Mplus model33latent 模型讲解

来自图书《MPlus中介调节模型》

Mplus复杂调节中介模型构建教程

• 理论模型
• 数学模型
• 数学推导
• Mplus代码解读

大家好，欢迎来到本场关于Mplus复杂调节中介模型构建教程的讲解。 本教程将带大家一步步学习如何使用Mplus构建包含中介、调节和调节中介效应的复杂模型。 我们将从理论模型开始，逐步建立起对模型的理解，之后讲解模型的数学表达，并详细推导其公式。 重点在于讲解如何利用Mplus代码进行模型构建和参数估计，以及如何通过模型约束获得在不同调节变量组合下的条件间接效应、条件直接效应和条件总效应。 整个教程结构清晰明了，涵盖了理论、方法和实践三个方面，您可以根据自己的需要选择性地学习。 本教程提供的代码可以直接复制粘贴到Mplus中使用，只需要修改变量名即可。 希望本教程能够帮助大家快速掌握Mplus的使用技巧，并更好地理解和分析复杂的调节中介模型。谢谢！

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是自变量，Y是因变量，M是中介变量，W、Z和V是调节变量。 箭头表示变量之间的影响关系，可以看到X对Y有直接影响，也有通过M的间接影响。 更重要的是，W、Z和V分别调节着X对M的影响，以及X对Y的直接影响。 V还调节M对Y的影响。这个模型包含了各种复杂的交互作用，例如X与W、Z、V的交互，以及它们之间的高阶交互作用。通过分析这些路径和交互作用，我们可以更全面地理解这些变量之间的关系。

数学模型

这张图展示了一个复杂的调节中介模型。我们来看一下各个变量：X是我们的自变量，Y是因变量，M是中介变量。W、Z和V是三个调节变量，它们会影响X、M和Y之间的关系。 X通过不同的路径影响M，这些路径都受到W和Z的调节，部分路径还受到V的调节。M再影响Y，其中一条路径还受到V的调节。同时，X也会直接影响Y，这个直接影响也受到W、Z和V的不同组合的调节。 图中箭头表示变量之间的影响方向，箭头旁边的字母代表路径系数，后面我们会详细讲解这些系数的含义和计算方法。

数学公式1

Y = b0 + b1M + b2MV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV

这是我们的模型方程，其中Y是因变量，M是中介变量，X是自变量，W、Z、V是控制变量。b0, b1, b2, c1’ … c9’ 是模型参数。

数学公式2

Y = b0 + b1M + b2MV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ

这是中介变量M的表达式，它受自变量X和控制变量W、Z的影响。

数学公式3

Y = b0 + b1M + b2MV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV
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)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV

将M的表达式代入Y的表达式。

数学公式4

Y = b0 + b1M + b2MV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV
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)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + a0b2V + a1b2XV + a2b2WV + a3b2ZV + a4b2XWV + a5b2XZV + a6b2WZV + a7b2XWZV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV

展开括号，进行化简。

数学公式5

Y = b0 + b1M + b2MV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV
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)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + a0b2V + a1b2XV + a2b2WV + a3b2ZV + a4b2XWV + a5b2XZV + a6b2WZV + a7b2XWZV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + a0b2V + a2b2WV + a3b2ZV + a6b2WZV + c2'W + c3'Z + c6'WZ + c8'V) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b2V + a4b2WV + a5b2ZV + a7b2WZV + c1' + c4'W + c5'Z + c7'WZ + c9'V)X

合并同类项，整理成Y = a + bX的形式。

数学公式6

Y = b0 + b1M + b2MV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV
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)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + a0b2V + a1b2XV + a2b2WV + a3b2ZV + a4b2XWV + a5b2XZV + a6b2WZV + a7b2XWZV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + a0b2V + a2b2WV + a3b2ZV + a6b2WZV + c2'W + c3'Z + c6'WZ + c8'V) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b2V + a4b2WV + a5b2ZV + a7b2WZV + c1' + c4'W + c5'Z + c7'WZ + c9'V)X
X 对 Y 的间接效应（在 W，Z，V 条件下）：(a1 + a4W + a5Z + a7WZ)(b1 + b2V)

