潜变量随机截距交叉滞后模型

文摘   2024-11-07 08:45   北京  


PSYCH统计实验室


前言

在心理学和社会科学领域,研究者常常需要分析一些复杂的潜在变量(如幸福感、自我效能感等)在时间上的变化及其相互之间的动态影响。随机截距交叉滞后面板模型(Random Intercept Cross-Lagged Panel Model,RI-CLPM)是一种广泛应用于分析纵向数据的统计工具,可以帮助研究者理解这些变量之间的因果关系。然而,在涉及复杂的潜在变量时,仅使用单一观测指标可能难以捕捉这些变量的全貌,这时引入多重指标显得尤为重要。

多重指标允许我们在模型中为每个潜在变量引入多个观测指标,以更精确地描述这些变量,减少测量误差对结果的影响,使我们对研究结果的信任度大幅提升。在本文中,我们将详细介绍RI-CLPM的多重指标扩展,包括其概念、作用以及如何在Mplus中实现。

RI-CLPM是一种在纵向研究中常用的统计模型,用于探讨多个时间点上的变量之间的相互影响和因果关系。与传统的交叉滞后面板模型(CLPM)相比,RI-CLPM引入了随机截距的概念,以解决变量间的个体稳定性问题,进而使得模型更加适合用于分析有显著个体差异的数据。

多重指标,即在模型中为每个潜在变量引入多个观测指标。为什么要这样做呢?在社会科学和心理学研究中,许多重要的构念是难以通过单一指标直接测量的,比如幸福感、自尊、压力等。这些复杂构念通常需要通过一组观测指标来进行间接测量。通过为潜在变量引入多个指标,我们能够:

提高测量精度:通过多维度的观测来捕捉潜在变量,避免单一指标的局限性。

增强信效度:减少测量误差的影响,从而增加结论的可靠性。

确保测量一致性:通过施加测量不变性约束,确保在多个时间点上测量的潜在变量具有相同的含义和结构。

在具体实施上,RI-CLPM的多重指标扩展包含几个关键步骤,接下来我们会逐步介绍如何构建这个模型并在软件Mplus中实现。


多重指标RI-CLPM的构建步骤


1

Step 1: 形态模型

(Configural Model)

在构建多重指标模型的第一步,我们需要为每个时间点的每个潜在变量指定多个观测指标。这一步被称为形态模型,目的是为潜在变量建立一个初始测量结构,使得每个潜在变量的观测指标在各时间点上保持一致。


2

Step 2: 弱测量不变性(Weak 

Factorial Invariance)

在形态好模型后,下一步是弱测量不变性,即约束每个时间点的因子载荷相等,以确保不同时间点测量的潜在变量具有相同的含义和结构。

3

Step 3:强测量不变性(Strong 

Factorial Invariance)

在确保弱测量不变性之后,下一步是强测量不变性,即进一步约束观测指标的截距在各时间点保持一致。这样可以确保在所有时间点上,潜在变量的观测指标具有相同的平均水平。

4

Step 4: 在潜变量层面应用

RI-CLPM

在完成测量不变性的基础上,我们可以在潜变量层面应用RI-CLPM进行路径分析,探索潜变量之间的动态因果关系和个体稳定性。随机截距的引入帮助我们捕捉到变量之间的个体差异,从而使模型更加精确。

代码


https://jeroendmulder.github.io/RI-CLPM/mplus.html

Step 1 形态模型

TITLE:      Multiple indicator RI-CLPM, 5 waves, with 3 indicators for

            each variable at each wave (30 observed variables) and with

            random intercepts for each indicator separately.

DATA:       FILE = RICLPM-MI.dat;

VARIABLE:   NAMES = x11 x12 x13 x21 x22 x23 x31 x32 x33

                    x41 x42 x43 x51 x52 x53 y11 y12 y13

                    y21 y22 y23 y31 y32 y33 y41 y42 y43

                    y51 y52 y53;

ANALYSIS:   MODEL = NOCOV;

MODEL:      

!构建每个时间点相同指标的随机截距

            RIX1 BY x11@1 x21@1 x31@1 x41@1 x51@1;

            RIX2 BY x12@1 x22@1 x32@1 x42@1 x52@1;

            RIX3 BY x13@1 x23@1 x33@1 x43@1 x53@1;

            RIY1 BY y11@1 y21@1 y31@1 y41@1 y51@1;

            RIY2 BY y12@1 y22@1 y32@1 y42@1 y52@1;

            RIY3 BY y13@1 y23@1 y33@1 y43@1 y53@1;

            RIX1-RIY3 WITH RIX1-RIY3;

!构建潜在变量

            WFX1 BY x11-x13;

            WFX2 BY x21-x23;

            WFX3 BY x31-x33;

