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Primary Submission Category: Multilevel Causal Inference

Multilevel Modeling under Multisite Quasi-experimental Trials: Considerations of Coding Strategies, Unbalanced Groups, and Heterogeneous Variances

Authors: Qian Zhang, Xiao Liu, Zijun Ke,

Presenting Author: Xiao Liu*

Multilevel models are often used to make causal inferences under multisite quasi-experimental trials, where participants are non-randomly assigned to treatment and control groups within each site. We are interested in inferring the average treatment effect associated with the dichotomous Level-1 treatment indicator. The dichotomous treatment indicator can be coded mainly in three ways: dummy coding, unweighted effect coding, and weighted effect coding. Among the three coding strategies, dummy coding and unweighted effect coding assume a 1:1 ratio between the treatment and control groups in the population; in contrast, weighted effect coding is recommended over dummy coding / unweighted effect coding in the situation where group proportions are unequal in the population. The goals of the study include (a) to analytically obtain the average treatment effect estimates and compare them under different coding strategies, (b) to analytically examine whether and how the inference about the average treatment effect may be impacted by heterogeneous variances of Level-1 residuals, (c) to conduct a simulation study to examine the inference accuracy about the average treatment effect using different coding strategies considering equal and unequal proportions of the two groups in the population, variability of group proportions across sites, and heterogeneous Level-1 residual variances, and (d) to illustrate the comparisons among different coding strategies via an empirical example.