arXiv subjects

J. R. Lockwood

Publications and source records attributed to J. R. Lockwood.

5 recordsLinked to original sources

arXiv2026

S2A3: Thompson Sampling and Stochastic Exposure Control for High-Stakes CATs

High-stakes computerized adaptive tests (CATs) require a continuous supply of calibrated items, yet traditional item piloting is slow, expensive, and operationally hazardous. We introduce the S2A3 framework -- Soft Scoring (S2) and Adaptive Adaptive Administration (A3) -- which unifies item calibration and test administration into a single online process. Thompson sampling enhances item selection by drawing provisional parameters from each item's posterior distribution and selecting the item maximizing expected Fisher information, naturally routing uncertain items to informative test-takers while maintaining measurement precision. Soft scoring integrates over parameter uncertainty so that incompletely calibrated items exert appropriately attenuated influence on ability estimates. A stochastic variant of Sympson-Hetter exposure control balances measurement efficiency against bank security via a tunable temperature parameter and item-specific weights. We validate S2A3 on Yes/No Vocabulary and Vocabulary-in-Context tasks from the Duolingo English Test, demonstrating rapid item calibration and preserved scoring reliability even when cold-start items constitute a significant fraction of the active pool.

stat.AP↗

arXiv2026

A Scalable Parametric Item Calibration Engine (SPICE) for Explanatory IRT with Sparse Data

We describe a Bayesian multidimensional explanatory IRT model, and an associated Markov Chain Monte Carlo (MCMC) estimation procedure and the corresponding development of calibration software, designed for psychometric analyses of large numbers of sparsely-linked persons and items. Such data structures can arise, for example, from adaptive assessments using large banks of automatically generated items with individual test takers receiving a very small proportion of the entire bank. We discuss how our choices for model specification, data structures, and algorithm implementation combine to create a scalable method for explanatory IRT that can support a variety of psychometric operations with sparse data.

stat.ME↗

arXiv2015

Inferring constructs of effective teaching from classroom observations: An application of Bayesian exploratory factor analysis without restrictions

Ratings of teachers' instructional practices using standardized classroom observation instruments are increasingly being used for both research and teacher accountability. There are multiple instruments in use, each attempting to evaluate many dimensions of teaching and classroom activities, and little is known about what underlying teaching quality attributes are being measured. We use data from multiple instruments collected from 458 middle school mathematics and English language arts teachers to inform research and practice on teacher performance measurement by modeling latent constructs of high-quality teaching. We make inferences about these constructs using a novel approach to Bayesian exploratory factor analysis (EFA) that, unlike commonly used approaches for identifying factor loadings in Bayesian EFA, is invariant to how the data dimensions are ordered. Applying this approach to ratings of lessons reveals two distinct teaching constructs in both mathematics and English language arts: (1) quality of instructional practices; and (2) quality of teacher management of classrooms. We demonstrate the relationships of these constructs to other indicators of teaching quality, including teacher content knowledge and student performance on standardized tests.

stat.AP↗

arXiv2011

Missing data in value-added modeling of teacher effects

The increasing availability of longitudinal student achievement data has heightened interest among researchers, educators and policy makers in using these data to evaluate educational inputs, as well as for school and possibly teacher accountability. Researchers have developed elaborate "value-added models" of these longitudinal data to estimate the effects of educational inputs (e.g., teachers or schools) on student achievement while using prior achievement to adjust for nonrandom assignment of students to schools and classes. A challenge to such modeling efforts is the extensive numbers of students with incomplete records and the tendency for those students to be lower achieving. These conditions create the potential for results to be sensitive to violations of the assumption that data are missing at random, which is commonly used when estimating model parameters. The current study extends recent value-added modeling approaches for longitudinal student achievement data Lockwood et al. [J. Educ. Behav. Statist. 32 (2007) 125--150] to allow data to be missing not at random via random effects selection and pattern mixture models, and applies those methods to data from a large urban school district to estimate effects of elementary school mathematics teachers. We find that allowing the data to be missing not at random has little impact on estimated teacher effects. The robustness of estimated teacher effects to the missing data assumptions appears to result from both the relatively small impact of model specification on estimated student effects compared with the large variability in teacher effects and the downweighting of scores from students with incomplete data.

stat.AP↗

arXiv2007

Controlling for individual heterogeneity in longitudinal models, with applications to student achievement

Longitudinal data tracking repeated measurements on individuals are highly valued for research because they offer controls for unmeasured individual heterogeneity that might otherwise bias results. Random effects or mixed models approaches, which treat individual heterogeneity as part of the model error term and use generalized least squares to estimate model parameters, are often criticized because correlation between unobserved individual effects and other model variables can lead to biased and inconsistent parameter estimates. Starting with an examination of the relationship between random effects and fixed effects estimators in the standard unobserved effects model, this article demonstrates through analysis and simulation that the mixed model approach has a ``bias compression'' property under a general model for individual heterogeneity that can mitigate bias due to uncontrolled differences among individuals. The general model is motivated by the complexities of longitudinal student achievement measures, but the results have broad applicability to longitudinal modeling.

stat.AP↗