Mplus model29latent 模型讲解

来自图书《MPlus中介调节模型》

使用Mplus构建包含调节中介效应的潜变量模型

• 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。今天我们将学习如何使用Mplus构建一个复杂的潜变量模型，这个模型包含中介效应、调节效应以及更复杂的调节中介效应。 我们将逐步讲解，从理论模型开始，建立模型的数学基础，然后进行数学推导，最终演示如何用Mplus代码实现这个模型，并解读代码。 这个模型包含一个自变量、一个中介变量、两个调节变量和一个因变量，所有变量都是潜变量，并且每个潜变量都由四个观测变量测量。 我们会详细解释如何利用Mplus计算在不同调节变量取值下的条件间接效应、直接效应和总效应，并用图表直观地展现这些效应。 本教程的目标是让大家快速上手Mplus，并将其作为速查工具，方便大家在需要时查阅，无需深入学习所有细节。 我们还会解释如何利用模型约束来计算不同调节变量水平下的效应值。 最后，我们将生成一个图形，清晰地展示在不同调节变量组合下，自变量对因变量的条件间接效应。 本教程的代码参考了Andrew Hayes的PROCESS分析，并做了相应的调整，方便大家理解和使用。

理论模型

我们来看这张图，它展示了我们今天要分析的模型。这是一个包含调节中介效应的模型。X是我们的自变量，Y是因变量，M是中介变量，W和V是调节变量。箭头表示变量之间的影响方向。X不仅直接影响Y，还通过M间接影响Y。同时，W调节X对M的影响，V调节M对Y的影响，W和V也分别调节X对Y的直接影响。 这个模型比较复杂，但我们会一步步地讲解如何用Mplus来分析它，最终得到清晰的结论。

数学模型

这张图展示了我们研究的数学模型。 X代表自变量，M代表中介变量，Y代表因变量。W和V是两个调节变量，它们分别影响X对M的影响（XW）和M对Y的影响（MV），以及X对Y的直接影响。图中的箭头表示变量之间的关系，箭头旁的字母代表路径系数，例如a1表示X对M的直接影响，b1表示M对Y的直接影响，c1’表示X对Y的直接影响。 XW、XV和MV代表了W、V与M之间的交互作用。这个模型展现了X如何通过M间接影响Y，同时还存在X对Y的直接影响，并且这些影响都受到W和V的调节。

数学公式1

Y = b0 + b1M + b2MV + c1'X + c2'W + c3'V + c4'XW + c5'XV

这是我们的模型方程，Y是因变量，X是自变量，M, V, W是调节变量。

数学公式2

Y = b0 + b1M + b2MV + c1'X + c2'W + c3'V + c4'XW + c5'XV
M = a0 + a1X + a2W + a3XW

这是M的表达式，它也是X, W的函数。

数学公式3

Y = b0 + b1M + b2MV + c1'X + c2'W + c3'V + c4'XW + c5'XV
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2(a0 + a1X + a2W + a3XW)V + c1'X + c2'W + c3'V + c4'XW + c5'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'V + c4'XW + c5'XV
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2(a0 + a1X + a2W + a3XW)V + c1'X + c2'W + c3'V + c4'XW + c5'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + a0b2V + a1b2XV + a2b2WV + a3b2XWV + c1'X + c2'W + c3'V + c4'XW + c5'XV

展开括号，得到一个更复杂的表达式。

数学公式5

Y = b0 + b1M + b2MV + c1'X + c2'W + c3'V + c4'XW + c5'XV
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2(a0 + a1X + a2W + a3XW)V + c1'X + c2'W + c3'V + c4'XW + c5'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + a0b2V + a1b2XV + a2b2WV + a3b2XWV + c1'X + c2'W + c3'V + c4'XW + c5'XV
Y = (b0 + a0b1 + a2b1W + a0b2V + a2b2WV + c2'W + c3'V) + (a1b1 + a3b1W + a1b2V + a3b2WV + c1' + c4'W + c5'V)X

