Abstract:  In recent years, multilevel models (MLM) have been frequently used for studying multilevel moderation in social sciences. However, there still exist sampling errors and measurement errors even after separating the between-group effects from the within-group effects of multilevel moderation. To solve this problem, a new method has been developed abroad by integrating MLM with structural equation models (SEM) under the framework of multilevel structural equation models (MSEM) to set latent variables and multiple indicators. It has been showed that the method could rectify sampling errors and measurement errors effectively and obtain more accurate estimation of moderating effects. After introducing the new method by modeling with random coefficient prediction and with latent moderated structural equations, we propose a procedure for analyzing multilevel moderation by using MSEM. An example is illustrated with the software Mplus. Totally 29 articles, published in Chinese psychological journals from 2010 to 2017, are reviewed for evaluating the situation of using multilevel moderation analysis methods in psychological researches in China. Directions for future study on multilevel moderation and MSEM were discussed at the end of the paper.

Key words: multilevel model, multilevel moderation, sampling error, random coefficient, Latent moderated structural equation