This study investigates the relationship between daily interpersonal stress (binary, time-varying) and suicidal behavior (binary, time-varying) using 90 days of daily diary data from 106 adolescents assessed immediately after discharge from acute psychiatric treatment. It addresses two key complexities: the rarity of suicidal events and non-monotone, non-ignorable missingness in both the outcome and the predictor. Because existing methods often fail to accommodate these complexities, leading to biased estimates, a Bayesian selection model is specified. The model integrates a mixed-effects complementary log–log regression for rare events with a missingness model that accounts for non-monotone, non-ignorable missingness in the outcome. A probit mixed-effects model is used for the time-varying predictor, along with a corresponding missingness model for its non-monotone, non-ignorable missingness. Empirical results support the applicability of the specified model to longitudinal studies involving rare events and complex missing-data structures. Furthermore, a simulation study demonstrates parameter recovery and highlights bias in focal parameters when sensitivity parameters in the outcome and missingness models are ignored.

Classical symmetric association measures, such as correlation and chi-square indices, are widely used in applied psychology. However, these indices have limitations in identifying asymmetric implicative relationships. Standard regression analysis of Y on X, frequently interpreted as evidence of a directed dependence $X\to Y$, does not preclude the reverse direction ($Y\to X$). While various proposals in the literature have sought to provide non-symmetric association measures between binary events, most have overlooked the potential information in the contrapositive ($\bar {B}\to \bar {A}$), in addition to the main assertion ($A\to B$). When multiple variables are involved, asymmetric dependence is frequently represented as intricate dependency networks, which can be challenging to summarize and interpret in terms of higher-order clusters or latent dimensions. This article introduces a novel statistical implication index designed to address both limitations. The efficacy of this asymmetric index is demonstrated through its ability to detect one-way implication relationships, using both positive and contrapositive evidence. It also facilitates dimensional reduction by establishing aligned sets of nodes in a graph representation, under the condition that a Rasch model holds on these nodes, thus filling the gap between graphical and dimensional models. The efficacy of this index is substantiated through both simulated and real-world data illustrations.

Pfadt et al. present accessible methods for estimating conditional standard errors of measurement (CSEMs) and implement them in the open-source software JASP. Their emphasis on individual-level precision represents an important contribution to applied measurement practice. This commentary discusses several conceptual issues that clarify and extend the authors’ treatment of dimensionality, error definition, and score interpretation. The aim is to strengthen alignment between CSEM estimation and the interpretive purposes for which test scores are used.

A discussion is provided of several issues related to behavioral measurement that arise from Pfadt et al. (2026, Psychometrika, 2026, 1–35). The note may be viewed in part as a complement to their developments regarding precision estimation for individual test scores.

Not-reached (dropout) and omitted (intermittent missingness) behaviors are often inevitable in timed computerized tests. These missingness behaviors may be related to the subject’s latent traits, the difficulty of the item, or even the unobserved item response itself. In order to better understand the underlying test-taking behaviors, a Bayesian hierarchical framework is adopted to jointly model the item response, the item response time, the not-reached, and the omitted behaviors. For missing data, a sequential multinomial model is developed for the not-reached behavior, and a conditional model is proposed for the omitted behavior conditioning on the not-reached behavior. A decomposed logarithm of the pseudo marginal likelihood (LPML) is then developed to assess the fit of the missing data models. It can be further used to quantify the importance of modeling item response and response time jointly versus individually in identifying the missing data mechanism. The empirical performance of the proposed models and the model assessment criterion are examined through extensive simulations. The proposed methodology is further applied to analyze the Program for International Student Assessment (PISA) 2018 Test.

Large-scale assessment data typically include numerous variables, often affected by missing values. Motivated by the challenges arising in this framework, we extend the knockoffs method for selecting predictors to settings with missing values. Our proposal relies on a preliminary phase of multiple imputation (MI) of missing values. Each imputed dataset is then processed using a suitable knockoff filter. We evaluate the performance of the proposed method through simulation studies, showing satisfactory results consistent with a recently advocated cutting-edge method. We apply the method to large-scale assessment data collected by INVALSI on test scores of Italian students in grade 5, including many background variables. This case study is challenging, as most predictors have unordered categories, a setting not considered by traditional knockoff methods. In addition, some of the key predictors are affected by missing values. Our proposal to implement the knockoffs method within an MI framework is feasible, flexible, and effective.

