Mplus model7latent 模型讲解

来自图书《MPlus中介调节模型》

使用Mplus分析复杂模型：中介、调节与调节中介模型

• 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。本节课将带大家学习如何使用Mplus软件分析复杂的中介、调节和调节中介模型。 首先，我们将从理论模型开始，帮助大家建立对模型的直观理解。 接下来，我们会讲解模型的数学表达，也就是数学模型，让大家了解模型背后的数学原理。 为了更清晰地理解模型的构建过程，我们会进行详细的数学推导，一步一步地解释模型是如何构建的。 最后，我们会深入讲解Mplus的代码，提供一个可直接使用的代码模板，并对代码进行详细的注释。 通过本教程，相信大家能够快速掌握使用Mplus分析复杂模型的方法。 有任何问题，欢迎随时提出。

理论模型

我们来看这张图，它展示了一个调节中介模型。X是自变量，Y是因变量，M是中介变量，W是调节变量。W调节的是X对M的影响。X不仅直接影响Y，还通过M间接影响Y。 模型中包含了X、W、以及X和W的交互作用对M的影响，M对Y的影响，以及X对Y的直接影响。 通过分析这些路径的系数，我们可以了解X对Y的总效应、间接效应和直接效应，以及W对这种影响的调节作用。

数学模型

这张图展示的是一个比较复杂的模型，它包含了中介效应和调节效应。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是调节变量。

X会直接影响M (a1)，W也会直接影响M (a2)， 并且X和W的交互作用XW也会影响M (a3)。M会直接影响Y (b1)，X也会直接影响Y (c’)。

箭头表示变量之间的影响方向，箭头旁边的字母代表着影响的强度，也就是路径系数。这个模型主要研究的是X通过M对Y的影响，以及W对X到M这条路径的调节作用。

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，M是中介变量，X是自变量，c’代表X对Y的直接效应。

数学公式2

Y = b0 + b1M + c'X
M = a0 + a1X + a2W + a3XW

这是中介变量M的方程，其中a1代表X对M的直接效应，a2代表W对M的直接效应，a3代表X和W的交互效应。

数学公式3

Y = b0 + b1M + c'X
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + 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 + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + c'X

展开括号，将公式展开。

数学公式5

Y = b0 + b1M + c'X
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + c'X
Y = (b0 + a0b1 + a2b1W) + (a1b1 + a3b1W + c')X

整理公式，使其符合Y = a + bX的形式。

数学公式6

Y = b0 + b1M + c'X
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + c'X
Y = (b0 + a0b1 + a2b1W) + (a1b1 + a3b1W + c')X
X 对 Y 的间接效应 (取决于 W)： a1b1 + a3b1W = (a1 + a3W)b1

这是X对Y的间接效应，它取决于W的取值。可以看到，间接效应并非一个常数，而是随着W的变化而变化。

数学公式7

Y = b0 + b1M + c'X
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + c'X
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + c'X
Y = (b0 + a0b1 + a2b1W) + (a1b1 + a3b1W + c')X
X 对 Y 的间接效应 (取决于 W)： a1b1 + a3b1W = (a1 + a3W)b1
X 对 Y 的直接效应： c'

这是X对Y的直接效应，它是一个常数，不受W的影响。

代码解读1

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Y1 Y2 Y3 Y4;

首先，我们定义了分析中使用的变量。X1到X4测量潜在变量X，也就是我们的自变量；M1到M4测量中介变量M；W1到W4测量调节变量W；Y1到Y4测量因变量Y。这一行代码清晰地列出了所有参与分析的变量。

代码解读2

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Y1 Y2 Y3 Y4;
ANALYSIS:

接下来，我们开始分析部分的设置。

代码解读3

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM; ESTIMATOR = ML; ALGORITHM = INTEGRATION;

这里我们指定模型类型为一般随机效应模型，使用最大似然估计法进行参数估计，并采用积分法进行计算。这对于处理潜在变量模型非常重要。

代码解读4

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM; ESTIMATOR = ML; ALGORITHM = INTEGRATION;
MODEL:

现在，我们进入模型设定阶段。

代码解读5

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; Y BY Y1 Y2 Y3 Y4;

这部分定义了测量模型。例如，‘X BY X1 X2 X3 X4;’ 表示潜在变量X由观测变量X1到X4测量。‘W BY W1* W2 W3 W4;’ 中的星号表示W1的因子载荷固定为1，对W进行标准化。

代码解读6

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; Y BY Y1 Y2 Y3 Y4;
W@1;

这一行代码将调节变量W的方差固定为1，同样是为了标准化。

代码解读7

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; Y BY Y1 Y2 Y3 Y4;
W@1;
XW | X XWITH W;

这里定义了X和W的交互作用项XW，这正是我们模型中调节效应的关键。

代码解读8

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; Y BY Y1 Y2 Y3 Y4;
W@1;
XW | X XWITH W;
Y ON M (b1); Y ON X (cdash); M ON X (a1); M ON W (a2); M ON XW (a3);

这一部分定义了结构模型，描述了变量之间的关系。比如，‘Y ON M (b1);’ 表示Y受M的影响，路径系数为b1。其他几行代码也类似地定义了其他路径。

代码解读9

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; Y BY Y1 Y2 Y3 Y4;
W@1;
XW | X XWITH W;
Y ON M (b1); Y ON X (cdash); M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT:

接下来是模型约束部分，我们在这里进行一些额外的计算和设定。

代码解读10

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; Y BY Y1 Y2 Y3 Y4;
W@1;
XW | X XWITH W;
Y ON M (b1); Y ON X (cdash); M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W IND_LOWW IND_MEDW IND_HIW IMM TOT_LOWW TOT_MEDW TOT_HIW);

