The Bayesian piecewise growth model (PGM) is a useful class of models for analyzing nonlinear change processes that consist of distinct growth phases. In applications of Bayesian PGMs, it is important to accurately capture growth trajectories and carefully consider knot placements. The presence of missing data is another challenge researchers…

In modeling missing data, the missing data latent variable of the confirmatory factor model accounts for systematic variation associated with missing data so that replacement of what is missing is not required. This study aimed at extending the modeling missing data approach to tetrachoric correlations as input and at exploring the consequences of…

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…

The fit of an item response model is typically conceptualized as whether a given model could have generated the data. We advocate for an alternative view of fit, "predictive fit", based on the model's ability to predict new data. We derive two predictive fit metrics for item response models that assess how well an estimated item response…

The present guide provides a practical guide to conducting latent profile analysis (LPA) in the Mplus software system. This guide is intended for researchers familiar with some latent variable modeling but not LPA specifically. A general procedure for conducting LPA is provided in six steps: (a) data inspection, (b) iterative evaluation of models,…

Knowledge components (KCs) have many applications. In computing education, knowing the demonstration of specific KCs has been challenging. This paper introduces an entirely data-driven approach for: (1) discovering KCs; and (2) demonstrating KCs, using students' actual code submissions. Our system is based on two expected properties of KCs: (1)…

Collapsing categories is a commonly used data reduction technique; however, to date there do not exist principled methods to determine whether collapsing categories is appropriate in practice. With ordinal responses under the partial credit model, when collapsing categories, the true model for the collapsed data is no longer a partial credit…

Many interventions are characterized by repeated observations on the same individuals (e.g., baseline, mid-intervention, two to three post-intervention observations), which offer the opportunity to consider differences in how individuals vary over time. Effective interventions may not be limited to changing means, but instead may also include…

Knowledge tracing is a fundamental area of educational data modeling that aims at gaining a better understanding of the learning occurring in tutoring systems. Knowledge tracing models fit various parameters on observed student performance and are evaluated through several goodness of fit metrics. Fitted parameter values are of crucial interest in…

In this work we use prior to tutor-session data to generate an individualized student knowledge model. Intelligent learning environments use student models to individualize curriculum sequencing and help messages. Researchers decompose the learning tasks into sets of Knowledge Components (KCs) that represent individual units of knowledge; the…

The use of individual patient data (IPD) in network meta-analysis (NMA) is becoming increasingly popular. However, as most studies do not report IPD, most NMAs are performed using aggregate data for at least some, if not all, of the studies. We investigate the benefits of including varying proportions of IPD studies in an NMA. Several models have…

Traditional knowledge-component models describe students' content knowledge (e.g., their ability to carry out problem-solving procedures or their ability to reason about a concept). In many STEM domains, instruction uses multiple visual representations such as graphs, figures, and diagrams. The use of visual representations implies a…

The multidimensional item response theory (MIRT) models with covariates proposed by Haberman and implemented in the "mirt" program provide a flexible way to analyze data based on item response theory. In this report, we discuss applications of the MIRT models with covariates to longitudinal test data to measure skill differences at the…

This study investigates the issue of the goodness of fit of different skills assessment models using both synthetic and real data. Synthetic data is generated from the different skills assessment models. The results show wide differences of performances between the skills assessment models over synthetic data sets. The set of relative performances…

Being able to characterize the size of raindrops is useful in a number of fields including meteorology, hydrology, agriculture and telecommunications. Associated with this article are data sets containing surface (i.e. ground-level) measurements of raindrop size from two different instruments and two different geographical locations. Students may…