The specification of the propensity score in cross-classified multilevel models: An examination of omitted cluster variable bias

In the last few decades, the Propensity Score (PS) methods have been advocated to strengthen the claim of causal inference when analyzing observational datasets. While the pure cluster dataset is commonly acknowledged and utilized in the field of education, the non-nested cluster dataset, such as the cross-classified multilevel model (CCMM), is rarely adopted together with the propensity score methods. This study focuses on the situation of one of the clusters being omitted when specifying PS in a CCMM setting and examines to what extent the omitted variable bias became problematic in estimating the Average Treatment Effect for Treated. Through Monte Carlo simulation, this study proposes the proper threshold for specifying PS in the CCMM context given different cluster characteristics such as cluster size, number of clusters, and clustering effect (i.e., intraclass correlation coefficient).

Embargo status: Restricted to TTU community only. To view, login with your eRaider (top right). Others may request the author grant access exception by clicking on the PDF link to the left.