The trace plot is seldom used in meta-analysis, yet it is a very informative plot. In this article, we define and illustrate what the trace plot is, and discuss why it is important. The Bayesian version of the plot combines the posterior density of [tau], the between-study standard deviation, and the shrunken estimates of the study effects as a…

Regression discontinuity (RD) designs are increasingly used for causal evaluations. For example, if a student's need for a literacy intervention is determined by a low score on a past performance indicator and that intervention is provided to all students who fall below a cutoff on that indicator, an RD study can determine the intervention's main…

Binary logistic regression is one of the most widely used statistical tools. The method uses odds, log odds, and odds ratios, which are difficult to understand and interpret. Understanding of logistic regression tends to fall down in one of three ways: (1) Many students and researchers come to believe that an odds ratio translates directly into…

Regression discontinuity (RD) designs are increasingly used for causal evaluations. However, the literature contains little guidance for conducting a moderation analysis within an RDD context. The current article focuses on moderation with a single binary variable. A simulation study compares: (1) different bandwidth selectors and (2) local…

Background/Context: In meta-analyses examining educational interventions, researchers seek to understand the distribution of intervention impacts, in order to draw generalizations about what works, for whom, and under what conditions. One common way to examine equity implications in such reviews is through moderator analysis, which involves…

Bayesian estimations of complex regression models with high-dimensional parameter spaces require advanced priors, capable of addressing both sparsity and multicollinearity in the data. The Dirichlet-horseshoe, a new prior distribution that combines and expands on the concepts of the regularized horseshoe and the Dirichlet-Laplace priors, is a…

Recurrent event analyses have found a wide range of applications in biomedicine, public health, and engineering, among others, where study subjects may experience a sequence of event of interest during follow-up. The R package reReg offers a comprehensive collection of practical and easy-to-use tools for regression analysis of recurrent events,…

Many students of statistics and econometrics express frustration with the way a problem known as "bad control" is treated in the traditional literature. The issue arises when the addition of a variable to a regression equation produces an unintended discrepancy between the regression coefficient and the effect that the coefficient is…

Background/Context: In meta-analysis examining educational intervention, characterizing heterogeneity and exploring the sources of variation in synthesized effects have become increasingly prominent areas of interest. When combining results from a collection of studies, statistical dependency among their effects size estimates will arise when a…

Higher education institutions have consistently strived to provide students with top-notch education. To achieve better outcomes, machine learning (ML) algorithms greatly simplify the prediction process. ML can be utilized by academicians to obtain insight into student data and mine data for forecasting the performance. In this paper, the authors…

"Simulation-based inference" is often considered a pedagogical strategy for helping students develop inferential reasoning, for example, giving them a visual and concrete reference for deciding whether the observed statistic is unlikely to happen by chance alone when the null hypothesis is true. In this article, we highlight for teachers…

In this Methods Showcase Article, we illustrate mixed-effects modeling with a multinomial dependent variable as a means of explaining complexities in language. We model data on future-time reference in second language Spanish, which consists of a nominal dependent variable that has three levels, measured over 73 participants. We offer step-by-step…

Predicting student performance has been a critical focus of educational research. With an effective predictive model, schools can identify potentially at-risk students and implement timely interventions to support student success. Recent developments in educational data mining (EDM) have introduced several machine learning techniques that can…

Though previously unacknowledged, a SMART (Sequential Multiple Assignment Randomized Trial) design uses both regression discontinuity (RD) and randomized controlled trial (RCT) designs. This combination structure creates a conceptual symbiosis between the two designs that enables both RCT- and previously unrecognized, RD-based inferential claims.…

Recently, deep learning has become a pervasive tool in prediction problems for structured and/or unstructured big data in various areas including science and engineering. In particular, deep neural network models (i.e. a basic core model of deep learning) can be viewed as an extension of statistical models by going through the incorporation of…