{"title":"Mode-Matched Inverse-Gamma Priors for Variance Components in Bayesian Multilevel Models.","authors":"Liu Liu","doi":"10.1080/00273171.2026.2740827","DOIUrl":"https://doi.org/10.1080/00273171.2026.2740827","url":null,"abstract":"<p><p>The present study introduces a strategy for specifying informative inverse-gamma (<i>IG</i>) priors for variance components in Bayesian multilevel models by matching the prior mode to a substantively plausible or empirically grounded target while keeping prior strength explicit. A Monte Carlo simulation compared maximum likelihood with Bayesian baseline, <i>IG</i>(0.01, 0.01), and mode-matched inverse-gamma priors across 162 two-level random-intercept conditions. In true-mode benchmark conditions, VarIGab improved estimation of the between-level residual variance, especially with small or moderate numbers of clusters. It reduced RMSE and mean absolute relative bias relative to the Bayesian baseline and <i>IG</i>(0.01, 0.01) priors while producing narrower intervals than the baseline. In a disjoint reference-sample illustration, the sample-calibrated prior reduced RMSE and interval width relative to the baseline but showed less favorable relative-bias performance when the number of clusters was very small. Variance-prior specification had little effect on fixed-effect point estimates among Bayesian approaches. A TIMSS 2019 U.S. Grade 8 illustration used a non-overlapping 243-school reference sample to calibrate prior modes for a separate 30-school target analysis. The findings illustrate both the potential and limitations of reference-informed inverse-gamma priors and underscore the importance of transparent calibration and sensitivity analysis.</p>","PeriodicalId":53155,"journal":{"name":"Multivariate Behavioral Research","volume":" ","pages":"1-19"},"PeriodicalIF":3.5,"publicationDate":"2026-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149240528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reducing Boundary Estimates and Increasing Power in Detecting Individual Differences in Change: The Effect of Adding a Quadratic Term.","authors":"Manshu Yang, Lijuan Wang, Scott E Maxwell","doi":"10.1080/00273171.2026.2731064","DOIUrl":"https://doi.org/10.1080/00273171.2026.2731064","url":null,"abstract":"<p><p>Accurately estimating and powerfully testing individual differences in change-<i>via</i> the variance of the average rate of change (ARC)-is important in longitudinal studies, yet boundary (i.e., zero) variance estimates with non-estimable standard errors and insufficient power for variance testing remain a common challenge. This study examines how frequently boundary estimates and biased ARC variance estimates occur when a straight-line growth (SLG) model is applied to quadratic growth data or a quadratic model is applied to SLG data. Analytical derivations using fully observed data and a simulation study with varying missing data conditions were conducted to evaluate three models: SLG, a quadratic growth model with a fixed quadratic effect (QGF), and one with a random quadratic effect (QGR). Results show that adding a quadratic term-fixed for three-wave data and random for four or more waves-reduced boundary estimates and improved power to detect individual differences in ARC, when growth data follow quadratic patterns. While underfitting (e.g., fitting SLG to quadratic data) yielded more boundary estimates and reduced power, overfitting (applying QGF/QGR to SLG data) did not harm ARC variance estimation and testing when sample size is adequate (<i>N</i> > 50). An empirical example illustrates model applications.</p>","PeriodicalId":53155,"journal":{"name":"Multivariate Behavioral Research","volume":" ","pages":"1-26"},"PeriodicalIF":3.5,"publicationDate":"2026-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149240523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Possible Solutions to Heywood Cases in Confirmatory Factor Analysis.","authors":"Yijun Cheng, Weicong Lyu, Oscar L Olvera Astivia","doi":"10.1080/00273171.2026.2741681","DOIUrl":"https://doi.org/10.1080/00273171.2026.2741681","url":null,"abstract":"<p><p>Heywood cases, where parameter estimates in confirmatory factor analysis (CFA) assume impossible values, challenge the accuracy of structural equation modeling. Common causes include small sample sizes, limited indicators per factor, and reliance on maximum likelihood estimation (MLE). Existing remedies, such as simply changing negative variances to zero or applying Bayesian estimation, offer partial solutions. This study introduces innovative approaches on MLE, including logistic-constrained loadings, exponential transformations and maximum a posteriori (MAP) estimation, to reduce Heywood cases and improve parameter estimation. These methods are evaluated using Monte Carlo simulations and a case study. The findings highlight their capacity to contribute meaningfully to psychometric modeling, both when the model is correctly specified and in the presence of model misfit.