我们定义了一些新的参数，用于计算间接效应和总效应。

代码解读11

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; Y BY Y1 Y2 Y3 Y4;
W@1;
XW | X XWITH W;
Y ON M (b1); Y ON X (cdash); M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W IND_LOWW IND_MEDW IND_HIW IMM TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = -1; MED_W = 0; HIGH_W = 1;

这里设定了调节变量W的低、中、高三个水平的值。

代码解读12

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; Y BY Y1 Y2 Y3 Y4;
W@1;
XW | X XWITH W;
Y ON M (b1); Y ON X (cdash); M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W IND_LOWW IND_MEDW IND_HIW IMM TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = -1; MED_W = 0; HIGH_W = 1;
IND_LOWW = a1*b1 + a3*b1*LOW_W; IND_MEDW = a1*b1 + a3*b1*MED_W; IND_HIW = a1*b1 + a3*b1*HIGH_W;

根据公式，我们计算了不同调节变量水平下的间接效应。

代码解读13

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; Y BY Y1 Y2 Y3 Y4;
W@1;
XW | X XWITH W;
Y ON M (b1); Y ON X (cdash); M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W IND_LOWW IND_MEDW IND_HIW IMM TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = -1; MED_W = 0; HIGH_W = 1;
IND_LOWW = a1*b1 + a3*b1*LOW_W; IND_MEDW = a1*b1 + a3*b1*MED_W; IND_HIW = a1*b1 + a3*b1*HIGH_W;
IMM = a3*b1;

计算调节效应指标。

代码解读14

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; Y BY Y1 Y2 Y3 Y4;
W@1;
XW | X XWITH W;
Y ON M (b1); Y ON X (cdash); M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W IND_LOWW IND_MEDW IND_HIW IMM TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = -1; MED_W = 0; HIGH_W = 1;
IND_LOWW = a1*b1 + a3*b1*LOW_W; IND_MEDW = a1*b1 + a3*b1*MED_W; IND_HIW = a1*b1 + a3*b1*HIGH_W;
IMM = a3*b1;
TOT_LOWW = IND_LOWW + cdash; TOT_MEDW = IND_MEDW + cdash; TOT_HIW = IND_HIW + cdash;

计算不同调节变量水平下的总效应，也就是间接效应加上直接效应。

代码解读15

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; Y BY Y1 Y2 Y3 Y4;
W@1;
XW | X XWITH W;
Y ON M (b1); Y ON X (cdash); M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W IND_LOWW IND_MEDW IND_HIW IMM TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = -1; MED_W = 0; HIGH_W = 1;
IND_LOWW = a1*b1 + a3*b1*LOW_W; IND_MEDW = a1*b1 + a3*b1*MED_W; IND_HIW = a1*b1 + a3*b1*HIGH_W;
IMM = a3*b1;
TOT_LOWW = IND_LOWW + cdash; TOT_MEDW = IND_MEDW + cdash; TOT_HIW = IND_HIW + cdash;
PLOT(LOMOD MEDMOD HIMOD); LOOP(XVAL,-3,3,0.1); LOMOD = IND_LOWW*XVAL; MEDMOD = IND_MEDW*XVAL; HIMOD = IND_HIW*XVAL;

这部分代码用于绘制图形，展示不同调节变量水平下，间接效应与自变量X的关系。

代码解读16

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; Y BY Y1 Y2 Y3 Y4;
W@1;
XW | X XWITH W;
Y ON M (b1); Y ON X (cdash); M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W IND_LOWW IND_MEDW IND_HIW IMM TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = -1; MED_W = 0; HIGH_W = 1;
IND_LOWW = a1*b1 + a3*b1*LOW_W; IND_MEDW = a1*b1 + a3*b1*MED_W; IND_HIW = a1*b1 + a3*b1*HIGH_W;
IMM = a3*b1;
TOT_LOWW = IND_LOWW + cdash; TOT_MEDW = IND_MEDW + cdash; TOT_HIW = IND_HIW + cdash;
PLOT(LOMOD MEDMOD HIMOD); LOOP(XVAL,-3,3,0.1); LOMOD = IND_LOWW*XVAL; MEDMOD = IND_MEDW*XVAL; HIMOD = IND_HIW*XVAL;
PLOT: TYPE = plot2;

指定绘图类型。

代码解读17

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; Y BY Y1 Y2 Y3 Y4;
W@1;
XW | X XWITH W;
Y ON M (b1); Y ON X (cdash); M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W IND_LOWW IND_MEDW IND_HIW IMM TOT_LOWW TOT_MEDW TOT_HIW);
LOW_W = -1; MED_W = 0; HIGH_W = 1;
IND_LOWW = a1*b1 + a3*b1*LOW_W; IND_MEDW = a1*b1 + a3*b1*MED_W; IND_HIW = a1*b1 + a3*b1*HIGH_W;
IMM = a3*b1;
TOT_LOWW = IND_LOWW + cdash; TOT_MEDW = IND_MEDW + cdash; TOT_HIW = IND_HIW + cdash;
PLOT(LOMOD MEDMOD HIMOD); LOOP(XVAL,-3,3,0.1); LOMOD = IND_LOWW*XVAL; MEDMOD = IND_MEDW*XVAL; HIMOD = IND_HIW*XVAL;
PLOT: TYPE = plot2;
OUTPUT: CINT;

最后，我们要求输出置信区间。

资源汇总

• 本视频讲义地址: https://mlln.cn/mplus-model-templates/model7latent.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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