Benjamin W. Domingue

Joy He-Yueya, Wanjing Anya Ma, Kanishk Gandhi et al. · stanford

Language models (LMs) are increasingly used to simulate human-like responses in scenarios where accurately mimicking a population's behavior can guide decision-making, such as in developing educational materials and designing public policies. The objective of these simulations is for LMs to capture the variations in human responses, rather than merely providing the expected correct answers. Prior work has shown that LMs often generate unrealistically accurate responses, but there are no established metrics to quantify how closely the knowledge distribution of LMs aligns with that of humans. To address this, we introduce "psychometric alignment," a metric that measures the extent to which LMs reflect human knowledge distribution. Assessing this alignment involves collecting responses from both LMs and humans to the same set of test items and using Item Response Theory to analyze the differences in item functioning between the groups. We demonstrate that our metric can capture important variations in populations that traditional metrics, like differences in accuracy, fail to capture. We apply this metric to assess existing LMs for their alignment with human knowledge distributions across three real-world domains. We find significant misalignment between LMs and human populations, though using persona-based prompts can improve alignment. Interestingly, smaller LMs tend to achieve greater psychometric alignment than larger LMs. Further, training LMs on human response data from the target distribution enhances their psychometric alignment on unseen test items, but the effectiveness of such training varies across domains.

Mike Wu, Richard L. Davis, Benjamin W. Domingue et al.

Item Response Theory (IRT) is a ubiquitous model for understanding human behaviors and attitudes based on their responses to questions. Large modern datasets offer opportunities to capture more nuances in human behavior, potentially improving psychometric modeling leading to improved scientific understanding and public policy. However, while larger datasets allow for more flexible approaches, many contemporary algorithms for fitting IRT models may also have massive computational demands that forbid real-world application. To address this bottleneck, we introduce a variational Bayesian inference algorithm for IRT, and show that it is fast and scalable without sacrificing accuracy. Applying this method to five large-scale item response datasets from cognitive science and education yields higher log likelihoods and higher accuracy in imputing missing data than alternative inference algorithms. Using this new inference approach we then generalize IRT with expressive Bayesian models of responses, leveraging recent advances in deep learning to capture nonlinear item characteristic curves (ICC) with neural networks. Using an eigth-grade mathematics test from TIMSS, we show our nonlinear IRT models can capture interesting asymmetric ICCs. The algorithm implementation is open-source, and easily usable.

Mike Wu, Richard L. Davis, Benjamin W. Domingue et al.

Item Response Theory (IRT) is a ubiquitous model for understanding humans based on their responses to questions, used in fields as diverse as education, medicine and psychology. Large modern datasets offer opportunities to capture more nuances in human behavior, potentially improving test scoring and better informing public policy. Yet larger datasets pose a difficult speed / accuracy challenge to contemporary algorithms for fitting IRT models. We introduce a variational Bayesian inference algorithm for IRT, and show that it is fast and scaleable without sacrificing accuracy. Using this inference approach we then extend classic IRT with expressive Bayesian models of responses. Applying this method to five large-scale item response datasets from cognitive science and education yields higher log likelihoods and improvements in imputing missing data. The algorithm implementation is open-source, and easily usable.

Ajay Shanker Tripathi, Benjamin W. Domingue

Item response theory (IRT) models are widely used in psychometrics and educational measurement, being deployed in many high stakes tests such as the GRE aptitude test. IRT has largely focused on estimation of a single latent trait (e.g. ability) that remains static through the collection of item responses. However, in contemporary settings where item responses are being continuously collected, such as Massive Open Online Courses (MOOCs), interest will naturally be on the dynamics of ability, thus complicating usage of traditional IRT models. We propose DynAEsti, an augmentation of the traditional IRT Expectation Maximization algorithm that allows ability to be a continuously varying curve over time. In the process, we develop CurvFiFE, a novel non-parametric continuous-time technique that handles the curve-fitting/regression problem extended to address more general probabilistic emissions (as opposed to simply noisy data points). Furthermore, to accomplish this, we develop a novel technique called grafting, which can successfully approximate distributions represented by graphical models when other popular techniques like Loopy Belief Propogation (LBP) and Variational Inference (VI) fail. The performance of DynAEsti is evaluated through simulation, where we achieve results comparable to the optimal of what is observed in the static ability scenario. Finally, DynAEsti is applied to a longitudinal performance dataset (80-years of competitive golf at the 18-hole Masters Tournament) to demonstrate its ability to recover key properties of human performance and the heterogeneous characteristics of the different holes. Python code for CurvFiFE and DynAEsti is publicly available at github.com/chausies/DynAEstiAndCurvFiFE. This is the full version of our ICDM 2019 paper.

