In this article, the beta-binomial model for count data is proposed and demonstrated in terms of its application in the context of oral reading fluency (ORF) assessment, where the number of words read correctly (WRC) is of interest. Existing studies adopted the binomial model for count data in similar assessment scenarios. The beta-binomial model,…

A test battery with two different levels of adaptation is presented: a within-subtest level for the selection of the items in the subtests and a between-subtest level to move from one subtest to the next. The battery runs on a two-level model consisting of a regular response model for each of the subtests extended with a second level for the joint…

Markov models are important tools for quantitative social research. In this article, new methods for discrete Markov chains are presented. These methods allow us to calculate the distribution of the occupation time in a subset of the state space, the distribution of the waiting time to first entry into a subset of the state space, and the…

Contributions: Prior studies on education have mostly followed the model of the cross-sectional study, namely, examining the pretest and the posttest scores. This article shows that students' knowledge throughout the intervention can be estimated by time-series analysis using a hidden Markov model (HMM). Background: Analyzing time series and the…

This study proposed a dynamic model of organizational technology adoption within a school institute culture. We described an implementation of a nonhomogeneous hidden Markov model based on a downscaling scheme that can project the cultural factors of the institute onto a teacher's implementation behavior. To reveal the dynamics of cultural…

In order to evaluate the effect of a policy or treatment with pre- and post-treatment outcomes, we propose an approach based on a transition model, which may be applied with multivariate outcomes and accounts for unobserved heterogeneity. This model is based on potential versions of discrete latent variables representing the individual…

Questionnaires are by far the most common tool for measuring noncognitive constructs in psychology and educational sciences. Response bias may pose an additional source of variation between respondents that threatens validity of conclusions drawn from questionnaire data. We present a mixture modeling approach that leverages response time data from…

We propose a new item response theory growth model with item-specific learning parameters, or ISLP, and two variations of this model. In the ISLP model, either items or blocks of items have their own learning parameters. This model may be used to improve the efficiency of learning in a formative assessment. We show ways that the ISLP model's…

American universities use a procedure based on a rolling six-year graduation rate to calculate statistics regarding their students' final educational outcomes (graduating or not graduating). As an alternative to the six-year graduation rate method, many studies have applied absorbing Markov chains for estimating graduation rates. In both cases, a…

There has been considerable interest in techniques for modelling student learning across practice problems to drive real-time adaptive learning, with particular focus on variants of the classic Bayesian Knowledge Tracing (BKT) model proposed by Corbett & Anderson, 1995. Over time researches have proposed many variants of BKT with…

Standard item response theory (IRT) models have been extended with testlet effects to account for the nesting of items; these are well known as (Bayesian) testlet models or random effect models for testlets. The testlet modeling framework has several disadvantages. A sufficient number of testlet items are needed to estimate testlet effects, and a…

As the international large-scale assessments (ILSAs) become more popular, policy makers and education practitioners are interested in collecting as much student background information as possible to better understand the learning context of their students. To collect such abundant information, administrators need to develop a lot of questions.…

Financial professionals involved in divorce proceedings, whether for a client or an attorney, often use software to project the ability of a dependent spouse to earn income off of her separate estate. These projections have historically relied on static inputs and use a Monte Carlo simulation to illustrate the paths a portfolio might take. Within…

Prompting students to generate constructed responses as they read provides a window into the processes and strategies that they use to make sense of complex text. In this study, Markov models examined the extent to which: (1) patterns of strategies; and (2) strategy combinations could be used to inform computational models of students' text…

Greater eyes-focused eye movement pattern during face recognition is associated with better performance in adults but not in children. We test the hypothesis that higher eye movement consistency across trials, instead of a greater eyes-focused pattern, predicts better performance in children since it reflects capacity in developing visual…