The analysis of moderation effects has become an important statistical method in multivariate studies. Methodological research on moderation effects in China’s mainland covers the following topics: moderation effects of observed variables, latent variables, multi-level data and longitudinal data; the single-level moderation effect analysis based on a two-level regression model; the integration model of moderation and mediation (see Wen et al. 2022).

Methodological research on the moderation effect of observed variables includes three aspects: standardized resolution, simple slope test, and the moderation effect of category variables. The research on latent moderation includes three aspects too: standardized resolution, model simplification, and comparison of analytical methods. Under the normal condition, latent moderated structural equations (LMS) are recommended to estimate the moderation effect of latent variables. Otherwise, after centralizing all indicators, the unconstrained product indicator method is recommended to establish a latent moderation model; Bayesian method is an alternative, especially in the case of a small sample.

The model development of multilevel moderation effect involves the conflated multilevel model, unconflated multilevel model (UMM), and multilevel structural equation model (MSEM). All independent variables at Level-1 are not centered in the conflated multilevel model, whereas in the UMM all independent variables at level-1 are centered using group-mean, and the group mean is included at Level-2. If the group-mean was treated as a latent variable, MSEM is recommended. Further, two ways are adopted to test multilevel moderation in the multilevel structural equation model: random coefficient prediction (RCP) for cross-level moderations, and LMS for same-level moderations.

The moderation effect analysis of longitudinal data is divided into three types. The first type is moderation analysis in two-instance repeated measures designs, in which only the dependent variable is repeated measurement. In the second type, there isn’t any moderator, while both the independent and dependent variables are repeated measurement (e.g., the cross-lagged model, and the contextual moderation model). In the third type, all variables are repeated measurement, such as the latent growth model and multilevel model.

Two-level regression model is recommended to analyze the moderation effect of single-level data. It can be employed to analyze the moderation effect of both observed variables and latent variables.

Some international frontiers of methodological research on moderation analysis are briefly introduced: the combination of LMS and Bayesian method, moderation analysis of multiple moderators; moderation analysis of longitudinal data.