Hierarchical Model Research Articles

Objective Bayesian Model Selection for Spatial Hierarchical Models with Intrinsic Conditional Autoregressive Priors

We develop Bayesian model selection via fractional Bayes factors to simultaneously assess spatial dependence and select regressors in Gaussian hierarchical models with intrinsic conditional autoregressive (ICAR) spatial random effects. Selection of covariates and spatial model structure is difficult, as spatial confounding creates a tension between fixed and spatial random effects. Researchers have commonly performed selection separately for fixed and random effects in spatial hierarchical models. Simultaneous selection methods relieve the researcher from arbitrarily fixing one of these types of effects while selecting the other. Notably, Bayesian approaches to simultaneously select covariates and spatial model structure are limited. Our use of fractional Bayes factors allows for selection of fixed effects and spatial model structure under automatic reference priors for model parameters, which obviates the need to specify hyperparameters for priors. We also show the equivalence between two ICAR specifications and derive the minimal training size for the fractional Bayes factor applied to the ICAR model under the reference prior. We perform a simulation study to assess the performance of our approach and we compare results to the Deviance Information Criterion and Widely Applicable Information Criterion. We demonstrate that our fractional Bayes factor approach assigns low posterior model probability to spatial models when data is truly independent and reliably selects the correct covariate structure with highest probability within the model space. Finally, we demonstrate our Bayesian model selection approach with applications to county-level median household income in the contiguous United States and residential crime rates in the neighborhoods of Columbus, Ohio.

Teaching Quality and Student Achievement Inequalities in Low- and Middle-income Countries: A Hierarchical Linear Model Analysis

Teaching quality is associated with student achievement, though the strength of this association may vary. This study employs hierarchical linear modeling using PISA-D data to examine the association between teaching quality (teacher support, classroom management, and cognitive support) and mathematics achievement, while disaggregating the analysis by student gender and socioeconomic status (SES). Our findings indicate that cognitive support is negatively associated with student achievement in Ecuador, with no significant association in Cambodia, Guatemala, Honduras, Paraguay, Senegal, or Zambia. Additionally, we found a positive association between classroom management and mathematics in Cambodia, Ecuador, Honduras, and Zambia, but no association in other countries. Similarly, teacher support showed a negative association with mathematics in Ecuador and Honduras, but no significant association in other countries. Beyond these direct associations, our findings suggest that the influence of teaching quality may vary across student gender and SES. We also discuss the policy implications of these findings.

Traffic Safety for All Road Users: A Paired Comparison Study of Small & Mid-Sized U.S. Cities with High/Low Bicycling Rates

Cities with high levels of bicycling tend to be some of the safest cities for all road users. This paper investigates why this relationship exists for fourteen small and mid-sized cities across the U.S. (seven with high bicycling rates and seven paired comparison cities) using ten years of data and hierarchical negative binomial regression models. Findings confirm that higher-bicycling cities are significantly associated with better overall road safety outcomes. In terms of mode choice differences, pedestrian ‘safety in numbers’ as well as reduced driving activity had a positive impact on pedestrian safety. Results from hierarchical negative binomial regressions also suggest that more compact cities were significantly associated with better road safety outcomes for all road users. In terms of socio-demographic and socio-economic factors, the results reveal equity concerns with areas with lower incomes and more non-White residents seeing more overall road fatalities.

Leveraging Technology to Address Social-Emotional Learning during the Pandemic: Findings from an Efficacy Trial

We used a cluster-randomized controlled trial to examine the impacts of a technology- and game-based social-emotional program, the Adventures Aboard the S.S. GRIN (Adventures), on students’ social skills development. Eighty-eight third-grade classrooms (N=1,645 third-grade students) across four California public school districts were randomized to treatment or control. Analysis of student demographic data indicated that 49% were male, 51% were female, approximately one-third were Latinx, and about 50% qualified for free and reduced lunch. Two-level hierarchical linear model analysis results indicated that Adventures had significant and meaningful impacts on students’ social-emotional learning (SEL) skills. The findings of Adventures shine new lights on a growing effort to support all students, including those identified by their teachers as having social-emotional challenges. It also expands our knowledge about the potential role of technology in addressing SEL competencies.

Spatio-temporal data fusion for the analysis of in situ and remote sensing data using the INLA-SPDE approach

We propose a Bayesian hierarchical model to address the challenge of spatial misalignment in spatio-temporal data obtained from in situ and satellite sources. The model is fit using the INLA-SPDE approach, which provides efficient computation. Our methodology combines the different data sources in a “fusion” model via the construction of projection matrices in both spatial and temporal domains. Through simulation studies, we demonstrate that the fusion model has superior performance in prediction accuracy across space and time compared to standalone “in situ” and “satellite” models based on only in situ or satellite data, respectively. The fusion model also generally outperforms the standalone models in terms of parameter inference. Such a modeling approach is motivated by environmental problems, and our specific focus is on the analysis and prediction of harmful algae bloom (HAB) events, where the convention is to conduct separate analyses based on either in situ samples or satellite images. A real data analysis shows that the proposed model is a necessary step towards a unified characterization of bloom dynamics and identifying the key drivers of HAB events.

