PsychometrikaPub Date : 2026-07-17DOI: 10.1017/psy.2026.10136
Heinz Holling, Rainer Schwabe
{"title":"A-Optimal Designs for Rasch Poisson Gamma Counts Models.","authors":"Heinz Holling, Rainer Schwabe","doi":"10.1017/psy.2026.10136","DOIUrl":"10.1017/psy.2026.10136","url":null,"abstract":"<p><p>In this article, we develop A-optimal designs for a longitudinal Rasch Poisson Gamma counts model (RPGCM). The model is particularly well suited for repeated testing designs in educational and psychological research when the outcomes are count data. Within the RPGCM framework, test scores depend on two types of parameters: respondents' abilities, which are modeled as gamma-distributed random effects, and item difficulties, which are treated as fixed parameters. To account for dependencies among repeated measurements, we incorporate a compound symmetry structure into the RPGCM. Parameter estimation is performed using maximum quasi-likelihood methods. Based on this framework, we derive A-optimal designs that allow for efficient estimation of mean abilities and commonly used functions thereof. In analogy to classical ANOVA models, no constraints are imposed on the mean structure. The resulting A-optimal designs are substantially less restrictive than commonly used D-optimal designs. Moreover, the derived designs are also valid for a more general class of longitudinal Poisson Gamma models with repeated measurements. These models can be applied to analyze growth curves for count data in other disciplines, including epidemiology, medicine, and criminology.</p>","PeriodicalId":54534,"journal":{"name":"Psychometrika","volume":" ","pages":"1-16"},"PeriodicalIF":2.9,"publicationDate":"2026-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148474201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
PsychometrikaPub Date : 2026-07-10DOI: 10.1017/psy.2026.10135
Steffen Grønneberg
{"title":"Mean and True Score Convergence in Nonparametric Item Response Theory.","authors":"Steffen Grønneberg","doi":"10.1017/psy.2026.10135","DOIUrl":"10.1017/psy.2026.10135","url":null,"abstract":"<p><p>Mean and sum scores are widely used in psychometric practice, but their behavior under weak assumptions is not fully understood. We study two basic questions under a latent variable framework with increasing-item asymptotics: when does the observed mean score approximate the true score of the administered form, and when is a true score insensitive to removing a vanishing fraction of items? For the first question, we introduce martingale factor models, which, for polytomous items, weaken conditional independence to a conditional-mean restriction, yet still yield concentration and asymptotic normality results for mean scores around their true scores. For the second question, we show that this stability is equivalent to the convergence of the true scores when the items are bounded, and we identify conditions under which this convergence takes place. These results clarify when mean scores can be interpreted as stable proxies for latent variables and yield psychometrically relevant consequences. Several theoretical and numerical illustrations are given, including a new interpretation of large-form mean-score correlations and a person-specific confidence interval procedure for the true score.</p>","PeriodicalId":54534,"journal":{"name":"Psychometrika","volume":" ","pages":"1-24"},"PeriodicalIF":2.9,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148426638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
PsychometrikaPub Date : 2026-07-09DOI: 10.1017/psy.2026.10133
Tzu-Yao Lin, Francis Tuerlinckx, Sophie Vanbelle
{"title":"Single-Item Reliability for Intensive Longitudinal Data: A Three-Level Linear Mixed-Effect Autoregressive Modeling Approach.","authors":"Tzu-Yao Lin, Francis Tuerlinckx, Sophie Vanbelle","doi":"10.1017/psy.2026.10133","DOIUrl":"10.1017/psy.2026.10133","url":null,"abstract":"<p><p>With the advancement of technology, intensive longitudinal data (ILD) are increasingly collected to study dynamic, moment-to-moment psychological and physiological processes. Despite their widespread use, the issues of measurement error and reliability are often inadequately addressed, particularly in the presence of serial correlation and complex multilevel structures. This article introduces a three-level linear mixed-effects model that explicitly accounts for nested structures (moments within days within persons) and incorporates two distinct autoregressive processes for moment- and day-level serial correlations, partitioning measurement error from within-person variability. Building on this model, we delineate two approaches to defining reliability: a variance partitioning approach and a correlation approach. This framework yields a multifaceted set of reliability coefficients, enabling researchers to distinguish between-person from within-person reliability, and to assess measurement agreement across different time scales (e.g., moment-to-moment and day-to-day). We further discuss the relationship between the proposed reliability measures and those derived from simpler models. We apply our model to study the reliability of a single negative affect item in an ILD study in which students were measured multiple times a day for several days before and after receiving their exam results.