Partitioning Variance for a Within-Level Predictor in Multilevel Models

Abstract

Multilevel modeling (MLM) is widely used for the multilevel data structure in social science. Two MLM limitations involve partitioning variance for a within-level predictor. First, MLM does not automatically partial out the between-level variance for a within-level predictor. Second, MLM assumes a within-level predictor to be measurement-error free. Thus, the error variance cannot be separated out. The study evaluated the impact of improperly partitioning two-level variances and measurement error variances for a within-level predictor in MLM. Our findings suggested (a) whether the research interest lies in a within-level or a between-level predictor, group-mean centering or latent-mean centering must be used to partition two-level variances; (b) for the measurement error variance, the within-level factor loadings should be as high as possible (≥0.80 in our simulation settings). If these two requirements are not met, multilevel structural equation modeling (MSEM) should always be adopted for the analysis.