Decomposing variables into between and within components are often required in multilevel analysis. This method of decomposition should not ignore possible unreliability of an observed group mean (i.e., arithmetic mean) that is due to small cluster sizes and can lead to substantially biased estimates. Adjustment procedures that allow unbiased…

Multilevel Rasch models are increasingly used to estimate the relationships between test scores and student and school factors. Response data were generated to follow one-, two-, and three-parameter logistic (1PL, 2PL, 3PL) models, but the Rasch model was used to estimate the latent regression parameters. When the response functions followed 2PL…

Measures of variability are successfully used in predictive modeling in research areas outside of education. This study examined how standard deviations can be used to address research questions not easily addressed using traditional measures such as group means based on index variables. Student survey data were obtained from the Organisation for…

The design of research studies utilizing binary multilevel models must necessarily incorporate knowledge of multiple factors, including estimation method, variance component size, or number of predictors, in addition to sample sizes. This Monte Carlo study examined the performance of random effect binary outcome multilevel models under varying…

Educational researchers commonly use the rule of thumb of "design effect smaller than 2" as the justification of not accounting for the multilevel or clustered structure in their data. The rule, however, has not yet been systematically studied in previous research. In the present study, we generated data from three different models…

Facilitating students' transition from less to more mathematically productive engagement in discussions is an important area of investigation. Research on mathematical whole-class discussions has consistently identified facilitating students' mathematical autonomy as a central component of this transition. Additionally, research commonly infers…