This paper presents a model of recurrent multinomial sequences. Though there exists a quite considerable literature on modeling autocorrelation in numerical data and sequences of categorical outcomes, there is currently no systematic method of modeling patterns of recurrence in categorical sequences. This paper develops a means of discovering…

With the development of technology-enhanced learning platforms, eye-tracking biometric indicators can be recorded simultaneously with students item responses. In the current study, visual fixation, an essential eye-tracking indicator, is modeled to reflect the degree of test engagement when a test taker solves a set of test questions. Three…

We consider an ordinal regression model with latent variables to investigate the effects of observable and latent explanatory variables on the ordinal responses of interest. Each latent variable is characterized by correlated observed variables through a confirmatory factor analysis model. We develop a Bayesian adaptive lasso procedure to conduct…

The future of education is human expertise and artificial intelligence working in conjunction, a revolution that will change the education as we know it. The Intelligent Tutoring System is a key component of this future. A quantitative measurement of efficacies of practice to heterogeneous learners is the cornerstone of building an effective…

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,…

The present study investigates different approaches to adding covariates and the impact in fitting mixture item response theory models. Mixture item response theory models serve as an important methodology for tackling several psychometric issues in test development, including the detection of latent differential item functioning. A Monte Carlo…

Additive Factors Model (AFM) and Performance Factors Analysis (PFA) are two popular models of student learning that employ logistic regression to estimate parameters and predict performance. This is in contrast to Bayesian Knowledge Tracing (BKT) which uses a Hidden Markov Model formalism. While all three models tend to make similar predictions,…

One of the vexing problems in the analysis of SSD is in the assessment of the effect of intervention. Serial dependence notwithstanding, the linear model approach that has been advanced involves, in general, the fitting of regression lines (or curves) to the set of observations within each phase of the design and comparing the parameters of these…

In the human sciences, ability tests or psychological inventories are often repeatedly conducted to measure growth. Standard item response models do not take into account possible autocorrelation in longitudinal data. In this study, the authors propose an item response model to account for autocorrelation. The proposed three-level model consists…

This study is aimed at addressing the criticisms that have been leveled at the currently available statistical procedures for analyzing single subject designs (SSD). One of the vexing problems in the analysis of SSD is in the assessment of the effect of intervention. Serial dependence notwithstanding, the linear model approach that has been…

In this article, a proposed Bayesian extension of the generalized beta spatial regression models is applied to the analysis of the quality of education in Colombia. We briefly revise the beta distribution and describe the joint modeling approach for the mean and dispersion parameters in the spatial regression models' setting. Finally, we motivate…

In this article, three multilevel models for meta-analysis are examined. Hedges and Olkin suggested that effect sizes follow a noncentral "t" distribution and proposed several approximate methods. Raudenbush and Bryk further refined this model; however, this procedure is based on a normal approximation. In the current research literature, this…

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite…

The increasing use of diary methods calls for the development of appropriate statistical methods. For the resulting panel data, latent Markov models can be used to model both individual differences and temporal dynamics. The computational burden associated with these models can be overcome by exploiting the conditional independence relations…