            WFX4 BY x41-x43;

            WFX5 BY x51-x53;   

            WFY1 BY y11-y13;

            WFY2 BY y21-y23;

            WFY3 BY y31-y33;

            WFY4 BY y41-y43;

            WFY5 BY y51-y53;

!个体内自回归和交叉滞后路径

            WFX2 WFY2 ON WFX1 WFY1;

            WFX3 WFY3 ON WFX2 WFY2;

            WFX4 WFY4 ON WFX3 WFY3;

            WFX5 WFY5 ON WFX4 WFY4;

!同一时间变量间相关

            WFX1 WITH WFY1;

            WFX2 WITH WFY2;

            WFX3 WITH WFY3;

            WFX4 WITH WFY4;

            WFX5 WITH WFY5;

OUTPUT:     TECH1 STDYX SAMPSTAT CINTERVAL;

 

Step 2 弱测量不变性

TITLE:      Multiple indicator RI-CLPM, 5 waves, with 3 indicators for

            each variable at each wave (30 observed variables) and with

            random intercepts for each indicator separately. Fitting a model

            with constraints to ensure weak factorial invariance.

DATA:       FILE = RICLPM-MI.dat;

VARIABLE:   NAMES = x11 x12 x13 x21 x22 x23 x31 x32 x33

                    x41 x42 x43 x51 x52 x53 y11 y12 y13

                    y21 y22 y23 y31 y32 y33 y41 y42 y43

                    y51 y52 y53;

ANALYSIS:   MODEL = NOCOV; ! Sets all default covariances to zero

MODEL:

            RIX1 BY x11@1 x21@1 x31@1 x41@1 x51@1;

            RIX2 BY x12@1 x22@1 x32@1 x42@1 x52@1;

            RIX3 BY x13@1 x23@1 x33@1 x43@1 x53@1;

        

            RIY1 BY y11@1 y21@1 y31@1 y41@1 y51@1;

            RIY2 BY y12@1 y22@1 y32@1 y42@1 y52@1;

            RIY3 BY y13@1 y23@1 y33@1 y43@1 y53@1;

            RIX1-RIY3 WITH RIX1-RIY3;

!加粗为在第一步基础上修改的代码,通过在语句的括号中填加相同的标签,限定潜变量的载荷相等

            WFX1 BY x11-x13 (a b c);

            WFX2 BY x21-x23 (a b c);

            WFX3 BY x31-x33 (a b c);

            WFX4 BY x41-x43 (a b c);

            WFX5 BY x51-x53 (a b c);   

            WFY1 BY y11-y13 (d e f);

            WFY2 BY y21-y23 (d e f);

            WFY3 BY y31-y33 (d e f);

            WFY4 BY y41-y43 (d e f);

            WFY5 BY y51-y53 (d e f);

            WFX2 WFY2 ON WFX1 WFY1;

            WFX3 WFY3 ON WFX2 WFY2;

            WFX4 WFY4 ON WFX3 WFY3;

            WFX5 WFY5 ON WFX4 WFY4;

            WFX1 WITH WFY1;

            WFX2 WITH WFY2;

            WFX3 WITH WFY3;

            WFX4 WITH WFY4;

            WFX5 WITH WFY5;

OUTPUT:     TECH1 STDYX SAMPSTAT CINTERVAL;

 

Step 3 强测量不变性

TITLE:      Multiple indicator RI-CLPM, 5 waves, with 3 indicators for

            each variable at each wave (30 observed variables) and with

            random intercepts for each indicator separately. Fitting a model

              with constraints to ensure strong factorial invariance.

DATA:       FILE = RICLPM-MI.dat;

VARIABLE:   NAMES = x11 x12 x13 x21 x22 x23 x31 x32 x33

                    x41 x42 x43 x51 x52 x53 y11 y12 y13

                    y21 y22 y23 y31 y32 y33 y41 y42 y43

                    y51 y52 y53;

ANALYSIS:   MODEL = NOCOV; ! Sets all default covariances to zero

MODEL:

            RIX1 BY x11@1 x21@1 x31@1 x41@1 x51@1;

            RIX2 BY x12@1 x22@1 x32@1 x42@1 x52@1;

            RIX3 BY x13@1 x23@1 x33@1 x43@1 x53@1;

            RIY1 BY y11@1 y21@1 y31@1 y41@1 y51@1;

            RIY2 BY y12@1 y22@1 y32@1 y42@1 y52@1;

            RIY3 BY y13@1 y23@1 y33@1 y43@1 y53@1;

            RIX1-RIY3 WITH RIX1-RIY3;

            WFX1 BY x11-x13 (a b c);

            WFX2 BY x21-x23 (a b c);

            WFX3 BY x31-x33 (a b c);