合并同类项，整理成Y = a + bX的形式，方便我们分析X对Y的影响。

数学公式6

Y = b0 + b1M + b2MV + c1'X + c2'W + c3'V + c4'XW + c5'XV
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2(a0 + a1X + a2W + a3XW)V + c1'X + c2'W + c3'V + c4'XW + c5'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + a0b2V + a1b2XV + a2b2WV + a3b2XWV + c1'X + c2'W + c3'V + c4'XW + c5'XV
Y = (b0 + a0b1 + a2b1W + a0b2V + a2b2WV + c2'W + c3'V) + (a1b1 + a3b1W + a1b2V + a3b2WV + c1' + c4'W + c5'V)X
X 对 Y 的间接效应（在 W，V 条件下）：a1b1 + a3b1W + a1b2V + a3b2WV = (a1 + a3W)(b1 + b2V)

这是X对Y的间接效应，通过调节变量M产生影响。注意，它取决于W和V的值。

数学公式7

Y = b0 + b1M + b2MV + c1'X + c2'W + c3'V + c4'XW + c5'XV
M = a0 + a1X + a2W + a3XW
Y = b0 + b1(a0 + a1X + a2W + a3XW) + b2(a0 + a1X + a2W + a3XW)V + c1'X + c2'W + c3'V + c4'XW + c5'XV
Y = b0 + a0b1 + a1b1X + a2b1W + a3b1XW + a0b2V + a1b2XV + a2b2WV + a3b2XWV + c1'X + c2'W + c3'V + c4'XW + c5'XV
Y = (b0 + a0b1 + a2b1W + a0b2V + a2b2WV + c2'W + c3'V) + (a1b1 + a3b1W + a1b2V + a3b2WV + c1' + c4'W + c5'V)X
X 对 Y 的间接效应（在 W，V 条件下）：a1b1 + a3b1W + a1b2V + a3b2WV = (a1 + a3W)(b1 + b2V)
X 对 Y 的直接效应（在 W，V 条件下）：c1' + c4'W + c5'V

这是X对Y的直接效应，不通过M产生影响。同样，它也取决于W和V的值。

代码解读1

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

首先，我们定义要使用的变量。X1到X4是自变量的指标变量，M1到M4是中介变量的指标变量，W1到W4和V1到V4分别是两个调节变量的指标变量，Y1到Y4是因变量的指标变量。这些变量名需要与你的数据文件一致。

代码解读2

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 V1 V2 V3 V4 Y1 Y2 Y3 Y4;
ANALYSIS: TYPE = GENERAL RANDOM; ESTIMATOR = ML; ALGORITHM = INTEGRATION;

接下来是分析设置。我们选择’GENERAL RANDOM’表示这是一个一般的随机效应模型，’ML’表示使用最大似然法进行估计，’INTEGRATION’表示使用积分算法处理潜在变量。

代码解读3

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; V BY V1* V2 V3 V4; Y BY Y1 Y2 Y3 Y4;

这是模型的测量部分。我们定义了五个潜在变量：X，M，W，V和Y，以及它们对应的指标变量。注意，W1和V1后加了星号，表示我们固定了W和V的方差为1，进行标准化处理。

代码解读4

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

这里再次明确固定W和V的方差为1，这与上一步骤的星号标注作用相同，只是这里更直接地表达了这一点。

代码解读5

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

这一部分定义了潜在变量的交互项。‘XWITH’表示两个变量之间的交互作用。例如，’MV | M XWITH V’ 表示创建了中介变量M和调节变量V的交互项。

代码解读6

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; V BY V1* V2 V3 V4; Y BY Y1 Y2 Y3 Y4;
W@1; V@1;
MV | M XWITH V; XW | X XWITH W; XV | X XWITH V;
Y ON M (b1); Y ON MV (b2); Y ON X (cdash1); Y ON W (cdash2); Y ON V (cdash3); Y ON XW (cdash4); Y ON XV (cdash5);