</p>","PeriodicalId":54534,"journal":{"name":"Psychometrika","volume":" ","pages":"1-32"},"PeriodicalIF":2.9,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148413988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Predicting Multilevel Growth Trajectories Using a Random-Effect Diagnostic Classification Model.","authors":"Kazuhiro Yamaguchi, Haruhiko Mitsunaga, Shun Saso, Yuri Uesaka","doi":"10.1017/psy.2026.10126","DOIUrl":"https://doi.org/10.1017/psy.2026.10126","url":null,"abstract":"<p><p>Learning diagnosis is essential for effective education, with formative assessments shown to significantly enhance academic performance. Diagnostic classification models (DCMs) have been developed to assess students' learning status and provide remedial instruction. However, the impact of mastery or non-mastery of specific attributes on long-term learning development remains uncertain. If certain non-mastered attributes hinder the growth of mathematical ability, early intervention becomes essential. In this study, we developed a random-effects DCM for multilevel growth curves (RDC-MGC) model to identify the specific effects of attribute mastery on individual-level mathematics ability growth. The simulation studies showed that the Bayesian estimation procedure provided appropriate parameter recovery and coverage probabilities, whereas ignoring the multilevel structure resulted in biased parameter estimates. The model was applied to arithmetic test data from second- to sixth-grade elementary school students. Diagnosis was conducted in the second grade, and the effects of mastery on mathematics ability growth from the third to sixth grades were assessed. The results showed that attribute mastery in second grade was associated with both the intercept and slope of individual ability growth, suggesting the potential importance of early-stage diagnostic information for understanding later mathematical development. Potential extensions of the proposed RDC-MGC model are also discussed.</p>","PeriodicalId":54534,"journal":{"name":"Psychometrika","volume":" ","pages":"1-46"},"PeriodicalIF":2.9,"publicationDate":"2026-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148406863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Capturing Heterogeneity in Levels, Variability, and Couplings across Persons and Time with a Hierarchical Time-Varying Coefficient Formulation of the Multivariate Normal.","authors":"Esther Ulitzsch, Steffen Nestler, Sverre Urnes Johnson, Therese Ruud Snuggerud, Oliver Lüdtke","doi":"10.1017/psy.2026.10125","DOIUrl":"https://doi.org/10.1017/psy.2026.10125","url":null,"abstract":"<p><p>Time-varying coefficient modeling (TVCM), which represents regression coefficients as smooth functions of continuous time, provides a flexible framework for uncovering complex patterns of change in levels and associations in intensive longitudinal data. However, conventional TVCM remains limited to investigating directional effects across individuals. By introducing a TVCM formulation of the multivariate normal distribution, the present study extends TVCM to explore change in undirected associations (couplings) and variability, thereby broadening its utility for psychological research. We discuss three versions of this approach: an aggregate-level model and two hierarchical versions capturing interindividual differences in unfolding change, either via person-specific intercepts accounting for onset differences or through fully person-specific coefficient functions smoothed via partial pooling. To illustrate the proposed developments, we apply them to six weeks of intensive longitudinal data from 16 anxiety patients undergoing therapy and examine unfolding changes in the level and volatility of nervousness and threat monitoring, their coupling, as well as between-person heterogeneity in each of these. We further show how inspecting first-order derivatives of the coefficient functions supports identifying periods of stability and change. Finally, we discuss extensions incorporating person-level characteristics to explain heterogeneity in patterns of change and predict outcomes.</p>","PeriodicalId":54534,"journal":{"name":"Psychometrika","volume":" ","pages":"1-26"},"PeriodicalIF":2.9,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148399776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
PsychometrikaPub Date : 2026-07-02DOI: 10.1017/psy.2026.10131
Giovanni Rebaudo, Fernando Llanos, Bharath Chandrasekaran, Abhra Sarkar
