ISSN 1671-3710
CN 11-4766/R

心理科学进展 ›› 2022, Vol. 30 ›› Issue (11): 2461-2472.doi: 10.3724/SP.J.1042.2022.02461

• 研究方法 • 上一篇    下一篇


方杰1, 温忠麟2()   

  1. 1广东财经大学新发展研究院/应用心理学系, 广州 510320
    2华南师范大学心理学院/心理应用研究中心, 广州 510631
  • 收稿日期:2021-10-16 出版日期:2022-11-15 发布日期:2022-11-09
  • 通讯作者: 温忠麟
  • 基金资助:

Moderation analysis for longitudinal data

FANG Jie1, WEN Zhonglin2()   

  1. 1Institute of New Development & Department of Applied Psychology, Guangdong University of Finance & Economics, Guangzhou 510320, China
    2Center for Studies of Psychological Application & School of Psychology, South China Normal University, Guangzhou 510631, China
  • Received:2021-10-16 Online:2022-11-15 Published:2022-11-09
  • Contact: WEN Zhonglin


目前调节效应检验主要是基于截面数据, 本文讨论纵向(追踪)数据的调节效应分析。如果自变量X和因变量Y有纵向数据, 调节效应可分为三类:调节变量Z不随时间变化、Z随时间变化、调节变量从自变量或因变量中产生。评介了基于多层模型、多层结构方程模型、交叉滞后模型和潜变量增长模型的纵向数据的多种调节效应分析方法。调节效应的分解和潜调节结构方程法的使用是纵向数据的调节效应分析的两大特点。对基于四类模型的调节效应分析方法进行综合比较后, 总结出一个纵向数据的调节效应分析流程。随后用实际例子演示如何进行纵向数据的调节效应分析, 并给出相应的Mplus程序。随后展望了纵向数据的调节效应分析的拓展方向, 例如基于动态结构方程模型的密集追踪数据的调节效应分析。

关键词: 纵向数据, 调节效应, 多层模型, 多层结构方程模型, 交叉滞后模型, 潜变量增长模型


At present, the analysis of moderating effect is mainly based on cross sectional data. This article discusses how to analyze the moderating effect with longitudinal data. If the independent variable X and the dependent variable Y are longitudinal data, longitudinal moderation models can be divided into three categories according to the type of moderator: time-invariant moderator, time-variant moderator, and moderator generated from X or Y. For example, Xtj is divided into two parts, time-varying intra-individual differences $X_{t j}-\bar{X}_{\bullet} j$ and time-invariant inter-individual differences$\bar{X}_{\boldsymbol{\bullet} j}$, and then the moderating effect of $\bar{X}_{\boldsymbol{\bullet} j}$ on the relationship between $(X_{t j}-\bar{X}_{\bullet} j)$ and Ytj can be analyzed. In that case, there will be no new moderator Z, which is characteristic of moderation research on longitudinal data in contrast to research on cross-sectional data.

Four types of longitudinal moderation analysis approaches are summarized: 1) Multilevel model (MLM); 2) Multilevel structural equation model (MSEM); 3) Cross-lagged model (CLM); 4) Latent growth model (LGM). It is found that the decomposition of the moderating effect and the use of the latent moderating structural equation (LMS) method are the two characteristics of the moderation analysis for longitudinal data. Specifically, MLM, MSEM, and CLM divide the moderating effect of longitudinal data into three parts: the time-varying intra-individual part, time-invariant inter-individual part, and the cross-level part. In addition, the moderating effect of longitudinal data can be decomposed into the moderating effect of initial level and rate of change by LGM.

In the present study, we propose a procedure to analyze longitudinal mediation analysis. The first step is to decide whether it is necessary to make a causal inference. If the aim of research is to make a causal inference, CLM should be adopted to analyze longitudinal moderation. Otherwise, proceed with the second step. The second step is to decide whether it is necessary to treat longitudinal data as multilevel data. If longitudinal data is treated as multilevel data, MSEM should be adopted to analyze longitudinal moderation, because MSEM and MLM are more suitable for describing individual differences. Otherwise, LGM should be adopted to analyze longitudinal moderation, because only an LGM can simultaneously examine the effect of some variables on change and how the change affects other variables. The third step is to decide whether MSEM converges. If MSEM converges, the result of MSEM should be reported. Otherwise, MLM should be adopted to analyze longitudinal moderation. Compared with MLM, MSEM takes sampling error into account when the group mean is calculated, but the convergence of the MSEM is more difficult. Therefore, the MSEM with sampling error taken into account is preferred. If convergence fails, MLM will be considered.

This paper exemplifies how to conduct the proposed procedure by using Mplus. Directions for future research on moderation analysis of longitudinal data are discussed, such as the moderation analysis for intensive longitudinal data based on the dynamic structural equation model.

Key words: longitudinal data, moderation effect, multilevel model, multilevel structural equation model, cross-lagged model, latent growth model