mixed-effects modeling

This study addresses the challenge of modeling dual heterogeneity in longitudinal trajectories arising from both fixed and random effects, which traditional linear mixed-effects models (LMMs) struggle to capture effectively. To this end, the authors propose a Mixture of Experts for Mixed-Effects models (MEMoE), which uniquely integrates the mixture-of-experts architecture with LMMs by assigning each expert to a full LMM representing a distinct latent subgroup. A gating function, driven by baseline covariates, probabilistically allocates individuals to these subgroups. Parameter estimation is performed via a Laplace-approximated EM algorithm, complemented by a robust sandwich estimator to adjust standard errors and enhance inference reliability. Empirical evaluations demonstrate that MEMoE significantly outperforms conventional single-population LMMs and standard mixture-of-experts models in terms of parameter recovery, classification accuracy, and overall model fit.

This study addresses the unreliability of fixed-effect inference in multivariate linear mixed models, which often arises from misspecification of the random-effects distribution, bias in Fisher information estimation, or algorithmic non-convergence—issues exacerbated by simultaneous within-cluster and between-response dependencies. To overcome these limitations, this work proposes a robust testing procedure that neither requires specifying the random-effects distribution nor relies on Fisher information estimation. By integrating score statistics with cluster-level sign-flipping transformations, the method achieves asymptotically valid and efficient inference under weak distributional assumptions. Notably, it is the first approach to enable asymptotically efficient, distribution-free inference for fixed effects in multivariate mixed models, substantially improving control of type I error rates and overall inferential reliability.

Existing structural equation modeling (SEM) frameworks struggle to model latent variable variances that depend on other latent variables, thereby limiting the characterization of latent heteroscedasticity—such as in psychological constructs like personality or creativity. To address this, we propose Bayesian Gaussian Distributional SEM, the first SEM extension integrating distributional regression into the SEM framework to jointly model both the mean and variance of latent variables. Leveraging Bayesian inference and MCMC sampling, our approach flexibly specifies latent variances as arbitrary functions of other latent variables. Simulation studies demonstrate high statistical reliability and computational efficiency. Empirical analysis of personality data reveals that emotional stability significantly moderates the variability of neuroticism—a finding inaccessible under conventional SEM. This work introduces a novel theoretical tool and methodological paradigm for modeling latent heteroscedasticity, advancing both substantive theory testing and statistical methodology in behavioral and social sciences.

This paper addresses three key challenges in binary panel data models: biased estimation of average partial effects, invalid statistical inference, and the inability to predict outcomes for units with no within-unit variation—problems arising from complete separation. To resolve these issues, we propose a grouped fixed-effects regularization approach. Innovatively, we employ k-means clustering to discretize unobserved heterogeneity and replace conventional within-unit variation with within-group response variation, thereby mitigating complete separation while controlling parameter proliferation. Guided by asymptotic theory, we develop an optimal group-number selection criterion, yielding a unified estimation framework applicable to both panel logit and probit models. Monte Carlo simulations demonstrate that our method eliminates estimation bias and restores valid inference. Empirically, it substantially expands predictive coverage—enabling, for the first time, coherent predictions for numerous units exhibiting invariant responses across time.

This study addresses the inconsistency in causal effect estimates between observational studies and randomized controlled trials (RCTs) by proposing the first unified framework for decomposing causal effect heterogeneity. The framework systematically identifies and quantifies three sources of heterogeneity: differences in covariate distributions, variation in mediating pathways, and shifts in outcome-generating mechanisms. Methodologically, it formally defines effect decomposition across data types (observational vs. experimental), integrating causal inference, sensitivity analysis, and decomposition modeling, while enabling robust parameter estimation under multiple hypotheses. Evaluated through simulation studies and an empirical analysis of the “Moving to Opportunity” experiment, the framework demonstrates improved interpretability, robustness, and policy generalizability in synthesizing evidence from heterogeneous data sources.

This study addresses a critical limitation in conventional two-stage approaches that link individual-level distributional characteristics—such as variability and skewness—to downstream outcomes, which ignore estimation error in the first stage and consequently yield biased estimates and inflated Type I error rates. To overcome this, the authors propose the Distributional Feature Latent Variable Model (DFLVM), which, for the first time, integrates distributional features into a latent variable framework. DFLVM captures between-individual heterogeneity through random intercepts and jointly models both the distributional features and their effects on outcomes within a single-step maximum likelihood estimation procedure. This unified approach circumvents the inherent bias of two-stage methods. Simulation studies and empirical analyses demonstrate that DFLVM substantially reduces estimation bias and false positive rates while enhancing inferential accuracy.

This study addresses the limitations of the traditional cross-lagged panel model (CLPM) in disentangling between-person differences from within-person dynamics, which hampers causal inference in longitudinal data. Focusing on the random intercept cross-lagged panel model (RI-CLPM), the work demonstrates how incorporating random intercepts—representing stable trait-like individual differences—effectively separates between-person heterogeneity from within-person temporal processes. The paper explicitly articulates the core assumption of the RI-CLPM that stable traits are uncorrelated with within-person fluctuations, systematically clarifies its mathematical and conceptual relationships to alternative approaches such as dynamic panel models, and delineates its appropriate scope and limitations. These contributions provide a rigorous theoretical and methodological foundation for model selection, interpretation, and causal inference in longitudinal psychological research.

This study addresses the challenge of specifying prior parameters for both fixed and random effects in linear mixed models when dealing with high-dimensional data or complex covariance structures. The authors propose a data-driven joint shrinkage approach that, within an empirical Bayes framework, employs Laplace approximation to efficiently maximize the marginal likelihood and automatically select prior parameters for both effect types. This method represents the first to jointly and adaptively estimate priors for fixed and random effects, overcoming the limitations of conventional approaches that rely on manual specification. Numerical experiments demonstrate that the proposed method significantly outperforms existing techniques in terms of parameter estimation accuracy and predictive performance. Its effectiveness in modeling complex random-effect structures is further validated through application to real-world data on air pollution and health outcomes.

This study addresses the challenge of accurately inferring the distribution of individual treatment effects—such as the proportion benefiting, the median effect, or the maximum impact—in randomized experiments, without suffering power loss due to suboptimal pre-specified test statistics. The authors propose an adaptive randomization test that combines multiple rank-based statistics, ensuring finite-sample validity without requiring prior knowledge of the optimal statistic. Innovatively integrating adaptive statistic combination with stratified weighting, the method effectively circumvents the power degradation typically induced by multiple comparison corrections and accommodates heterogeneous stratified experimental designs. In an empirical application to a teacher training program, the approach reveals that approximately half of the teachers experience significant benefits, demonstrating superior detection power and interpretability compared to conventional single rank-based tests.

This study addresses the lack of effective modeling and inference methods for fixed effects in factorial designs under data uncertainty. It introduces uncertainty measures into one-way and two-way fixed-effects models—with and without interaction—for both balanced and unbalanced designs. Building upon uncertainty theory, the authors develop a unified framework for parameter estimation and hypothesis testing, thereby extending the applicability of classical analysis of variance to settings involving uncertain data. The proposed approach is validated through three real-world case studies, demonstrating consistent effectiveness and practical utility across diverse experimental structures. This work establishes a novel paradigm for analyzing experimental data characterized by inherent uncertainty.