This paper explores multilevel modeling approaches for 2-group randomized experiments in which a treatment condition involving clusters of individuals is compared to a control condition involving only ungrouped individuals, otherwise known as partially nested cluster randomized designs (PNCRTs). Strategies for comparing groups from a PNCRT in the multilevel modeling framework include pseudo-clustering the control condition (Model 1), treating the control condition as one large cluster (Model 2), or treating the controls as singletons within their own clusters, using either a random intercept-fixed treatment slope model or a fixed intercept-random treatment slope model (Models 3a and 3b, respectively). In Study 1, a Monte Carlo simulation program was constructed in SAS to evaluate the performance of the four strategies with small samples (N = 40 with n = 20 in each experimental condition), across 96 conditions comprising six levels of treatment intraclass correlations, four levels of treatment effect sizes, and four combinations of number of treatment clusters:cluster sizes. Three methods for degrees of freedom estimation were also compared for generalizability to popular multilevel modeling software. Results from Study 1 showed that, under most realistic conditions (i.e., when the treatment intraclass correlation is between .1 and .3), treating controls as singleton clusters in a model that uses a random treatment slope (Model 3b), is preferred over the other strategies in terms of controlling Type I error and achieving the greatest power using the fewest parameter estimates. On the other hand, none of the four strategies were robust when the dataset involved a very small ratio of treatment clusters: cluster sizes. In Study 2, the four strategies were applied to a dataset from a previously published study. Results from Study 2 showed no substantive differences among models for estimating parameters. Overall, this paper demonstrates that multilevel modeling using popular software can be appropriate and feasible for many PNCRT designs that are likely to occur in educational research.
|School:||University of Washington|
|School Location:||United States -- Washington|
|Source:||DAI-A 72/07, Dissertation Abstracts International|
|Subjects:||Educational tests & measurements, Educational psychology, Quantitative psychology|
|Keywords:||Cluster randomized trials, Heterogeneous variance, Multilevel modeling, Partial nesting|
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