这一部分定义了结构模型中Y与其他变量的关系。例如，’Y ON M (b1)’表示Y受M的影响，路径系数用b1表示。其他语句类似，定义了Y与其他变量和交互项之间的关系。

代码解读7

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; V BY V1* V2 V3 V4; Y BY Y1 Y2 Y3 Y4;
W@1; V@1;
MV | M XWITH V; XW | X XWITH W; XV | X XWITH V;
Y ON M (b1); Y ON MV (b2); Y ON X (cdash1); Y ON W (cdash2); Y ON V (cdash3); Y ON XW (cdash4); Y ON XV (cdash5);
M ON X (a1); M ON W (a2); M ON XW (a3);

这一部分定义了结构模型中M与其他变量的关系。例如，’M ON X (a1)’表示M受X的影响，路径系数用a1表示。

代码解读8

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; V BY V1* V2 V3 V4; Y BY Y1 Y2 Y3 Y4;
W@1; V@1;
MV | M XWITH V; XW | X XWITH W; XV | X XWITH V;
Y ON M (b1); Y ON MV (b2); Y ON X (cdash1); Y ON W (cdash2); Y ON V (cdash3); Y ON XW (cdash4); Y ON XV (cdash5);
M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT: NEW(LOW_W MED_W HIGH_W LOW_V MED_V HIGH_V ...); LOW_W = -1; MED_W = 0; HIGH_W = 1; LOW_V = -1; MED_V = 0; HIGH_V = 1; ...

模型约束部分。我们定义了调节变量W和V的三个水平：低、中、高，分别对应-1, 0, 1。后续部分将根据这些水平计算条件间接效应、条件直接效应和条件总效应。

代码解读9

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; V BY V1* V2 V3 V4; Y BY Y1 Y2 Y3 Y4;
W@1; V@1;
MV | M XWITH V; XW | X XWITH W; XV | X XWITH V;
Y ON M (b1); Y ON MV (b2); Y ON X (cdash1); Y ON W (cdash2); Y ON V (cdash3); Y ON XW (cdash4); Y ON XV (cdash5);
M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT: NEW(LOW_W MED_W HIGH_W LOW_V MED_V HIGH_V ...); LOW_W = -1; MED_W = 0; HIGH_W = 1; LOW_V = -1; MED_V = 0; HIGH_V = 1; ...
ILOW_LOV = a1*b1 + a3*b1*LOW_W + a1*b2*LOW_V + a3*b2*LOW_W*LOW_V; ... 其他类似语句

这里用公式计算了不同调节变量组合下的条件间接效应 (ILOW_LOV 等)。这些公式直接对应模型的代数推导结果。

代码解读10

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; V BY V1* V2 V3 V4; Y BY Y1 Y2 Y3 Y4;
W@1; V@1;
MV | M XWITH V; XW | X XWITH W; XV | X XWITH V;
Y ON M (b1); Y ON MV (b2); Y ON X (cdash1); Y ON W (cdash2); Y ON V (cdash3); Y ON XW (cdash4); Y ON XV (cdash5);
M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT: NEW(LOW_W MED_W HIGH_W LOW_V MED_V HIGH_V ...); LOW_W = -1; MED_W = 0; HIGH_W = 1; LOW_V = -1; MED_V = 0; HIGH_V = 1; ...
ILOW_LOV = a1*b1 + a3*b1*LOW_W + a1*b2*LOW_V + a3*b2*LOW_W*LOW_V; ... 其他类似语句
DLOW_LOV = cdash1 + cdash4*LOW_W + cdash5*LOW_V; ... 其他类似语句

