Multilevel Regression Discontinuity Models with Latent Variables
Yang, Ji Seung
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Regression discontinuity (RD) designs allow estimating a local average treatment effect (LATE) when assignment of an individual to treatment is determined by their location on a running variable in relation to a cutoff value. The design is especially useful in education settings, where ethical concerns can forestall the use of randomization. Applications of RD in education research typically share two characteristics, which can make the use of the conventional RD model inappropriate: 1) The use of latent constructs, and 2) The hierarchical structure of the data. The running variables often used in education research represent latent constructs (e.g., math ability), which are measured by observed indicators such as categorical item responses. While the use of a latent variable model to account for the relationships among item responses and the latent construct is the preferred approach, conventional RD analyses continue to use observed scores, which can result in invalid or less informative conclusions. The current study proposes a multilevel latent RD model which accounts for the prevalence of clustered data and latent constructs in education research, allows for the generalizability of the LATE to individuals further from the cutoff, and allows researchers to quantify the heterogeneity in the treatment effect due to measurement error in the observed running variable. Models are derived for two of the most commonly used multilevel RD designs. Due to the complex and high-dimensional nature of the proposed models, they are estimated in one stage using full-information likelihood via the Metropolis-Hastings Robbins-Monro algorithm. The results of two simulation studies, under varying sample size and test length conditions, indicate the models perform well when using the full sample with at least moderate-length assessments. A proposed model is used to examine the effects of receiving an English language learner designation on science achievement using the Early Childhood Longitudinal Study. Implications of the results of these studies and future directions for the research are discussed.