Mplus model44 模型讲解

Mplus复杂模型构建教程：包含中介、调节和调节中介效应

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。本教程将手把手教大家如何使用Mplus构建一个复杂的模型，这个模型包含中介效应、调节效应以及调节中介效应。我们会一步步地讲解，首先我们会从理论模型出发，用图示和文字清晰地描述模型结构。然后，我们会建立相应的数学模型，用方程式来表达变量之间的关系。接下来，我们会详细推导计算间接效应和条件效应的公式，让大家理解这些效应是如何计算出来的。最后，我们会详细解读Mplus代码，并展示如何用代码来拟合这个复杂的模型，包括如何处理不同类型的变量，以及如何计算和绘制在不同调节变量取值组合下的条件间接效应。本教程提供了详细的步骤和解释，即使是初学者也能轻松上手。大家可以根据自己的需要选择性地阅读不同部分，无需从头到尾全部学习。让我们开始吧！

理论模型

数学模型

这张图展示的是一个复杂的统计模型，它包含多个变量以及它们之间的相互作用。

首先，我们来看自变量X，它会通过不同的路径影响因变量Y。其中，X会直接影响Y，也会间接通过中介变量M影响Y。M代表中介变量，它受到X的影响，同时也会影响Y。

模型中还有三个调节变量：W、V和Q。这些调节变量会改变X和M对Y的影响强度。比如，XW代表X和W的交互作用，它会影响M，进而影响Y。类似的，XV, MV, MQ, VQ, MVQ分别代表X和V，M和V，M和Q，V和Q，M和V和Q的交互作用，它们都会影响Y。

图中每一个箭头都代表了一个路径，箭头上的字母代表着路径系数，这些系数会告诉我们每个路径的影响有多大。通过分析这些路径系数，我们可以了解X对Y的直接影响、间接影响以及调节效应。总之，这张图描述了一个复杂的模型，它可以帮助我们更全面地理解变量之间的关系。

数学公式1

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'W + c3'XW + c4'V + c5'XV

数学公式2

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'W + c3'XW + c4'V + c5'XV
M = a0 + a1X + a2W + a3XW

数学公式3

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'W + c3'XW + c4'V + c5'XV
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2Q + b3(a0 + a1X + a2W + a3XW)V + b4(a0 + a1X + a2W + a3XW)Q + b5VQ + b6(a0 + a1X + a2W + a3XW)VQ + c1'X + c2'W + c3'XW + c4'V + c5'XV

数学公式4

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'W + c3'XW + c4'V + c5'XV
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2Q + b3(a0 + a1X + a2W + a3XW)V + b4(a0 + a1X + a2W + a3XW)Q + b5VQ + b6(a0 + a1X + a2W + a3XW)VQ + c1'X + c2'W + c3'XW + c4'V + c5'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2Q + a0b3V + a1b3XV + a2b3WV + a3b3XWV + a0b4Q + a1b4XQ + a2b4WQ + a3b4XWQ + b5VQ + a0b6VQ + a1b6XVQ + a2b6WVQ + a3b6XWVQ + c1'X + c2'W + c3'XW + c4'V + c5'XV

数学公式5

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'W + c3'XW + c4'V + c5'XV
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2Q + b3(a0 + a1X + a2W + a3XW)V + b4(a0 + a1X + a2W + a3XW)Q + b5VQ + b6(a0 + a1X + a2W + a3XW)VQ + c1'X + c2'W + c3'XW + c4'V + c5'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2Q + a0b3V + a1b3XV + a2b3WV + a3b3XWV + a0b4Q + a1b4XQ + a2b4WQ + a3b4XWQ + b5VQ + a0b6VQ + a1b6XVQ + a2b6WVQ + a3b6XWVQ + c1'X + c2'W + c3'XW + c4'V + c5'XV
Y = (b0 + a0b1 + a2b1W + b2Q + a0b3V + a2b3WV + a0b4Q + a2b4WQ + b5VQ + a0b6VQ + a2b6WVQ + c2'W + c4'V) + (a1b1 + a3b1W + a1b3V + a3b3WV + a1b4Q + a3b4WQ + a1b6VQ + a3b6WVQ + c1' + c3'W + c5'V)X

