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Montessori pedagogy is a century-old, whole-school system increasingly used in the public sector. In the United States, public Montessori schools are typically Title I schools that mostly serve children of color. The present secondary, exploratory data analysis examined outcomes of 134 children who entered a lottery for admission to public Montessori schools in the northeastern United States at age 3; half were admitted and enrolled and the rest enrolled at other preschool programs. About half of the children were identified as White, and half were identified as African American, Hispanic, or multiracial. Children were tested in the fall when they enrolled and again in the subsequent three springs (i.e., through the kindergarten year) on a range of measures addressing academic outcomes, executive function, and social cognition. Although the Black, Hispanic, and multiracial group tended to score lower in the beginning of preschool in both conditions, by the end of preschool, the scores of Black, Hispanic, and multiracial students enrolled in Montessori schools were not different from the White children; by contrast, such students in the business-as-usual schools continued to perform less well than White children in academic achievement and social cognition. The study has important limitations that lead us to view these findings as exploratory, but taken together with other findings, the results suggest that Montessori education may create an environment that is more conducive to racial and ethnic parity than other school environments. 

Growth curve models (GCMs), with their ability to directly investigate within-subject change over time and between-subject differences in change for longitudinal data, are widely used in social and behavioral sciences. While GCMs are typically studied with the normal distribution assumption, empirical data often violate the normality assumption in applications. Failure to account for the deviation from normality in data distribution may lead to unreliable model estimation and misleading statistical inferences. A robust GCM based on conditional medians was recently proposed and outperformed traditional growth curve modeling when outliers are present resulting in nonnormality. However, this robust approach was shown to perform less satisfactorily when leverage observations existed. In this work, we propose a robust double medians growth curve modeling approach (DOME GCM) to thoroughly disentangle the influence of data contamination on model estimation and inferences, where two conditional medians are employed for the distributions of the within-subject measurement errors and of random effects, respectively. Model estimation and inferences are conducted in the Bayesian framework, and Laplace distributions are used to convert the optimization problem of median estimation into a problem of obtaining the maximum likelihood estimator for a transformed model. A Monte Carlo simulation study has been conducted to evaluate the numerical performance of the proposed approach, and showed that the proposed approach yields more accurate and efficient parameter estimates when data contain outliers or leverage observations. The application of the developed robust approach is illustrated using a real dataset from the Virginia Cognitive Aging Project to study the change of memory ability. 

Bayesian non-parametric (BNP) modeling has been developed and proven to be a powerful tool to analyze messy data with complex structures. Despite the increasing popularity of BNP modeling, it also faces challenges. One challenge is the estimation of the precision parameter in the Dirichlet process mixtures. In this study, we focus on a BNP growth curve model and investigate how non-informative prior, weakly informative prior, accurate informative prior, and inaccurate informative prior affect the model convergence, parameter estimation, and computation time. A simulation study has been conducted. We conclude that the non-informative prior for the precision parameter is less preferred because it yields a much lower convergence rate, and growth curve parameter estimates are not sensitive to informative priors.