Mplus model4c 模型讲解

使用Mplus分析二元中介效应模型(Model 4c)

理论模型
数学模型
数学推导 (包括McKinnon & Dwyer (1993)方法的应用)
代码解读 (包含Mplus代码及详细解释)

大家好，欢迎来到本教程。今天我们将学习如何使用Mplus软件分析二元中介变量的模型，也就是Model 4c。这个教程会一步一步地带大家完成分析过程，从理论模型到最终的Mplus代码解读，都涵盖在内。我们会先讲解模型的理论基础，然后介绍相关的数学模型和公式，重点是理解如何用McKinnon & Dwyer (1993)的方法来处理二元中介变量的情况，因为在这种情况下，Mplus的MODEL INDIRECT命令是失效的。接着，我们会进行详细的数学推导，让大家理解公式的来源。最后，我们会讲解Mplus代码，并一步步解读代码的含义以及如何得到最终的结果。本教程旨在帮助大家快速上手，所以内容比较精简，大家可以根据自己的需求选择性学习。

理论模型

数学模型

数学公式1

SD(X), SD(M), Var(X), Var(M), Cov(X,M)

数学公式2

SD(X), SD(M), Var(X), Var(M), Cov(X,M)
adjusted a1 = a1*SD(X)/(sqrt(a1*a1*Var(X) + π²/3))

数学公式3

SD(X), SD(M), Var(X), Var(M), Cov(X,M)
adjusted a1 = a1*SD(X)/(sqrt(a1*a1*Var(X) + π²/3))
adjusted b1 = b1*SD(M)/(sqrt(c’*c’*Var(X) + b1*b1*Var(M) + 2*b1*c’*Cov(X,M)))

数学公式4

SD(X), SD(M), Var(X), Var(M), Cov(X,M)
adjusted a1 = a1*SD(X)/(sqrt(a1*a1*Var(X) + π²/3))
adjusted b1 = b1*SD(M)/(sqrt(c’*c’*Var(X) + b1*b1*Var(M) + 2*b1*c’*Cov(X,M)))
adjind = adja1 * adjb1

代码解读1

USEVARIABLES = X M Y;

代码解读2

USEVARIABLES = X M Y;
CATEGORICAL = M;

代码解读3

USEVARIABLES = X M Y;
CATEGORICAL = M;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;

代码解读4

USEVARIABLES = X M Y;
CATEGORICAL = M;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
MODEL:
Y ON M (b1);
Y ON X (cdash);
M ON X (a1);

代码解读5

USEVARIABLES = X M Y;
CATEGORICAL = M;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
MODEL:
Y ON M (b1);
Y ON X (cdash);
M ON X (a1);
MODEL CONSTRAINT:
NEW(SDX SDM COVXM pi adja1 adjb1 adjind);

代码解读6

USEVARIABLES = X M Y;
CATEGORICAL = M;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
MODEL:
Y ON M (b1);
Y ON X (cdash);
M ON X (a1);
MODEL CONSTRAINT:
NEW(SDX SDM COVXM pi adja1 adjb1 adjind);
SDX = #SDX;
SDM = #SDM;
COVXM = #COVXM;

代码解读7

USEVARIABLES = X M Y;
CATEGORICAL = M;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
MODEL:
Y ON M (b1);
Y ON X (cdash);
M ON X (a1);
MODEL CONSTRAINT:
NEW(SDX SDM COVXM pi adja1 adjb1 adjind);
SDX = #SDX;
SDM = #SDM;
COVXM = #COVXM;
pi = 3.141592653589793;

代码解读8

USEVARIABLES = X M Y;
CATEGORICAL = M;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
MODEL:
Y ON M (b1);
Y ON X (cdash);
M ON X (a1);
MODEL CONSTRAINT:
NEW(SDX SDM COVXM pi adja1 adjb1 adjind);
SDX = #SDX;
SDM = #SDM;
COVXM = #COVXM;
pi = 3.141592653589793;
adja1 = a1*SDX/(sqrt((a1*a1*SDX*SDX) + ((pi*pi)/3)));
adjb1 = b1*SDM/(sqrt((cdash*cdash*SDX*SDX) + (b1*b1*SDM*SDM) + (2*b1*cdash*COVXM)));
adjind = adja1*adjb1;

代码解读9

USEVARIABLES = X M Y;
CATEGORICAL = M;
ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;
MODEL:
Y ON M (b1);
Y ON X (cdash);
M ON X (a1);
MODEL CONSTRAINT:
NEW(SDX SDM COVXM pi adja1 adjb1 adjind);
SDX = #SDX;
SDM = #SDM;
COVXM = #COVXM;
pi = 3.141592653589793;
adja1 = a1*SDX/(sqrt((a1*a1*SDX*SDX) + ((pi*pi)/3)));
adjb1 = b1*SDM/(sqrt((cdash*cdash*SDX*SDX) + (b1*b1*SDM*SDM) + (2*b1*cdash*COVXM)));
adjind = adja1*adjb1;
OUTPUT:
STAND CINT(bcbootstrap);

资源汇总

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