Previous research explicates ordinal and disordinal interactions through the concept of the "crossover point." This point is determined via simple regression models of a focal predictor at specific moderator values and signifies the intersection of these models. An interaction effect is labeled as disordinal (or ordinal) when the…

The following study shows how reparameterizations and constraints of the general linear model can serve to parse quantitative and qualitative aspects of predictors. We demonstrate three different approaches. The study uses data from the High School Longitudinal Study of 2009 on mathematics course-taking and achievement as an example. Results show…

Simulation studies are the basic tools of quantitative methodologists used to obtain empirical solutions to statistical problems that may be impossible to derive through direct mathematical computations. The successful execution of many simulation studies relies on the accurate generation of correlated multivariate data that adhere to a particular…

A mixture of logit models is proposed that discriminates between responses to rating questions that are affected by a tendency to prefer middle or extremes of the scale regardless of the content of the item (response styles) and purely content-driven preferences. Explanatory variables are used to characterize the content-driven way of answering as…

Machine learning (ML) methods for causal inference have gained popularity due to their flexibility to predict the outcome model and the propensity score. In this article, we provide a within-group approach for ML-based causal inference methods in order to robustly estimate average treatment effects in multilevel studies when there is cluster-level…

This review covers the core concepts and design decisions of TensorFlow. TensorFlow, originally created by researchers at Google, is the most popular one among the plethora of deep learning libraries. In the field of deep learning, neural networks have achieved tremendous success and gained wide popularity in various areas. This family of models…

In causal matching designs, some control subjects are often left unmatched, and some covariates are often left unmodeled. This article introduces "rebar," a method using high-dimensional modeling to incorporate these commonly discarded data without sacrificing the integrity of the matching design. After constructing a match, a researcher…

This article proposes a flexible extension of the Fay--Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon,…

This article describes the analysis of regression-discontinuity designs (RDDs) using the R packages rdd, rdrobust, and rddtools. We discuss similarities and differences between these packages and provide directions on how to use them effectively. We use real data from the Carolina Abecedarian Project to show how an analysis of an RDD can be…

This article proposes a latent variable regression four-level hierarchical model (LVR-HM4) that uses a fully Bayesian approach. Using multisite multiple-cohort longitudinal data, for example, annual assessment scores over grades for students who are nested within cohorts within schools, the LVR-HM4 attempts to simultaneously model two types of…

A latent multivariate regression model is developed that employs a generalized asymmetric Laplace (GAL) prior distribution for regression coefficients. The model is designed for high-dimensional applications where an approximate sparsity condition is satisfied, such that many regression coefficients are near zero after accounting for all the model…

Social networks in education commonly involve some form of grouping, such as friendship cliques or teacher departments, and blockmodels are a type of statistical social network model that accommodate these grouping or blocks by assuming different within-group tie probabilities than between-group tie probabilities. We describe a class of models,…

Aggregate-level conditional status metrics (ACSMs) describe the status of a group by referencing current performance to expectations given past scores. This article provides a framework for these metrics, classifying them by aggregation function (mean or median), regression approach (linear mean and nonlinear quantile), and the scale that supports…

Structural equation mixture models (SEMMs), when applied as a semiparametric model (SPM), can adequately recover potentially nonlinear latent relationships without their specification. This SPM is useful for exploratory analysis when the form of the latent regression is unknown. The purpose of this article is to help users familiar with structural…

We extend to the longitudinal setting a latent class approach that was recently introduced by Lanza, Coffman, and Xu to estimate the causal effect of a treatment. The proposed approach enables an evaluation of multiple treatment effects on subpopulations of individuals from a dynamic perspective, as it relies on a latent Markov (LM) model that is…