</p>","PeriodicalId":53155,"journal":{"name":"Multivariate Behavioral Research","volume":" ","pages":"1-15"},"PeriodicalIF":3.5,"publicationDate":"2026-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149240554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"MI-<i>Random rPQL</i>: A Variable Selection Method for Linear Mixed Models with Missing Data.","authors":"Yutian T Thompson, Yaqi Li","doi":"10.1080/00273171.2026.2738735","DOIUrl":"https://doi.org/10.1080/00273171.2026.2738735","url":null,"abstract":"<p><p>Variable selection, a statistical approach for identifying important predictors of an outcome, becomes particularly challenging when data are both clustered and incomplete. Despite the widespread use of linear mixed models (LMMs) in social and behavioral research, limited work has addressed variable selection in LMMs with incomplete data. Missing data can reduce estimation precision and distort the relationships between predictors and outcomes. Although multiple imputation (MI) is commonly used to handle missing data in clustered settings, aggregating variable selection results across imputed datasets, especially for both fixed and random effects, remains a methodological challenge. This issue is further compounded in high-dimensional contexts, where the number of predictors equals or exceeds the number of within-cluster observations. To address these limitations, we propose MI-<i>random rPQL</i>, a regularization-based method for variable selection in LMMs with incomplete clustered data. The method integrates multiple imputation with <i>random rPQL</i> to jointly identify important fixed and random effects. A simulation study was conducted to evaluate its performance. The results show that MI-<i>random rPQL</i> effectively selects important predictors even under substantial missingness, offering a flexible and robust solution for variable selection in high-dimensional, clustered datasets with incomplete data.</p>","PeriodicalId":53155,"journal":{"name":"Multivariate Behavioral Research","volume":" ","pages":"1-20"},"PeriodicalIF":3.5,"publicationDate":"2026-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149229190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Joshua B Gilbert, Edward J Kim, Zachary Himmelsbach, Esther Ulitzsch, Lijin Zhang
{"title":"Idiographic Item Response Theory: Modeling Person-Specific Differential Item Functioning in Intensive Longitudinal Data.","authors":"Joshua B Gilbert, Edward J Kim, Zachary Himmelsbach, Esther Ulitzsch, Lijin Zhang","doi":"10.1080/00273171.2026.2740068","DOIUrl":"https://doi.org/10.1080/00273171.2026.2740068","url":null,"abstract":"<p><p>Idiographic theories of psychological measurement emphasize that the relationships between item responses and a latent trait may vary across individuals, yet typical item response theory (IRT) models assume item parameters are constant across persons. We propose an IRT approach for modeling person-specific (idiographic) heterogeneity in item functioning in intensive longitudinal data. We extend the two-parameter logistic IRT model to allow item location parameters to vary across individuals through person-by-item interaction random effects. We apply a Bayesian estimator to estimate item-specific interaction variances and use a regularizing spike-and-slab likelihood mixture to identify items with non-negligible heterogeneity. A simulation study indicates that the model recovers such heterogeneity reasonably well when person sample sizes and the number of repeated measurements are at least moderate. We then apply our approach to empirical data from a depression study and find substantial variation across items in the degree of person-specific item functioning. The proposed model and estimator contribute to emerging work on idiographic measurement by extending IRT to settings where repeated observations can be used to estimate individual departures from group-level item parameters, providing a new tool for studying differential item functioning, measurement invariance, and broader forms of individual variation in intensive longitudinal data.