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.

Tower tasks are popular tools used to measure planning skills. The sequences of moves undertaken by the respondents in solving tower tasks might provide important and useful information to shed light on their planning skills. The article focuses on the distinction between a situation where planning occurs before action (pre-planning) from one where planning and action are interlaced all along the execution of the task (interim-planning). While the model for pre-planning was already developed by Stefanutti et al. (2021), an alternative model for the interim-planning is proposed. The two models are compared with one another in an empirical study. In accordance with the literature on the development of planning skills, the pre-planning model better fits data collected on individuals aged 14 on, while the interim-planning model displays a better fit with data collected on individuals aged 4–8. This result is further corroborated by the analysis of the time performance.

In this study, we review interpretations and connections of chance-corrected agreement coefficients with quadratic weights, applicable when raters classify objects or subjects on an ordinal scale. Whereas correlation interpretations exist for coefficients with noninterchangeable raters, represented by Cohen’s two-rater and Conger’s multirater kappas, interpretations are essentially absent for interchangeable raters, represented by Fleiss’ kappa and its two-rater version, Scott’s pi. We show that Fleiss’ quadratically weighted kappa equals Lin’s generalized concordance correlation coefficient after recentering the rater means and covariance matrix at the grand mean. Furthermore, it equals the Pearson product–moment correlation and associated regression slope for two random raters, computed after concatenating the ratings from all possible rater pairs, including reversed rater order. Next, we demonstrate that Fleiss’ and Conger’s quadratically weighted kappas are linear transformations of each other, entirely determined by the pairwise differences in rater means and corresponding variances. As these kappas coincide if the rater means coincide, the conceptual distinction between interchangeable and noninterchangeable raters becomes empirically irrelevant if raters have (approximately) the same mean rating, even with substantially different rating distributions. Finally, Fleiss’ quadratically weighted kappa (i.e., interchangeable raters) cannot exceed Conger’s (i.e., noninterchangeable raters).

In this study, we develop statistical methods for bivariate causal learning using higher-order moment information from two-wave longitudinal data. Within the framework of linear non-Gaussian models, we derive tests based on joint cumulants and propose a multiple-testing algorithm to detect the existence of a longitudinal causal path in the presence of hidden confounders. By combining temporal information from longitudinal designs with higher-order distributional properties of the observed data, the proposed method allows researchers to draw valid causal conclusions under realistic scenarios commonly encountered in psychological studies. The performance of the proposed algorithm is evaluated through simulation studies. As expected for higher-moment methods, the proposed algorithm may require larger sample sizes than typically needed for second-moment methods to achieve high statistical power. Results demonstrate that the proposed algorithm provides sufficient evidence to establish the existence of a longitudinal causal path, particularly in large-scale data analysis. We then present two real-world data examples to illustrate the application of the causal learning algorithm in psychological research. Finally, we discuss practical implications and potential future research directions.

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.