The Risk of Using an Average Score as a Latent Variable in Multilevel Models

Abstract

Educational researchers frequently work with data measured as multilevel structures; sometimes, they are also interested in latent constructs that cannot be directly observed and measured. Therefore, handling data dependency and measurement error issues is particularly important in statistical modeling. Multilevel Structural Equation Modeling (MSEM) is a promising approach to dealing with both issues. However, educational researchers still prefer Multi-Level Modeling (MLM) to MSEM. Conventional MLM cannot address the data dependency issue in within-level predictors. In addition, it cannot include a measurement model to handle measurement errors and construct a latent factor. As such, computing an average score to represent a latent factor in MLM is a common alternative approach in educational studies. This study evaluated the consequence of using an average score to represent a latent factor in MLM. The simulation results suggested that the bias of using an average score to represent a latent predictor in MLM is acceptable only when the following criterion are met: (1) group-mean centering or latent-mean centering is utilized; (2) the within-level factor loading of each item is equal to or above .80 (i.e., within-level composite reliability ω ≥ 0.88). Otherwise, MSEM is recommended.