这里计算不同调节变量组合下的条件直接效应 (DLOW_LOV 等)。

代码解读11

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; V BY V1* V2 V3 V4; Y BY Y1 Y2 Y3 Y4;
W@1; V@1;
MV | M XWITH V; XW | X XWITH W; XV | X XWITH V;
Y ON M (b1); Y ON MV (b2); Y ON X (cdash1); Y ON W (cdash2); Y ON V (cdash3); Y ON XW (cdash4); Y ON XV (cdash5);
M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT: NEW(LOW_W MED_W HIGH_W LOW_V MED_V HIGH_V ...); LOW_W = -1; MED_W = 0; HIGH_W = 1; LOW_V = -1; MED_V = 0; HIGH_V = 1; ...
ILOW_LOV = a1*b1 + a3*b1*LOW_W + a1*b2*LOW_V + a3*b2*LOW_W*LOW_V; ... 其他类似语句
DLOW_LOV = cdash1 + cdash4*LOW_W + cdash5*LOW_V; ... 其他类似语句
TLOW_LOV = ILOW_LOV + DLOW_LOV; ... 其他类似语句

这里计算不同调节变量组合下的条件总效应 (TLOW_LOV 等)，它是条件间接效应和条件直接效应之和。

代码解读12

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; V BY V1* V2 V3 V4; Y BY Y1 Y2 Y3 Y4;
W@1; V@1;
MV | M XWITH V; XW | X XWITH W; XV | X XWITH V;
Y ON M (b1); Y ON MV (b2); Y ON X (cdash1); Y ON W (cdash2); Y ON V (cdash3); Y ON XW (cdash4); Y ON XV (cdash5);
M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT: NEW(LOW_W MED_W HIGH_W LOW_V MED_V HIGH_V ...); LOW_W = -1; MED_W = 0; HIGH_W = 1; LOW_V = -1; MED_V = 0; HIGH_V = 1; ...
ILOW_LOV = a1*b1 + a3*b1*LOW_W + a1*b2*LOW_V + a3*b2*LOW_W*LOW_V; ... 其他类似语句
DLOW_LOV = cdash1 + cdash4*LOW_W + cdash5*LOW_V; ... 其他类似语句
TLOW_LOV = ILOW_LOV + DLOW_LOV; ... 其他类似语句
PLOT(PLOW_LOV PMEW_LOV PHIW_LOV ...); LOOP(XVAL,-3,3,0.1); PLOW_LOV = ILOW_LOV*XVAL; ... 其他类似语句; PLOT: TYPE = plot2;

最后，我们定义了绘图部分。循环语句让X取值从-3到3，用于绘制条件效应与X的关系图。‘PLOT: TYPE = plot2;’ 指定了图表的类型。

代码解读13

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4 W1 W2 W3 W4 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; V BY V1* V2 V3 V4; Y BY Y1 Y2 Y3 Y4;
W@1; V@1;
MV | M XWITH V; XW | X XWITH W; XV | X XWITH V;
Y ON M (b1); Y ON MV (b2); Y ON X (cdash1); Y ON W (cdash2); Y ON V (cdash3); Y ON XW (cdash4); Y ON XV (cdash5);
M ON X (a1); M ON W (a2); M ON XW (a3);
MODEL CONSTRAINT: NEW(LOW_W MED_W HIGH_W LOW_V MED_V HIGH_V ...); LOW_W = -1; MED_W = 0; HIGH_W = 1; LOW_V = -1; MED_V = 0; HIGH_V = 1; ...
ILOW_LOV = a1*b1 + a3*b1*LOW_W + a1*b2*LOW_V + a3*b2*LOW_W*LOW_V; ... 其他类似语句
DLOW_LOV = cdash1 + cdash4*LOW_W + cdash5*LOW_V; ... 其他类似语句
TLOW_LOV = ILOW_LOV + DLOW_LOV; ... 其他类似语句
PLOT(PLOW_LOV PMEW_LOV PHIW_LOV ...); LOOP(XVAL,-3,3,0.1); PLOW_LOV = ILOW_LOV*XVAL; ... 其他类似语句; PLOT: TYPE = plot2;
OUTPUT: CINT;

最后，我们要求Mplus输出置信区间。

资源汇总

• 本视频讲义地址: https://mlln.cn/mplus-model-templates/model29latent.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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