AUTHOR=Guo Siwen , Houang Richard T. , Schmidt William H. TITLE=The Decomposition of Between and Within Effects in Contextual Models JOURNAL=Frontiers in Psychology VOLUME=12 YEAR=2021 URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2021.541803 DOI=10.3389/fpsyg.2021.541803 ISSN=1664-1078 ABSTRACT=

In contextual studies, group compositions are often extracted from individual data in the sample, in order to estimate the group compositional effects [e.g., school socioeconomic status (SES) effect] controlling for interindividual differences in multilevel models. As the same variable is used at both group level and individual level, an appropriate decomposition of between and within effects is a key to providing a clearer picture of these organizational and individual processes. The current study developed a new approach with within-group finite population correction (fpc). Its performances were compared with the manifest and latent aggregation approaches in the decomposition of between and within effects. Under a moderate within-group sampling ratio, the between effect estimates from the new approach had a lesser degree of bias and higher observed coverage rates compared with those from the manifest and latent aggregation approaches. A real data application was also used to illustrate the three analysis approaches.