Conrad Borchers, Lijin Zhang, Kexin Yang et al.

Adaptive learning systems can produce substantial learning gains, yet many students engage for too brief or too superficial a period to benefit. A central obstacle is measuring effort. Effort during multi-step problem solving is rarely directly observed, and common log-based proxies, such as time on task, cannot distinguish between a student working carefully and a student encountering a harder problem. We examine step-to-step response time as a scalable effort signal by modeling trait-like differences in students' typical response timing during tutoring (while adjusting for skill difficulty). Using step-level logs from eight classroom deployments of algebra tutoring systems (2020 to 2023) across six U.S. schools (794 students), we estimate student- and knowledge-component-level propensities using hierarchical models and relate them to learning efficiency, defined as performance improvement per completed solution step. Response-time propensities show moderate to strong stability within students, supporting their use as an individual differences measure beyond correctness. At the same time, their relationship to learning is not uniform but conditional on the learner and context. Slower propensities predict greater learning efficiency for higher-proficiency students, consistent with constructive processing, whereas for lower-proficiency students, slower propensities are weakly related or even negative, consistent with unproductive struggle or idling. These associations are strongest early in practice sequences and attenuate later in the class period, highlighting an actionable window for detecting emerging disengagement and low persistence. Overall, response-time propensities provide a practical way to incorporate temporal process data into learner models and to target adaptive supports when effort is most diagnostic.

Hansol Lee, Guilherme Lichand, Cristina Barnard et al.

A 2023 \textit{PNAS} study by Koedinger et al. (2023) fit the individual Additive Factors Model (iAFM) to 27 educational datasets and reported an ``astonishing regularity'' in student learning rates: students vary substantially in initial knowledge but learn at remarkably similar rates with practice. We probe a largely unexamined assumption underlying this finding -- that observation length in student log data is ignorable for mixed-effects estimation -- by refitting the iAFM on 26 of the original datasets while systematically truncating practice sequences at various depths, holding the set of students and knowledge components constant. Capping at the first ten opportunities per student-skill pair inflates the median estimated IQR of student learning rates by 75\%; capping at five inflates it by 205\%, with individual datasets ranging from negligible to 17-fold. The magnitude of this sensitivity diverges from what standard estimation theory predicts under ignorable truncation, and the dataset-specific heterogeneity is substantial. Three candidate mechanisms from adjacent literatures could account for the pattern -- informative observation length, functional-form misspecification, and identification weakness from sparse per-pair data -- but observational analysis on these data alone cannot adjudicate among them. We argue that practice sequence length distributions are an unexamined property of mixed-effects estimation on observational learning data, deserving explicit reporting before conclusions about learning-rate heterogeneity are drawn.

Radhika Kapoor, Sang T. Truong, Nick Haber et al.

Prediction of item difficulty based on its text content is of substantial interest. In this paper, we focus on the related problem of recovering IRT-based difficulty when the data originally reported item p-value (percent correct responses). We model this item difficulty using a repository of reading passages and student data from US standardized tests from New York and Texas for grades 3-8 spanning the years 2017-23. This repository is annotated with meta-data on (1) linguistic features of the reading items, (2) test features of the passage, and (3) context features. A penalized regression prediction model with all these features can predict item difficulty with RMSE 0.52 compared to baseline RMSE of 0.92, and with a correlation of 0.77 between true and predicted difficulty. We supplement these features with embeddings from LLMs (ModernBERT, BERT, and LlAMA), which marginally improve item difficulty prediction. When models use only item linguistic features or LLM embeddings, prediction performance is similar, which suggests that only one of these feature categories may be required. This item difficulty prediction model can be used to filter and categorize reading items and will be made publicly available for use by other stakeholders.

AJ Alvero, Noah Arthurs, anthony lising antonio et al.

College admissions in the United States is carried out by a human-centered method of evaluation known as holistic review, which typically involves reading original narrative essays submitted by each applicant. The legitimacy and fairness of holistic review, which gives human readers significant discretion over determining each applicant's fitness for admission, has been repeatedly challenged in courtrooms and the public sphere. Using a unique corpus of 283,676 application essays submitted to a large, selective, state university system between 2015 and 2016, we assess the extent to which applicant demographic characteristics can be inferred from application essays. We find a relatively interpretable classifier (logistic regression) was able to predict gender and household income with high levels of accuracy. Findings suggest that data auditing might be useful in informing holistic review, and perhaps other evaluative systems, by checking potential bias in human or computational readings.