数学公式6

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'W + c3'XW + c4'V + c5'XV
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2Q + b3(a0 + a1X + a2W + a3XW)V + b4(a0 + a1X + a2W + a3XW)Q + b5VQ + b6(a0 + a1X + a2W + a3XW)VQ + c1'X + c2'W + c3'XW + c4'V + c5'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2Q + a0b3V + a1b3XV + a2b3WV + a3b3XWV + a0b4Q + a1b4XQ + a2b4WQ + a3b4XWQ + b5VQ + a0b6VQ + a1b6XVQ + a2b6WVQ + a3b6XWVQ + c1'X + c2'W + c3'XW + c4'V + c5'XV
Y = (b0 + a0b1 + a2b1W + b2Q + a0b3V + a2b3WV + a0b4Q + a2b4WQ + b5VQ + a0b6VQ + a2b6WVQ + c2'W + c4'V) + (a1b1 + a3b1W + a1b3V + a3b3WV + a1b4Q + a3b4WQ + a1b6VQ + a3b6WVQ + c1' + c3'W + c5'V)X
X 对 Y 的间接效应（在 W, V, Q 条件下）：
a1b1 + a3b1W + a1b3V + a3b3WV + a1b4Q + a3b4WQ + a1b6VQ + a3b6WVQ = (a1 + a3W)(b1 + b3V + b4Q + b6VQ)

数学公式7

Y = b0 + b1M + b2Q + b3MV + b4MQ + b5VQ + b6MVQ + c1'X + c2'W + c3'XW + c4'V + c5'XV
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2Q + b3(a0 + a1X + a2W + a3XW)V + b4(a0 + a1X + a2W + a3XW)Q + b5VQ + b6(a0 + a1X + a2W + a3XW)VQ + c1'X + c2'W + c3'XW + c4'V + c5'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + b2Q + a0b3V + a1b3XV + a2b3WV + a3b3XWV + a0b4Q + a1b4XQ + a2b4WQ + a3b4XWQ + b5VQ + a0b6VQ + a1b6XVQ + a2b6WVQ + a3b6XWVQ + c1'X + c2'W + c3'XW + c4'V + c5'XV
Y = (b0 + a0b1 + a2b1W + b2Q + a0b3V + a2b3WV + a0b4Q + a2b4WQ + b5VQ + a0b6VQ + a2b6WVQ + c2'W + c4'V) + (a1b1 + a3b1W + a1b3V + a3b3WV + a1b4Q + a3b4WQ + a1b6VQ + a3b6WVQ + c1' + c3'W + c5'V)X
X 对 Y 的间接效应（在 W, V, Q 条件下）：
a1b1 + a3b1W + a1b3V + a3b3WV + a1b4Q + a3b4WQ + a1b6VQ + a3b6WVQ = (a1 + a3W)(b1 + b3V + b4Q + b6VQ)
X 对 Y 的直接效应（在 W, V 条件下）：
c1' + c3'W + c5'V

代码解读1

USEVARIABLES = X M W V Q Y XW XV VQ MV MQ MVQ;

代码解读2

USEVARIABLES = X M W V Q Y XW XV VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XV = X*V;
 VQ = V*Q;
 MVQ = M*V*Q;

代码解读3

USEVARIABLES = X M W V Q Y XW XV VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XV = X*V;
 VQ = V*Q;
 MVQ = M*V*Q;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;

代码解读4

USEVARIABLES = X M W V Q Y XW XV VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XV = X*V;
 VQ = V*Q;
 MVQ = M*V*Q;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON Q (b2);
 Y ON MV (b3);
 Y ON MQ (b4);
 Y ON VQ (b5);
 Y ON MVQ (b6);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 Y ON V (cdash4);
 Y ON XV (cdash5);
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON XW (a3);

代码解读5

USEVARIABLES = X M W V Q Y XW XV VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XV = X*V;
 VQ = V*Q;
 MVQ = M*V*Q;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON Q (b2);
 Y ON MV (b3);
 Y ON MQ (b4);
 Y ON VQ (b5);
 Y ON MVQ (b6);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 Y ON V (cdash4);
 Y ON XV (cdash5);
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON XW (a3);
MODEL CONSTRAINT:
 NEW(...);
 LOW_W = #LOWW;
 ...
 ILWLVLQ = a1*b1 + a3*b1*LOW_W + a1*b3*LOW_V + a3*b3*LOW_W*LOW_V + ...; ...