</p>","PeriodicalId":53155,"journal":{"name":"Multivariate Behavioral Research","volume":" ","pages":"1-22"},"PeriodicalIF":3.5,"publicationDate":"2026-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149220777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Testing Group Differences in Nonlinear Growth Curve Modeling with Penalized Spline.","authors":"Han Du, Yang Liu, Zhiyong Zhang","doi":"10.1080/00273171.2026.2728649","DOIUrl":"https://doi.org/10.1080/00273171.2026.2728649","url":null,"abstract":"<p><p>Longitudinal data analysis in social and behavioral sciences often assumes a linear change over time, but human behavior is complex and frequently exhibits nonlinear patterns. Regression spline is a popular approach in machine learning to model nonlinear trajectories. While traditional machine learning prioritizes prediction, researchers in social and behavioral sciences focus on testing and interpreting the significance of group differences. This study compares six spline models for evaluating group differences in group-mean trajectories across multiple time points: the frequentist truncated power basis model, the frequentist piecewise basis model, the frequentist B-spline basis model, the Bayesian truncated power basis model, the Bayesian piecewise basis model, and the Bayesian B-spline basis model. Through simulation, we found that for non-censored data, the frequentist models demonstrated stability and robust performance. However, these models showed potential issues with statistical inference such as coverage rates and Type I error rates when the data are censored (e.g., floor and ceiling effects). For the latter cases, we recommend either using the frequentist models with an unstructured level-2 covariance matrix if computation time permits, or using the Bayesian B-spline model with an unstructured level-2 covariance matrix.</p>","PeriodicalId":53155,"journal":{"name":"Multivariate Behavioral Research","volume":" ","pages":"1-24"},"PeriodicalIF":3.5,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149197831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Homogeneity-Pursuit Calibration of Item Response Theory Models with Limited Samples and Sparse Response Data.","authors":"Shiyu Wang, Cong Cheng, Yuan Ke, Zichu Liu","doi":"10.1080/00273171.2026.2737426","DOIUrl":"https://doi.org/10.1080/00273171.2026.2737426","url":null,"abstract":"<p><p>Calibrating item response theory models is challenging when item banks are large relative to available sample sizes and response data are sparsely observed, as commonly occurs in classroom assessment, low-stakes testing, and early-stage item bank development. These challenges are particularly pronounced for the two-parameter logistic model, where unconstrained estimation often yields unstable or extreme item parameter estimates. To address this problem, we propose a new calibration framework based on homogeneity pursuit (HP), which stabilizes estimation by adaptively pooling information across items with similar psychometric properties. Rather than aiming to recover exact latent groupings, HP reduces effective model complexity through data-driven equality constraints, improving finite-sample estimation accuracy. We develop two variants of the proposed framework-HP-Scott and HP-Silhouette-that differ in the criteria used to guide adaptive pooling. Three simulation studies evaluate the performance of HP under idealized and realistic item-bank settings, including continuous parameter variation, small sample sizes, and high missing-response rates. Across these conditions, HP consistently reduces estimation error and mitigates extreme parameter estimates compared with baseline approaches. A real classroom assessment application with over 60% missing responses further demonstrates that HP produces more plausible item parameter estimates and superior model fit.</p>","PeriodicalId":53155,"journal":{"name":"Multivariate Behavioral Research","volume":" ","pages":"1-24"},"PeriodicalIF":3.5,"publicationDate":"2026-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149197874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"When Nesting is Nuisance in Cluster Sampled Longitudinal Research.","authors":"James Peugh, Francis Huang, Sonja D Winter","doi":"10.1080/00273171.2026.2720958","DOIUrl":"https://doi.org/10.1080/00273171.2026.2720958","url":null,"abstract":"<p><p>Cluster sampling is an efficient means of recruiting and retaining an optimal sample size for a longitudinal study, but results in sample data nested at three levels (repeated measures [level 1] collected from participants [level 2] sampled from within cluster units [level 3]) when research questions often only involve the first two. Researchers have three options when analyzing cluster sampled longitudinal data to avoid inferential errors when the third level of nesting is nuisance: 1) model it, 2) control it, or 3) a hybrid combination of both. The purpose of this paper is twofold. First, a smaller-scale Monte Carlo simulation was conducted to determine if options to control for nuisance nesting can achieve comparable parameter estimate accuracy, confidence interval coverage, and statistical power levels obtainable when nuisance nesting is modeled. Second, we demonstrate the three methods to address nuisance nesting using data from a previously published multi-site longitudinal study. The <i>R</i> and <i>rblimp</i> syntax scripts used to impute missingness and analyze the example data in keeping with a \"nesting is nuisance\" approach are included.