multilevel regression analysis

This paper addresses bias and standard error misspecification in multilevel models (MLMs) for estimating treatment effects under generalized linear models (GLMs) when group-level confounding is present. We demonstrate that, unlike in linear models, MLMs are not equivalent to regularized fixed-effects (FE) estimators in GLMs, and their default standard errors typically underestimate within-group dependence-induced variability. To remedy this, we propose bias-corrected MLM (bcMLM), which reduces estimation bias relative to FE, as confirmed through simulations and empirical analysis. Furthermore, we show that cluster bootstrap inference substantially outperforms default standard errors in accounting for clustering structure. Our work provides a theoretically grounded, computationally feasible estimation framework for causal inference in nonlinear GLMs—filling critical gaps in both the theoretical understanding of bias mechanisms and the practical implementation of bias correction for MLMs in generalized settings.

This study investigates the statistical performance of linear mixed models (LMMs) and mixed-effects location-scale models (MELSMs) under heteroscedasticity and model misspecification. Using large-scale longitudinal Monte Carlo simulations, we systematically evaluate estimation bias and confidence interval coverage. Key contributions are: (1) When heteroscedasticity is ignored, LMMs severely overestimate random-effect standard deviations and yield invalid confidence intervals; (2) We first demonstrate an asymmetric impact of misspecification in MELSMs: misspecification of the location component substantially biases scale-parameter estimates, whereas misspecification of the scale component does not affect consistency of location-parameter estimators; (3) We establish that MELSMs maintain robustness for location inference even under scale-structure misspecification, thereby providing a more reliable foundation for modeling non-normal outcomes, joint models, and survival analyses.

This study addresses the bias and uncertainty in parameter estimation arising from missing not at random (MNAR) data in linear multilevel models. The authors propose a sensitivity analysis approach that jointly models the outcome variable and the dropout mechanism, incorporating an interpretable sensitivity parameter. Under assumptions weaker than missing at random, this method enables partial identification of model parameters and constructs corresponding uncertainty intervals. To the best of our knowledge, this is the first integration of sensitivity analysis with multilevel modeling. The validity of the proposed approach is demonstrated through simulation studies, and its practical utility is illustrated in an empirical analysis examining the effects of loneliness and physical activity on memory trajectories, yielding robust and more interpretable inferences.

To address the challenges of jointly selecting fixed and random effects in multilevel functional regression—and the inability of existing methods to capture cluster-specific heterogeneity—this paper proposes MuFuMES, the first sparse simultaneous selection framework tailored for multilevel functional mixed-effects models. MuFuMES integrates spline basis expansion, a spike-and-slab group Lasso prior, and an expectation-conditional maximization (ECM) algorithm to enable efficient maximum a posteriori (MAP) estimation. Simulation studies demonstrate near-zero false positive and false negative rates. Applied to accelerometer data from NHANES 2011–2012, MuFuMES successfully identifies age- and race-specific diurnal activity pattern heterogeneities, uncovering biologically interpretable, hierarchical covariate effect structures.

In linear mixed models, conventional asymptotic inference fails when the random-effects covariance matrix approaches or lies on the parameter boundary—e.g., zero variances or correlation coefficients tending to ±1. To address this, we propose a unified, finite-sample distributional approximation method. Our approach quantifies the deviation between linear combinations of score functions and standard normality, integrating uniform approximation theory with high-dimensional statistical techniques to construct computationally tractable confidence regions. The method accommodates both cluster-independent and crossed random-effects structures and is valid under high-dimensional asymptotics—where the number of parameters grows jointly with the number of random effects. We establish theoretical guarantees: the resulting confidence regions achieve near-nominal coverage in finite samples and remain robust under boundary scenarios. Extensive simulations confirm superior small-sample performance and computational feasibility.

Conventional approaches to deciding whether to use multilevel models based on point estimates of the intraclass correlation coefficient (ICC) ignore sampling uncertainty and lack a foundation in statistical inference. This study proposes the "Negligible Effect Significance Test" (NEST), which introduces equivalence testing into ICC assessment for the first time. By constructing an ICC pivotal quantity from the F-statistic and incorporating design effect considerations, NEST defines a threshold for a “negligible” ICC that quantifies an acceptable level of variance inflation. The method provides a statistically rigorous decision rule for determining when multilevel modeling is warranted, accompanied by an R implementation to help researchers evaluate whether clustering structures merit explicit modeling—thereby avoiding misjudgments arising from neglecting sampling variability.

Traditional epidemiological approaches struggle to disentangle hierarchical variation and structural disparities in cardiovascular disease (CVD) mortality across multiscale geographic units. This study proposes a reproducible multilevel statistical inference framework that integrates Gaussian, Poisson, and population-offset Poisson models to separate demographic effects from structural risk factors within a county-nested hierarchy. Fixed effects—including year, sex, race, PM2.5, and O₃—along with county-level random intercepts are incorporated, using data from Ohio and Pennsylvania between 1999 and 2020. Findings reveal that Pennsylvania experienced a steeper decline in age-standardized CVD mortality, though several CVD subtypes plateaued or rebounded after 2010. Black populations exhibited significantly elevated risk, and PM2.5 showed stronger associations with ischemic and hypertensive heart diseases. The inclusion of a population offset notably reduced unexplained variance, demonstrating the framework’s utility as a generalizable tool for environmental health assessment and health equity research.

This work proposes an efficient fitting approach for generalized linear mixed-effects models in which the response variable follows a non-Gaussian distribution and its mean is nonlinearly related to the linear predictor through a link function. Built within the lme4 framework, the method jointly estimates fixed effects, conditional modes of random effects, and their variance–covariance structure via penalized iteratively reweighted least squares. High-accuracy approximations to the likelihood are achieved using either Laplace approximation or adaptive Gauss–Hermite quadrature. The approach accommodates user-specified exponential family distributions and link functions, supporting common non-Gaussian responses such as binomial and Poisson outcomes. By balancing computational efficiency with modeling flexibility, the proposed method substantially extends the applicability of generalized linear mixed models while maintaining robust performance.

本文提出了一种多层社会关系模型，通过双采样方法调整报告者效应，并利用MCMC方法估计模型参数，以解决不同集群间个体联系的网络分析问题。

This study addresses the severe undercoverage of conventional confidence intervals in linear mixed models when variance parameters approach boundary values. We propose a novel method based on a modified profile score statistic derived from the restricted likelihood, which constructs confidence intervals by estimating nuisance parameters within an expanded parameter space and inverting the test statistic. This approach enables accurate inference in challenging boundary scenarios, such as near-zero random-effect variances or strong correlations. Simulation studies demonstrate that the proposed method maintains coverage rates stably near the nominal 95% level while reducing interval widths by 1.7 to 3.1 times compared to general-purpose inference procedures, alongside a 47-fold improvement in computational efficiency. The practical utility of this framework is further validated through its successful application to a longitudinal autism study.