This article synthesizes popular approaches to Bayesian estimation of psychometric models that rely on the multivariate normal distribution, including point estimation of posterior central tendency, Gibbs sampling, and Hamiltonian sampling. We place emphasis on the geometry of the posterior distribution, on building intuition by drawing connections to regression, and on providing background about how relevant matrix results are obtained. We also consider how the results can be extended to handle related psychometric models, including popular item response models. The goal is to provide researchers with ideas and tools for designing their own Bayesian estimation methods, which we hope will lead to continued developments and improvements.

Recent research shows that amortized variational inference (AVI) can be used to efficiently estimate high-dimensional latent variable models on large datasets. However, its use has remained limited to item response theory (IRT), and generalizing the approach to discrete latent variable models is not straightforward. We propose two ways to deal with this problem. In an initial simulation, we verify that these approaches can be used to estimate simple discrete latent variable models, such as latent class analysis and the generalized deterministic inputs, noisy and gate model. In these cases, AVI provides accurate parameter estimates, although the computational advantage over marginal maximum likelihood (MML) and standard variational inference (VI) is limited. We then apply the same approach to estimate mixture IRT models. In this case, AVI is computationally faster than MML estimation and standard VI. To demonstrate the practical applicability of our AVI approach, we use it to fit a seven-dimensional mixture IRT model to a narcissism inventory. Whereas quadrature-based methods cannot feasibly estimate models of this dimensionality, the efficient AVI approach even allows for computation of bootstrapped standard errors. We provide our code, along with an easy-to-use tool for fitting these models to new datasets.

Test speededness, caused by time constraints, can impact examinees’ performance, leading to decreased response accuracy, particularly toward the end of the test. Most existing methods for detecting test speededness rely on specific distributional assumptions for response times (RTs), such as the lognormal distribution, which may lead to incorrect statistical inference if the true data distribution deviates from these assumptions. This article proposes a novel Bootstrap-CUSUM method for detecting test speededness, which is robust to non-normality in log-RTs. By constructing a cumulative sum (CUSUM) person-fit statistic for log-RTs and using the multiplier bootstrap to estimate its empirical distribution, our method facilitates individual-level detection and changepoint estimation. We prove the theoretical consistency of the method under both null and alternative hypotheses. Simulation studies show that the Bootstrap-CUSUM method outperforms the likelihood ratio test, Wald test, and score test in terms of correct classification rate, true detection rate, and false positive rate, demonstrating superior robustness and adaptability across different data distributions. The real data analysis further demonstrates the practical utility of the proposed method for detecting test speededness.

We propose a latent trait model for the responses and response times on tests that separates capability from persistence. Core of the model is a race between a diffusion process and a censoring process. The diffusion process represents item-level cognitive processing and determines the processing time of a test taker. The censoring process sets the maximal time a test taker is willing to invest into an item. If the processing time is shorter than the maximal time, the response is generated by the diffusion process; otherwise, the response is generated differently. In the first version of the model, the response is generated by a random guess. In the second version of the model, the response is determined by the actual level of the diffusion process. We relate the diffusion process to the capability and response caution of a test taker and the censoring process to his willingness to invest time. Similar to models for rapid guessing, the proposed models take account of disengaged responding, but allow for individual differences in persistence and informed guessing. The model also provides a mathematical specification of persistence. In a simulation study, we investigate model fitting by marginal maximum likelihood estimation. We also apply the model to two empirical data sets.

Identifying which individual-, cluster-, and item-level predictors explain binary responses requires balancing flexibility and statistical rigor. Generalized linear mixed models (GLMMs) explicitly partition fixed and random effects and capture multilevel structure, but they make it challenging to model nonlinear relationships and higher-order interactions. In contrast, tree ensembles, such as extreme gradient boosting (XGBoost), flexibly capture nonlinearities and interactions but typically ignore clustering and random effects. This study introduces an iterative GLMM–XGBoost algorithm that replaces the penalized weighted least squares step in the penalized IRLS (PIRLS) routine with a boosted-tree learner, while retaining Laplace-approximation-based updates of the random effects via their conditional modes. Weighted C-projection and global centering enforce orthogonality between the tree component and grouping factors, avoiding redundancy. The algorithm yields an approximate Newton–Fisher scoring update, preserves the ability to model random effects, and maintains the flexibility of XGBoost. In addition, a group-aware conditional permutation importance measure and its associated uncertainty measure are developed to identify predictor contributions under multilevel data. Results indicate that iterative GLMM–XGBoost improves predictive accuracy and importance ranking relative to standalone XGBoost under clustering and random effects. It also remains competitive with alternative methods across both smooth and tree-based fixed-effects specifications while accounting for random variation.