这是X对Y的间接效应，通过中介变量M实现。

数学公式7

Y = b0 + b1M + b2MV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV
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)V + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + a0b2V + a1b2XV + a2b2WV + a3b2ZV + a4b2XWV + a5b2XZV + a6b2WZV + a7b2XWZV + c1'X + c2'W + c3'Z + c4'XW + c5'XZ + c6'WZ + c7'XWZ + c8'V + c9'XV
Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + a0b2V + a2b2WV + a3b2ZV + a6b2WZV + c2'W + c3'Z + c6'WZ + c8'V) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b2V + a4b2WV + a5b2ZV + a7b2WZV + c1' + c4'W + c5'Z + c7'WZ + c9'V)X
X 对 Y 的间接效应（在 W，Z，V 条件下）：(a1 + a4W + a5Z + a7WZ)(b1 + b2V)
X 对 Y 的直接效应（在 W，Z，V 条件下）：c1' + c4'W + c5'Z + c7'WZ + c9'V

这是X对Y的直接效应，不通过中介变量M。

代码解读1

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

首先，我们定义了分析中使用的变量。X1到X4是自变量的四个指标；M1到M4是中介变量的四个指标；W1到W4，Z1到Z4，V1到V4分别是三个调节变量的指标；Y1到Y4是因变量的四个指标。 这些变量名清晰地指明了它们在模型中的角色。

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，我们设置分析方法。’TYPE = GENERAL RANDOM’表示我们使用的是一般性随机效应模型；’ESTIMATOR = ML’表示采用最大似然估计法进行参数估计；’ALGORITHM = INTEGRATION’表示使用数值积分法来处理模型中的潜变量，因为我们的模型比较复杂。

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;
  W@1;  Z@1;  V@1;

这一部分定义了测量模型。我们把潜变量X、M、W、Z、V分别与它们的指标变量联系起来。 星号*表示将W, Z, V的第一个指标的载荷固定为1，也就是对调节变量进行标准化。

代码解读4

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
W1 W2 W3 W4 Z1 Z2 Z3 Z4 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;
XV | X XWITH V;
WZ | W XWITH Z;
XWZ | X XWITH WZ;

这里定义了潜变量之间的交互效应。例如，’MV | M XWITH V’表示中介变量M与调节变量V的交互作用。其他的语句也类似地定义了其他交互作用，构建了一个复杂的调节中介模型。

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;
XV | X XWITH V;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON MV (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
Y ON WZ (cdash6);
Y ON XWZ (cdash7);
Y ON V (cdash8);
Y ON XV (cdash9);

这一部分定义了结构模型，描述了潜变量之间的关系。例如，’Y ON M (b1)’表示因变量Y受中介变量M的影响，参数命名为b1。其余语句也类似地描述了其他路径的影响。

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;
XV | X XWITH V;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON MV (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
Y ON WZ (cdash6);
Y ON XWZ (cdash7);
Y ON V (cdash8);
Y ON XV (cdash9);
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);

这段代码描述了中介变量M如何受到自变量X和调节变量W, Z的影响，以及它们之间的交互作用。

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;
XV | X XWITH V;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON MV (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
Y ON WZ (cdash6);
Y ON XWZ (cdash7);
Y ON V (cdash8);
Y ON XV (cdash9);
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_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 + a7*b1*LOW_W*LOW_Z + ...;

这一部分是模型约束，我们定义了调节变量的三个水平（低、中、高），并通过公式计算在不同调节变量组合下的间接效应（IL…）、直接效应（DL…）以及总效应（TL…）。 这些公式是根据模型推导出来的。

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;
XV | X XWITH V;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON MV (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
Y ON WZ (cdash6);
Y ON XWZ (cdash7);
Y ON V (cdash8);
Y ON XV (cdash9);
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_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 + a7*b1*LOW_W*LOW_Z + ...;
PLOT: TYPE = plot2;

最后，我们指定了绘图类型，以便可视化结果。

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;
XV | X XWITH V;
WZ | W XWITH Z;
XWZ | X XWITH WZ;
Y ON M (b1);
Y ON MV (b2);
Y ON X (cdash1);
Y ON W (cdash2);
Y ON Z (cdash3);
Y ON XW (cdash4);
Y ON XZ (cdash5);
Y ON WZ (cdash6);
Y ON XWZ (cdash7);
Y ON V (cdash8);
Y ON XV (cdash9);
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_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 + a7*b1*LOW_W*LOW_Z + ...;
PLOT: TYPE = plot2;
OUTPUT: CINT;

这一行代码指定输出置信区间，用于评估参数估计的精度。

资源汇总

• 本视频讲义地址: https://mlln.cn/mplus-model-templates/model33latent.html
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• 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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