关键词: 有调节的中介效应, 潜结构方程模型, bootstrap, 乘积指标

Abstract: The analyses of moderated mediation effects are frequently applied to the studies of psychology, education, and other social science disciplines. A moderated mediation model is a combination of both moderation and mediation models. When a mediation effect is moderated by a moderator, the effect is termed moderated mediation and the model is a moderated mediation model. There are three common types of moderated mediation models: first-stage moderated mediation, second-stage moderated mediation, and dual-stage moderated mediation. Researchers have been searching for the most appropriate analytical method for testing moderated mediation. The observed variable regression approach has been the most popular. One critical limitation of regression approach is that regression analyses assume that variables are measured without error, which result in biased estimates of moderated mediation effect. Structural equation modeling (SEM) method has been extensively used to estimate moderated mediation effect because it corrects for measure errors. Product-indicator method was dominantly used to analyze latent moderated mediation model. There are at least two weaknesses frequently found in moderated mediation effects by product-indicator method. First, product-indicator method involve some type of multiplication of indicators to form the indicators of the latent variable that represents the product of the two latent variables, the generation of product indicators make users feel difficult to use. Second, product-indicators are not normal distributed, estimates based on normal assumption may be bias. In order to improve the above shortcomings, the researchers suggest that moderated mediation effects should be analyzed by Latent Moderated Structural Equations method. The purpose of the present study is to summary an effective procedure for analyzing moderated mediation effects based on Latent Moderated Structural Equations. LMS is a distribution analysis. Compared to analyzing moderated mediation by linear regression and product-indicator method, Latent Moderated Structural Equations (LMS) has many advantages. First, LMS uses the raw data of indicator variables directly for estimation and not require the forming of any products of indicator variables. Second, LMS account for the nonlinearity in estimating the parameters of the model. Thirdly, the simulation researches show that LMS generated unbiased parameter estimations and standard errors under the usual assumption. At the present study, we propose a procedure to analyze the moderated model by LMS. The first step is to decide how well the model would fit by running a baseline model where the latent interaction term is not included. If the SEM model is not fitted well, stop the moderated mediation analysis. Otherwise, go to the second step. In the second step, AIC or log-likelihood ratio test is used to decide how well the model would fit by running a moderated mediation model where the latent interaction term is included. If the SEM model is not fitted well, stop the analysis. Otherwise, go to the third step. In the third step, product of coefficients approach by Hayes (2013), which can be implemented easily by MPLUS and LISREL software, is recommended to analyze moderated mediation effects. It shows that the moderated mediation effect is significant if a bias-corrected percentile Bootstrap confidence interval of the targeted product of coefficients does not include zero. We used an example to illustrate how to conduct the proposed procedure by using MPLUS software. MPLUS program is attached to facilitate the implementation of bias-corrected percentile Bootstrap method to analyze moderated mediation effects. The programs can be managed easily by empirical researchers. Directions for future study on moderated mediation are discussed at the end of the paper. In fact, the primary criticism of the LMS approach is that it is computationally intensive. Researcher suggest that simple model with smaller number of latent variables should be used. Another option would be to use parceling to reduce the number of indicators per latent variable.

Key words: Moderated mediation effects, Latent moderated structural equation, Bootstrap, Product-indicator