代码解读6

USEVARIABLES = X M W V Q Y XW XV VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XV = X*V;
 VQ = V*Q;
 MVQ = M*V*Q;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON Q (b2);
 Y ON MV (b3);
 Y ON MQ (b4);
 Y ON VQ (b5);
 Y ON MVQ (b6);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 Y ON V (cdash4);
 Y ON XV (cdash5);
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON XW (a3);
MODEL CONSTRAINT:
 NEW(...);
 LOW_W = #LOWW;
 ...
 ILWLVLQ = a1*b1 + a3*b1*LOW_W + a1*b3*LOW_V + a3*b3*LOW_W*LOW_V + ...; ...
PLOT(...);

代码解读7

USEVARIABLES = X M W V Q Y XW XV VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XV = X*V;
 VQ = V*Q;
 MVQ = M*V*Q;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON Q (b2);
 Y ON MV (b3);
 Y ON MQ (b4);
 Y ON VQ (b5);
 Y ON MVQ (b6);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 Y ON V (cdash4);
 Y ON XV (cdash5);
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON XW (a3);
MODEL CONSTRAINT:
 NEW(...);
 LOW_W = #LOWW;
 ...
 ILWLVLQ = a1*b1 + a3*b1*LOW_W + a1*b3*LOW_V + a3*b3*LOW_W*LOW_V + ...; ...
PLOT(...);
LOOP(XVAL,1,5,0.1); ...

代码解读8

USEVARIABLES = X M W V Q Y XW XV VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XV = X*V;
 VQ = V*Q;
 MVQ = M*V*Q;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON Q (b2);
 Y ON MV (b3);
 Y ON MQ (b4);
 Y ON VQ (b5);
 Y ON MVQ (b6);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 Y ON V (cdash4);
 Y ON XV (cdash5);
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON XW (a3);
MODEL CONSTRAINT:
 NEW(...);
 LOW_W = #LOWW;
 ...
 ILWLVLQ = a1*b1 + a3*b1*LOW_W + a1*b3*LOW_V + a3*b3*LOW_W*LOW_V + ...; ...
PLOT(...);
LOOP(XVAL,1,5,0.1); ...
PLOT: TYPE = plot2;

代码解读9

USEVARIABLES = X M W V Q Y XW XV VQ MV MQ MVQ;
DEFINE:
 MQ = M*Q;
 MV = M*V;
 XW = X*W;
 XV = X*V;
 VQ = V*Q;
 MVQ = M*V*Q;
ANALYSIS:
 TYPE = GENERAL;
 ESTIMATOR = ML;
 BOOTSTRAP = 10000;
MODEL:
 [Y] (b0);
 Y ON M (b1);
 Y ON Q (b2);
 Y ON MV (b3);
 Y ON MQ (b4);
 Y ON VQ (b5);
 Y ON MVQ (b6);
 Y ON X (cdash1);
 Y ON W (cdash2);
 Y ON XW (cdash3);
 Y ON V (cdash4);
 Y ON XV (cdash5);
 [M] (a0);
 M ON X (a1);
 M ON W (a2);
 M ON XW (a3);
MODEL CONSTRAINT:
 NEW(...);
 LOW_W = #LOWW;
 ...
 ILWLVLQ = a1*b1 + a3*b1*LOW_W + a1*b3*LOW_V + a3*b3*LOW_W*LOW_V + ...; ...
PLOT(...);
LOOP(XVAL,1,5,0.1); ...
PLOT: TYPE = plot2;
OUTPUT: STAND CINT(bcbootstrap);

资源汇总

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