The Decomposition of Between and Within Effects in Contextual Models - Guo, Siwen; Houang, Richard T.; Schmidt, William H. (Frontiers in Psychology, 2021)
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 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, and 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 were of less degrees of biases and higher observed coverage rates compared to those from the manifest and latent aggregation approaches. A real data application was also used to illustrate the three analysis approaches.