This article proposes a genetic algorithm, the array histogram-based sampling algorithm (AHBSA), to assemble linear multidimensional forced-choice questionnaires (MFCQs), which are increasingly popular for measuring personality, with forced-choice items including any number of statements (block size). The algorithm also works for traditional multidimensional Likert and cognitive test forms, where items can be seen as having a block size of one. Real and simulated statement pools are used to evaluate AHBSA’s performance in terms of test reliability and running speed in assembling Likert forms and MFCQs with two (pair) and three (triplet) statements. Compared to mixed integer programming (MIP) and random assembly, AHBSA achieves as high or higher reliabilities under all conditions: in Likert forms, AHBSA reaches optimal solutions as MIP does, and in the MFCQs, AHBSA gains notable increases in reliabilities over MIP when the forms have no constraint on item direction (i.e., positively versus negatively keyed statements). AHBSA takes more time to converge than MIP. The findings and limitations are discussed, and suggestions for future work are provided.

This article develops an analysis pipeline for quantifying and relating mouth shape variation to the emotions perceived from facial expressions. We use open-source data that contains ratings from 802 fairgoers on 27 smile-like expressions. Each rater was given a list of seven emotions (happy, sad, anger, contempt, fear, surprise, and disgust) and asked to select all of the words that best described the facial expression. To develop a generalizable method for quantifying mouth shape variation, we leverage statistical shape analysis techniques to parameterize each mouth’s shape in terms of 30 systematically placed landmarks that outline the upper and lower lips. Furthermore, we demonstrate that a three-dimensional representation of these landmark coordinates produces an interpretable feature set that outperforms the original and full-dimensional feature sets in terms of predictive performance. To connect the mouth shape features to the emotion ratings, we develop a nonparametric multinomial regression model that is capable of shrinkage and selection with high-dimensional predictors. Our results demonstrate that the proposed method can produce easily interpretable model predictions that enhance our understanding of the nature in which subtle variations in mouth shape affect the perception of a facial expression.

Several textbooks give the incorrect formula to calculate the standard error estimates for standardized regression coefficients. As a remedy, two analytic methods have been developed: (1) the delta method and (2) the covariance structure modeling method. However, neither method is applicable to compute the standard error estimates for unstandardized regression coefficients of products of Z-scores. In the literature, a nonparametric bootstrap procedure is advocated to test the significance of unstandardized regression coefficients of products of Z-scores. In this article, we propose a simple analytic approach that can produce the standard error estimates not only for standardized regression coefficients when interaction terms are not included, but also for unstandardized regression coefficients when interaction terms of Z-scores are included. Two numeric examples are used to compare our analytic approach with the existing methods, and simulation studies are conducted to further evaluate the performances of regular regression, our analytic approach, and the nonparametric bootstrap procedure at finite sample sizes. It is found that (1) regular regression performs well only when the variances of predictor variables are small, (2) our analytic approach performs well at the sample size of 200 or larger, and (3) the nonparametric bootstrap procedure performs (almost) perfectly in all conditions.

Traditional perceptual models are ill-equipped for the high-dimensional data, such as text embeddings, central to modern psychology and AI. We introduce the double machine learning lens model, a framework that utilizes machine learning to handle such data. We applied this model to analyze how a modern AI and human perceivers judge social class from 9,513 aspirational essays written by 11-year-olds in 1969. A systematic comparison of 45 analytical approaches revealed that regularized linear models using dimensionality-reduced language embeddings significantly outperformed traditional dictionary-based methods and more complex non-linear models. Our top model accurately predicted human $(R^{2}_{CV} =0.61)$ and AI $(R^{2}_{CV} =0.56)$ social class perceptions, capturing over 85% of the total accuracy. These results suggest that “unmodeled knowledge” in perception may be an artifact of insufficient measurement tools rather than an unmeasurable intuitive process. We find that both AI and humans use many of the same textual cues (e.g., grammar, occupations, and cultural activities), only a subset of which are valid. Both appear to amplify subtle, real-world patterns into powerful, yet potentially discriminatory heuristics, where a small difference in actual social class creates a large difference in perception.

