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Three-Level Models for Partially Nested Data Structures


Partially nested data structures occur when some units (typically individuals) are nested within groups while others are not nested. An adjustment to the standard multilevel model for 2-level data structures to accommodate partially nested data was proposed by Bauer, Sterba, and Hallfors, where individuals at Level 1 are either nested within treatment groups or are independent at Level 2. The model was heteroscedastic, estimating separate Level 1 residuals for control and treatment arms. The focus of the current body of work was on extending this 2-level model in two ways. The extension in the first simulation study involved incorporating a higher level of nesting, such as schools. The extension in the second study involved incorporating a lower level of nesting, inclusive of repeated measures. This heteroscedastic longitudinal partially nested model included separate estimates of individual-level variance in intercepts, variance in slopes for the time effect, and the covariance between them. Given the strengths of such a model, a third study examined various methods for formally testing the hypothesis that individuals within treatment groups become similar as a function of time. Finally, findings from all three simulation studies were demonstrated using data from an intervention targeting slow readers. While performance of the model incorporating a higher level of nesting was not overly problematic, the longitudinal model did not perform well. As parameter estimates were biased in the longitudinal model, performance of tests proposed in the third study could not be properly evaluated. Implications for partially nested model extensions are discussed.

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