Abstract: The advantage of multilevel modeling (MLM) is to examine the data with nested structure which is frequently collected in the social and educational research. The effect of level-1 independent variable Xij on Yij would be decomposed into within-group and between-group effects by group mean centering with the means reintroduced into the level-2 intercept model, whose difference was called contextual effect and the reintroduced mean score of independent variable .j was called contextual variable. In order to estimate the complex structure of sampling error and measurement error occurring in multilevel modeling, multilevel structural equation modeling (MSEM) treats the contextual variable as latent with multiple indicators. The superiority of MSEM is the integration of MLM and SEM to simultaneously analyze nested data structure and estimate latent variable. By taken as an example, the contextual effects of Competitive atmosphere of the class on Competitive behavior of individual students was introduced for illustrating how the analysis of contextual effects was achieved by MSEM. The future research direction of contextual effects, unbiased estimation of the effect and contextual variable is discussed at the end of the paper.

Key words: multilevel model, multilevel structural equations modeling, contextual effect, contextual variable, sampling error, measurement error