Multilevel nonnested data structures are common in many research areas. The traditional hierarchical linear modeling requires purely nested data structures and thus cannot be utilized to analyze multilevel nonnested data. In the context of student mobility in educational research, this dissertation proposes a reparameterized multiple membership model for multilevel nonnested longitudinal data. The reparameterized multiple membership model assumes that school effects on student growth rates are cumulative and thus the effects of all schools attended by mobile students are weighted. It has a more tenable assumption than that of the existing cross-classified approach to student mobility. It is more parsimonious than the existing cross-classified multiple membership approach to student mobility. Therefore, it is a strong alternative approach to modeling student mobility in longitudinal studies.
Three studies are conducted to evaluate the estimation performance of the reparameterized multiple membership model and investigate the consequences of model misspecification under various simulation conditions. In the first study, the Early Childhood Longitudinal Study Kindergarten Cohort data are analyzed to compare different approaches to modeling student mobility and achievement growth in longitudinal studies. Guided by real data analyses, two Monte Carlo simulation studies are conducted to evaluate the estimation performance of both correctly specified models and misspecified models under simulation conditions that emulate student mobility in educational research. The first simulation study uses the cross-classified multiple membership model as the true model for data generation. The second simulation study treats the reparameterized multiple membership model as the true model for data generation. In both simulation studies, simulated data are analyzed by the hierarchical linear model, the cross-classified multiple membership model, and the reparameterized multiple membership model.
Results indicate that Bayesian Monte Carlo Markov Chain estimation can successfully recover various parameters of the reparameterized multiple membership model under all simulation conditions. However, the cross-classified multiple membership model has difficulty to recover random effects parameters at the school level in case of low mobility rate or low percentage of variance between schools. Though some parameters in both models tend to be overestimated when the number of schools is small, biases in the reparameterized multiple membership model are smaller.
Model misspecification does not affect estimates of fixed effects parameters, but it induces substantial biases into estimates of random effects parameters, particularly for the slope variances at the student level and the school level. The mobility rate and the percentage of variance between schools affect the magnitudes of biases in misspecified models. The hierarchical linear model ignores student mobility and underestimates the percentage of variance between schools, and thus may result in inappropriate inferences about school effects and school accountability. The implications of this dissertation for educational research and practice are discussed.