Fairness in psychological and educational measurement has been a long-standing issue. Meanwhile, fairness is an issue that has been receiving an increasing amount of attention in the machine learning (ML) and artificial intelligence (AI) community, particularly in the last decade. While there is some recognition by the AI/ML community of the early roots of fairness definitions and operational metrics in the testing context, especially the parallel between fairness in AI/ML and test fairness in a regression and prediction context, there has not been a systematic introduction about the rapidly developing research of AI/ML fairness and bias mitigation to the measurement professionals. There is an urgent need to build a shared foundation of fairness notions and criteria between the two fields, particularly given that AI/ML has started to play an ever increasingly important role in measurement and personnel selection. This article therefore draws parallel between the testing workflow and the AI/ML fairness paradigm, and explores the similarities and dissimilarities of fairness definitions and operational ways to evaluate fairness in both fields, as well as ways to address and mitigate bias. The exploration leads to a discussion of areas of future research, training, and collaborations.

This article proposes a mixed-effects machine-learning framework for modeling complex, nonlinear relations between predictors and continuous outcomes in multilevel cross-classified data. The proposed method, termed LMM–XGBoost, embeds extreme gradient boosting (XGBoost) within a linear mixed model (LMM) to combine flexible modeling of nonlinear and interaction effects with random effects that model dependence. In addition, an iterative estimation procedure for LMM–XGBoost is developed, a group-aware permutation importance measure that respects multilevel dependence is proposed, and a combined-group cross-validation (CV) strategy for hyperparameter tuning, out-of-fold (OOF) prediction, and importance estimation is developed for cross-classified designs. The simulation study shows that the proposed estimation method for LMM–XGBoost yields good parameter recovery under non-zero random-effect variances. In addition, relative to standard LMM and XGBoost, LMM–XGBoost achieves lower OOF prediction error and more accurate recovery of variable importance. The study further shows that combined-group CV and group-aware permutation importance yield less biased error estimates and substantially higher agreement with the true importance rankings than conventional permutation measures. An empirical application using the Add Health study illustrates how the proposed methods can identify important factors across multiple domains associated with adolescent depressive symptoms.

Change point analysis (CPA) detects structural shifts in a response sequence by partitioning it into segments with different statistical properties. This paper proposes three CPA approaches based on the Schwarz information criterion (SIC; hereafter SIC-CPA): response data only, response time (RT) data only, and the combination of response and RT data, to detect the prevalent test speededness in time-limit tests. To comprehensively investigate the efficiency and accuracy of the proposed approaches, six simulation studies were conducted under diverse conditions. Simulation results demonstrate that SIC-CPA can effectively enhance the power of change point detection and reduce Type I errors, while improving computational efficiency compared to the likelihood ratio and Wald tests. Moreover, the SIC-CPA combining response and RT data outperforms the SIC-CPA based solely on RTs, and the latter is substantially superior to the SIC-CPA based solely on responses. In addition, SIC-CPA accurately identifies two change points in RT patterns, corresponding to early warm-up and later test speededness. Using an iterative detect–clean–recalibrate procedure, SIC-CPA achieves more reliable Type I error control than likelihood ratio and Wald tests when item parameters are estimated from contaminated data. A real data analysis was conducted to show the application of the proposed approaches.

Computerized adaptive tests (CATs) play a crucial role in educational assessment and diagnostic screening in behavioral health. Unlike traditional linear tests that administer a fixed set of pre-assembled items, CATs adaptively tailor the test to an examinee’s latent trait level based on their previous responses. We introduce a novel CAT system that builds on recent advances in Bayesian multivariate IRT. Our approach leverages direct sampling from the latent factor posterior distributions, significantly accelerating existing information-theoretic item-selection methods by eliminating the need for computationally intensive Markov chain Monte Carlo simulations. To address the potential suboptimality of one-step-ahead item-selection rules, we also develop a double deep Q-learning algorithm that efficiently learns an optimal item-selection policy offline using a calibrated item bank. Through simulation and real-data studies, we demonstrate that our approach not only accelerates existing item-selection methods but also highlights the potential of reinforcement learning (RL) in CATs. Notably, our Q-learning-based strategy consistently achieves the fastest posterior variance reduction, leading to earlier test termination. These results demonstrate the promise of combining exact posterior sampling with RL to deliver scalable, high-precision CATs.