{"title":"Bayesian Mixed Multidimensional Scaling for Auditory Processing.","authors":"Giovanni Rebaudo, Fernando Llanos, Bharath Chandrasekaran, Abhra Sarkar","doi":"10.1017/psy.2026.10131","DOIUrl":"10.1017/psy.2026.10131","url":null,"abstract":"<p><p>The human brain distinguishes speech sounds by mapping acoustic signals into a latent perceptual space. This space can be estimated via multidimensional scaling (MDS), preserving the similarity structure in lower dimensions. However, individual and group-level heterogeneity, especially between native and non-native listeners, remains poorly understood. Prior approaches often ignore such variability or cannot capture shared structure, limiting principled comparisons. Moreover, the literature often focuses on latent distances rather than the underlying features themselves. To address these issues, we develop a Bayesian mixed MDS method that accounts for both subject- and group-level heterogeneity, allows for the recovery of unique, identifiable latent features, facilitating their biological interpretability, while also determining the effective dimensionality of the latent space in an automated, data-adaptive manner. Simulations and an auditory neuroscience application demonstrate how these features reconstruct observed distances and vary with individual and language background, revealing novel insights.</p>","PeriodicalId":54534,"journal":{"name":"Psychometrika","volume":" ","pages":"1-23"},"PeriodicalIF":2.9,"publicationDate":"2026-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148370885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
PsychometrikaPub Date : 2026-06-25DOI: 10.1017/psy.2026.10130
Martin Jann, Martin Spiess
{"title":"Testing linear hypotheses in repeated measures generalized linear models using external information.","authors":"Martin Jann, Martin Spiess","doi":"10.1017/psy.2026.10130","DOIUrl":"https://doi.org/10.1017/psy.2026.10130","url":null,"abstract":"","PeriodicalId":54534,"journal":{"name":"Psychometrika","volume":" ","pages":"1-43"},"PeriodicalIF":2.9,"publicationDate":"2026-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148320730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
PsychometrikaPub Date : 2026-06-16DOI: 10.1017/psy.2026.10129
Jules L Ellis, Klaas Sijtsma
{"title":"When Do Unifactorial Items Increase the Reliability?","authors":"Jules L Ellis, Klaas Sijtsma","doi":"10.1017/psy.2026.10129","DOIUrl":"10.1017/psy.2026.10129","url":null,"abstract":"<p><p>In the context of classical test theory, we study under which conditions addition of an item to a unifactorial test increases the reliability of the test score. We distinguish item weights used to construct a sum score and item factor loadings. We show that the reliability of a weighted sum score increases if the scoring weight of the new item is set sufficiently low. We conclude that any negative contribution to the reliability is not caused by inclusion of the new item per se, but by inadequate weighting of the new item. We also show that if the unweighted sum score is being used with items that have equal error variances, inclusion of a new item increases reliability if the factor loading of the new item is greater than about half of the mean loading of the other items. For standardized items, with loadings based on correlations, we derive lower bounds for the loading of a new item based on the mean and variance of the existing loadings. Instead of removing items when their factor loading is below 0.30, we recommend lowering their scoring weight if they reduce reliability.</p>","PeriodicalId":54534,"journal":{"name":"Psychometrika","volume":" ","pages":"1-27"},"PeriodicalIF":2.9,"publicationDate":"2026-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148260716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
PsychometrikaPub Date : 2026-06-15DOI: 10.1017/psy.2026.10128
Trung Tran Quoc Le, Steven Andrew Culpepper, Jeff Douglas
{"title":"Longitudinal Designs for Diagnostic Models: Identification and Estimation.","authors":"Trung Tran Quoc Le, Steven Andrew Culpepper, Jeff Douglas","doi":"10.1017/psy.2026.10128","DOIUrl":"10.1017/psy.2026.10128","url":null,"abstract":"<p><p>Recent studies on cognitive diagnostic models (CDMs) have extended the framework to longitudinal data. Various methods combined CDMs and hidden Markov models (HMMs) to assess changes in attributes over time and to evaluate the effects of interventions and covariates. A requirement for model fitting, inference, and interpretation is that models are identifiable. In this article, we derive identifiability conditions for experimental design used in education research. Specifically, we consider three designs: pretest/posttest single-group design, counterbalancing, and multiple-group longitudinal design. Drawing on existing HMM research, we examine the extent to which these designs satisfy common identifiability assumptions and propose new constraints for the counterbalancing and multiple-group longitudinal designs. These two setups are recommended in situations where item parameters differ over time or when there is heterogeneity in transition patterns across groups. We introduce a general HMM model for the multiple-group longitudinal design and a Gibbs sampling algorithm to estimate the parameters. We assess parameter recovery through a Monte Carlo simulation study and apply the model to a dataset from a study which evaluates the effectiveness of two interventions relative to a control condition. The results demonstrate the flexibility of the model and its potential to offer new insights into learning processes.</p>","PeriodicalId":54534,"journal":{"name":"Psychometrika","volume":" ","pages":"1-30"},"PeriodicalIF":2.9,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148254429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}