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…

Predictive analytics is widely used in various domains, including education, to inform decision-making and improve outcomes. However, many predictive models are proprietary and inaccessible for evaluation or modification by researchers and practitioners, limiting their accountability and ethical design. Moreover, predictive models are often opaque…

Background/Context: Predictive analytics has emerged as an indispensable tool in the education sector, offering insights that can improve student outcomes and inform more equitable policies (Friedler et al., 2019; Kleinberg et al., 2018). However, the widespread adoption of predictive models is hindered by several challenges, including the lack of…

Multivariate count data is ubiquitous in many areas of research including the physical, biological, and social sciences. These data are traditionally modeled with the Dirichlet Multinomial distribution (DM). A new, more flexible Dirichlet-Tree Multinomial (DTM) model is gaining in popularity. Here, we consider Bayesian DTM regression models. Our…

In this article, I present a new multivariate regression model for analyzing outcomes with network dependence. The model is capable to account for two types of outcome dependence including the mean dependence that allows the outcome to depend on selected features of a known dependence network and the error dependence that allows the outcome to be…

The clustered observational study (COS) design is the observational study counterpart to the clustered randomized trial. In a COS, a treatment is assigned to intact groups, and all units within the group are exposed to the treatment. However, the treatment is non-randomly assigned. COSs are common in both education and health services research. In…

Purpose: This article provides a tutorial introduction to ordinal pattern analysis, a statistical analysis method designed to quantify the extent to which hypotheses of relative change across experimental conditions match observed data at the level of individuals. This method may be a useful addition to familiar parametric statistical methods…

Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial membership across clusters. With this flexibility come challenges in uniquely identifying,…

Standard methods for the meta-analysis of medical tests, without assuming a gold standard, are limited to dichotomous data. Multivariate probit models are used to analyse correlated dichotomous data, and can be extended to model ordinal data. Within the context of an imperfect gold standard, they have previously been used for the analysis of…

In this paper, we provide an introduction to the factored regression framework. This modeling framework applies the rules of probability to break up or "factor" a complex joint distribution into a product of conditional regression models. Using this framework, we can easily specify the complex multivariate models that missing data…

Advancements in item response theory (IRT) have led to models for dual dependence, which control for cluster and method effects during a psychometric analysis. Currently, however, this class of models does not include one that controls for when the method effects stem from two method sources in which one source functions differently across the…

Tests administered in studies of student achievement often have a certain amount of not-reached items (NRIs). The propensity for NRIs may depend on the proficiency measured by the test and on additional covariates. This article proposes a semiparametric model to study such relationships. Our model extends Glas and Pimentel's item response theory…

Multiple group modeling is one of the methods to address the measurement noninvariance issue. Traditional studies on multiple group modeling have mainly focused on item responses. In computer-based assessments, joint modeling of response times and action counts with item responses helps estimate the latent speed and action levels in addition to…

A log-linear model (LLM) is a well-known statistical method to examine the relationship among categorical variables. This study investigated the performance of LLM in detecting differential item functioning (DIF) for polytomously scored items via simulations where various sample sizes, ability mean differences (impact), and DIF types were…

This book presents different data collection and representation techniques: elementary descriptive statistics, confirmatory statistics, multivariate approaches and statistical modeling. It exposes the possibility of giving more robustness to the classical methodologies of education sciences by adding a quantitative approach. The fundamentals of…