Subjects: Psychology >> Social Psychology submitted time 2023-03-28 Cooperative journals: 《心理科学进展》
Abstract： Being able to analyze the influence mechanism of independent variables on dependent variables, the analysis of mediation effect has become an important statistical method in multivariate research. Since the first publication of Chinese paper on the mediation effect and its analytical methods in 2004, the mediation effect has become one focus of methodological research in Chinese Mainland, which is systematically reviewed in this paper. Firstly, the simple mediation model is reviewed with concept identification: how to distinguish between mediation and suppression effects, partial and complete mediation effects, and mediation effect and moderation effect. Then, methodological research on mediation effects in China’s Mainland is divided into five aspects: testing method for mediation effects, mediation effect size measure, mediation effect involving categorical variables or longitudinal data, and extended mediation model. They are summarized as follows. To test ab≠0,the easiest way is to test a≠0 and b≠0. These sequential tests are actually not the same as the joint significance tests because the Type-I error rates are rather different. If the test result is a≠0 and b≠0, then ab≠0 can be inferred with the Type-I error rate less than the significance level 0.05 (the preset significance level), while the Type-I error rate of the joint significance tests is 0.0975. However, if at least one of a≠0 and b≠0 does not hold, the sequential tests should not be used, since its statistical power is less than other alternative test methods discussed in the paper. Anyway, Bootstrap methods are preferred because they provide interval estimation of the mediation effect with a higher power. Furthermore, if appropriate prior information is available, the Bayesian method is also recommended. It is believed that κ2, R2-type and so on are not suitable as mediation effect size measures because of no monotonicity. Although υ=(ab)2υ=(ab)2\upsilon ={{(ab)}^{2}} is monotonic, it is not as simple and clear as the mediation effect (ab) itself. It is recommended that when the signs of ab and c are consistent, the standardized estimation of ab and ab/c should be reported. Mediation analysis with multi-categorical independent variables and with a two-condition within-participant design are discussed when categorical variables are concerned in mediation effect models. There are two types of model development in mediation analysis with longitudinal data. One is continuous time model and multilevel time-varying coefficient model that could be used to test time-varying effect of mediation effect. The other is random-effects cross-lagged panel model and multilevel autoregressive mediation model that could be adopted to examine individuals-varying effect of mediation effect. In addition, latent growth mediation model or multilevel mediation model in mediation effect analysis could be adopted only when the involved causal relationship is instant. Otherwise, cross-lagged panel model, continuous time model, or multilevel autoregressive mediation model should be adopted. The extensions of the mediation model include multiple mediation model, multilevel mediation model, single-level and multilevel moderated mediation model as well as mediated moderation model. These extended models can be used for both the analysis of observed variables and latent variables. Finally, the recent development of foreign methodological research on mediation effects is discussed, including potential outcome mediation analysis, confounder control in mediation analysis, robust mediation analysis, and power analysis of mediation effects. Moreover, integration of new statistical techniques has become a new feature of methodological research of mediation effects, for example, exploratory mediation analysis via regularization, bi-factor mediation analysis, latent class mediation analysis, and network mediation analysis.
Subjects: Psychology >> Social Psychology submitted time 2023-03-28 Cooperative journals: 《心理科学进展》
Abstract： 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.
Subjects: Psychology >> Statistics in Psychology submitted time 2021-10-12
Abstract： Analyzing the interaction effect of latent variables has become an important topic in both theoretical and empirical studies. Standardized estimation plays an important role in model interpretation and effect comparison. Although Wen et al. (2010) has formulated the appropriate standardized estimation for the latent interaction effects, there is no popular commercial software that provides the appropriate standardized estimation before the launch of Mplus 8.2 in 2019. Previous comparisons of methods for estimating latent interaction were based on the original estimation. In this study, through a simulation experiment, the appropriate standardized estimation of latent interaction effects is obtained respectively by four methods: the product indicator (PI) approach, Latent Moderated Structural Equations (LMS), Bayesian method without prior information (BN), and Bayesian method with prior information (BI). Then these estimations are compared in terms of the bias of estimation, the bias of standard error, type Ⅰ error rate and statistical power. The true model in the simulation is based on the structural equation η=0.4ξ_1+0.4ξ_2+γ_3 ξ_1 ξ_2+ζ where the latent variables η, ξ_1, ξ_2 each had three indicators with a standardized factor loading of 0.7. Experiment factors include the distribution of two exogenous latent variables (normal, non-normal), correlation ϕ_12 between two exogenous latent variables (0, 0.3 and 0.7), interaction effect γ_3 (0, 0.2), sample size N (100, 200, and 500) and estimation method (PI, LMS, BN, BI). There are five main findings. (1) the proportion of proper solution of LMS and the two Bayesian methods were close to 100% in all treatments, while PI was almost fully proper when N = 500. (2) Under the normal condition, the bias of standardized estimation of latent interaction obtained by LMS, BI and BN was ignorable, and PI was acceptable when N = 500. Under the non-normal condition, the bias of LMS and Bayesian methods inflated seriously with increasing correlation of two exogenous latent variables, but PI was still acceptable when N = 500. (3) Under both distribution conditions, the bias of standard error of standardized estimation of latent interaction obtained by LMS and BN was small and acceptable, while PI was acceptable when N = 500, and BI tended to overestimate the standard error. (4) Under normal conditions, the type I error rates of LMS were acceptable only when the sample size was large, while the other methods were acceptable in all conditions. Under the non-normal condition, the type I error rates of PI were still acceptable, while the other methods were acceptable only when the sample size was small or the correlation between two exogenous latent variables was low. (5) The statistical power of latent interaction obtained by PI was lower than that by any other method, and a large sample size (e.g., N=500) was required to ensure the PI with statistical power over 80%; LMS and BN had higher statistical power, while BI had the highest one in all conditions. For the latent interaction, the results of comparing different methods in standardized estimation are quite similar to those in the original estimation. Under the normal condition, it is recommended to use LMS to estimate the interaction effect of latent variables, with the caution of Type I error rate and effect size for inference. If accurate prior information can be obtained, Bayesian method is preferred, especially in the case of a small sample. When the variables are not normally distributed, the unconstrained product indicator approach is recommended, which is more robust than the other methods, but the sample size should be large enough (N =500 or above). If the correlation between exogenous latent variables is low (it can be estimated and tested by confirmatory factor analysis), Bayesian method without prior information can be considered for small samples.
Subjects: Psychology >> Statistics in Psychology submitted time 2021-08-26
Abstract： The mediation effect analysis is able to reveal the process and mechanism of the impact of independent variables on a dependent variable. As an important statistical method, the mediation effect analysis has become a hot topic in methodology research in the last twenty years. The development of domestic research on the methodology of mediation effect was systematically reviewed from the five aspects, including testing method, effect size, the mediation effect test of categorical variables and longitudinal data, and model expansion. Specifically, model expansions include multiple mediation models, multilevel mediation models, moderated mediation model and mediated moderation model. Finally, recent progresses of foreign methodological studies on mediation effect and the future research directions were discussed.
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