZ; ... THWHZHV = ...;
PLOT(PLWLZLV PMWLZLV PHWLZLV ...);
LOOP(XVAL,-3,3,0.1);
PLWLZLV = ILWLZLV*XVAL; ... PHWHZHV = IHWHZHV*XVAL;
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/model24latent.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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