            WFX4 BY x41-x43 (a b c);

            WFX5 BY x51-x53 (a b c);   

            WFY1 BY y11-y13 (d e f);

            WFY2 BY y21-y23 (d e f);

            WFY3 BY y31-y33 (d e f);

            WFY4 BY y41-y43 (d e f);

            WFY5 BY y51-y53 (d e f);

!加粗为在第二步基础上修改的代码,方括号为估计截距,通过在语句的括号中填加相同的标签,限定潜变量的载荷相等,同时使用星号,自由估计潜变量的截距。

            [x11 x12 x13] (g h i);

            [x21 x22 x23] (g h i);

            [x31 x32 x33] (g h i);

            [x41 x42 x43] (g h i);

            [x51 x52 x53] (g h i);

            [y11 y12 y13] (j k l);

            [y21 y22 y23] (j k l);

            [y31 y32 y33] (j k l);

            [y41 y42 y43] (j k l);

            [y51 y52 y53] (j k l);

            [WFX2* WFX3* WFX4* WFX5*];

            [WFY2* WFY3* WFY4* WFY5*];

            WFX2 WFY2 ON WFX1 WFY1;

            WFX3 WFY3 ON WFX2 WFY2;

            WFX4 WFY4 ON WFX3 WFY3;

            WFX5 WFY5 ON WFX4 WFY4;

            WFX1 WITH WFY1;

            WFX2 WITH WFY2;

            WFX3 WITH WFY3;

            WFX4 WITH WFY4;

            WFX5 WITH WFY5;

OUTPUT:     TECH1 STDYX SAMPSTAT CINTERVAL;

 

Step 4 在潜变量层面应用RI-CLPM(最终模型)

TITLE:      Multiple indicator RI-CLPM, 5 waves with 3 indicators for each

            variable at each wave (30 observed variables). Fitting a model

            with constraints to ensure strong factorial invariance, with

            the RI-CLPM at the latent level.

DATA:       FILE = RICLPM-MI.dat;

VARIABLE:   NAMES = x11 x12 x13 x21 x22 x23 x31 x32 x33

                    x41 x42 x43 x51 x52 x53 y11 y12 y13

                    y21 y22 y23 y31 y32 y33 y41 y42 y43

                    y51 y52 y53;

ANALYSIS:   MODEL = NOCOV; ! Sets all default covariances to zero

MODEL:

            FX1 BY x11-x13 (a b c);

            FX2 BY x21-x23 (a b c);

            FX3 BY x31-x33 (a b c);

            FX4 BY x41-x43 (a b c);

            FX5 BY x51-x53 (a b c);   

            FY1 BY y11-y13 (d e f);

            FY2 BY y21-y23 (d e f);

            FY3 BY y31-y33 (d e f);

            FY4 BY y41-y43 (d e f);

            FY5 BY y51-y53 (d e f);

            [x11 x12 x13] (g h i);

            [x21 x22 x23] (g h i);

            [x31 x32 x33] (g h i);

            [x41 x42 x43] (g h i);

            [x51 x52 x53] (g h i);

            [y11 y12 y13] (j k l);

            [y21 y22 y23] (j k l);

            [y31 y32 y33] (j k l);

            [y41 y42 y43] (j k l);

            [y51 y52 y53] (j k l);        

            [FX2* FX3* FX4* FX5*];

            [FY2* FY3* FY4* FY5*];

            RIX BY FX1@1 FX2@1 FX3@1 FX4@1 FX5@1;

            RIY BY FY1@1 FY2@1 FY3@1 FY4@1 FY5@1;

            RIX WITH RIY;

            FX1-FY5@0;

            WFX1 BY FX1@1;

            WFX2 BY FX2@1;

            WFX3 BY FX3@1;

            WFX4 BY FX4@1;

            WFX5 BY FX5@1;

            WFY1 BY FY1@1;

            WFY2 BY FY2@1;

            WFY3 BY FY3@1;

            WFY4 BY FY4@1;

            WFY5 BY FY5@1;

            WFX2 WFY2 ON WFX1 WFY1;

            WFX3 WFY3 ON WFX2 WFY2;

            WFX4 WFY4 ON WFX3 WFY3;

            WFX5 WFY5 ON WFX4 WFY4;

            WFX1 WITH WFY1;

            WFX2 WITH WFY2;

            WFX3 WITH WFY3;

            WFX4 WITH WFY4;

            WFX5 WITH WFY5;

OUTPUT:     TECH1 STDYX SAMPSTAT CINTERVAL;


PSYCH统计实验室

写在后面

希望这些内容能够帮助大家更深入地掌握多群组RI-CLPM的模型构建与分析过程。如果您在实际应用中遇到问题,欢迎继续交流探讨。



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共有四讲内容:

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