</p>","PeriodicalId":53155,"journal":{"name":"Multivariate Behavioral Research","volume":" ","pages":"1-23"},"PeriodicalIF":3.5,"publicationDate":"2026-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149118318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mirka Henninger, Sandro Menegola, Niels Vanhasbroeck, Francis Tuerlinckx
{"title":"Affect Dynamics or Response Bias? Extreme Response Style in Daily-Life Assessments.","authors":"Mirka Henninger, Sandro Menegola, Niels Vanhasbroeck, Francis Tuerlinckx","doi":"10.1080/00273171.2026.2721527","DOIUrl":"https://doi.org/10.1080/00273171.2026.2721527","url":null,"abstract":"<p><p>Intensive longitudinal data (ILD) are increasingly used to study affect dynamics such as intraindividual variability and inertia. These parameters are often interpreted as substantive individual differences, yet they may be biased by stable response style tendencies, in particiular extreme response style (ERS). In the present study, we investigated whether ERS is systematically associated with affect dynamics estimated from multiple experience sampling method (ESM) datasets (total <math><mrow><mi>N</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>254</mn></mrow></math>). Using a joint Bayesian IRTree-location-scale modeling approach, we estimated person-specific ERS alongside affective variability and inertia across multiple ESM datasets and synthesized study-level associations using a meta-analytic approach. We find that higher ERS is consistently associated with greater intraindividual variability. In contrast, we find no evidence that ERS was related to affective or emotional inertia. These results suggest that commonly used measures of intraindividual variability may partly reflect systematic response behavior rather than solely genuine affective fluctuations. Ignoring ERS may therefore bias variability estimates obtained from location-scale and related multilevel dynamic models. Overall, this study highlights the importance of accounting for response styles when modeling affect dynamics and interpreting person-specific variability parameters in ILD research.</p>","PeriodicalId":53155,"journal":{"name":"Multivariate Behavioral Research","volume":" ","pages":"1-38"},"PeriodicalIF":3.5,"publicationDate":"2026-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148946140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xinran Song, Qian Zhang, Kaizong Ye, Antonio R Linero
{"title":"Automatic Mediation Analysis Under Measurement Error Via Bayesian Machine Learning.","authors":"Xinran Song, Qian Zhang, Kaizong Ye, Antonio R Linero","doi":"10.1080/00273171.2026.2660129","DOIUrl":"10.1080/00273171.2026.2660129","url":null,"abstract":"<p><p>This paper considers the problem of causal mediation analysis (CMA) when the outcome, mediator, or both are modeled as latent variables that are measured with error from multiple indicators. Traditional structural equation modeling approaches rely on restrictive parametric assumptions and struggle to capture nonlinear relationships or interactions among covariates, outcomes, and mediators; additionally, accounting for measurement error is difficult when nonlinearities are present. We address these challenges using Bayesian causal mediation forests to model the structural relationships, which were shown by Linero and Zhang to perform well for estimating mediation effects. To infer the latent variables, we consider (a) a full hierarchical Bayesian model and (b) an approximation based on composite scores that is easier to implement. We evaluate our approach through simulation experiments and apply our methodology to data from the Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE) study, which is a publicly available, large-scale, multi-site randomized controlled trial designed to evaluate the effectiveness of cognitive training interventions in order to improve the cognitive abilities of older adults. We find a nonlinear relationship between the ability to perform daily activities (the outcome) and reasoning ability (the mediator), with reasoning training improving the outcome through the mediator.</p>","PeriodicalId":53155,"journal":{"name":"Multivariate Behavioral Research","volume":" ","pages":"830-848"},"PeriodicalIF":3.5,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147823416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}