Frequency-Aware Feature Fusion for Dense Image Prediction.

Dense image prediction tasks demand features with strong category information and precise spatial boundary details at high resolution. To achieve this, modern hierarchical models often utilize feature fusion, directly adding upsampled coarse features from deep layers and high-resolution features from lower levels. In this paper, we observe rapid variations in fused feature values within objects, resulting in intra-category inconsistency due to disturbed high-frequency features. Additionally, blurred boundaries in fused features lack accurate high frequency, leading to boundary displacement. Building upon these observations, we propose Frequency-Aware Feature Fusion (FreqFusion), integrating an Adaptive Low-Pass Filter (ALPF) generator, an offset generator, and an Adaptive High-Pass Filter (AHPF) generator. The ALPF generator predicts spatially-variant low-pass filters to attenuate high-frequency components within objects, reducing intra-class inconsistency during upsampling. The offset generator refines large inconsistent features and thin boundaries by replacing inconsistent features with more consistent ones through resampling, while the AHPF generator enhances high-frequency detailed boundary information lost during downsampling. Comprehensive visualization and quantitative analysis demonstrate that FreqFusion effectively improves feature consistency and sharpens object boundaries. Extensive experiments across various dense prediction tasks confirm its effectiveness.

High-Dimensional Bayesian Semiparametric Models for Small Samples: A Principled Approach to the Analysis of Cytokine Expression Data.

In laboratory medicine, due to the lack of sample availability and resources, measurements of many quantities of interest are commonly collected over a few samples, making statistical inference particularly challenging. In this context, several hypotheses can be tested, and studies are not often powered accordingly. We present a semiparametric Bayesian approach to effectively test multiple hypotheses applied to an experiment that aims to identify cytokines involved in Crohn's disease (CD) infection that may be ongoing in multiple tissues. We assume that the positive correlation commonly observed between cytokines is caused by latent groups of effects, which in turn result from a common cause. These clusters are effectively modeled through a Dirichlet Process (DP) that is one of the most popular choices as nonparametric prior in Bayesian statistics and has been proven to be a powerful tool for model-based clustering. We use a spike-slab distribution as the base measure of the DP. The nonparametric part has been included in an additive model whose parametric component is a Bayesian hierarchical model. We include simulations that empirically demonstrate the effectiveness of the proposed testing procedure in settings that mimic our application's sample size and data structure. Our CD data analysis shows strong evidence of a cytokine gradient in the external intestinaltissue.

Factors of individual differences between the speeds of the hand and ball during baseball pitching: Assessment of middle finger function based on the hierarchical linear model

ABSTRACT This study aimed to reveal individual differences between the speeds of the hand and ball and clarify the factors affecting those differences. Motion data from 20 highly skilled baseball pitchers, captured using a 16-camera motion analysis system with a sampling frequency of 1,000 hz, were used for correlation and hierarchical linear model analyses. For the hierarchical linear models, the speed of the metacarpophalangeal joint was the independent variable in the 1st level. The independent variables chosen in the 2nd level were the variables regarding the finger length, mean peak angular velocities, and mean peak accelerations of the middle finger joint. Intra-subject correlation analysis showed high positive correlation coefficients between the metacarpophalangeal joint and ball speeds, ranging from 0.803 to 0.992. The difference between the hand and ball speeds ranged from 8.4 m∙s−1 to 12.0 m∙s−1. The hierarchical linear model analyses indicated that the individual differences between the speeds of the hand and ball were partly accounted for by the mean peak accelerations of the proximal and distal interphalangeal joints, suggesting that the force exerted by proximal interphalangeal joint flexion plays an important role in ball speed increment.

Dangerous depths of bifurcation: the rise of “inter-national security narcissists” and undersea cable (dis) connections

ABSTRACT This article examines the rising bifurcation in global undersea cable networks amid growing U.S.-China tensions, building on the “weaponized interdependence” (WI) framework. While WI sheds light on how states leverage network centrality for strategic benefits, it falls short of capturing the proactive reshaping of network topologies for national security. We argue this bifurcation fosters parallel, redundant systems that, despite increased costs, enhance control and security. A sequential game model illustrates how U.S. and Chinese security-driven decisions contribute to network divergence, while a hierarchical Q-learning model explores how path dependency and lock-in effects sustain this split. Empirical cases, like the Cap-1 project, demonstrate the practical impact, emphasizing security’s role in reconfiguring global communications infrastructure.

Symptom trajectories over time by cannabis use status among patients undergoing cancer treatment.

Adults with cancer may perceive cannabis as beneficial for managing their cancer-related symptoms, but the evidence supporting its medical use is varied and inconclusive. This study characterized associations of cannabis use with cancer-related symptom trajectories. Participants were adults undergoing cancer treatment at the Stephenson Cancer Center (SCC; n = 218) in Oklahoma; they were 71% female, 10% minoritized race, and 45% had stage III or IV cancer. Participants completed surveys at baseline and 2-, 4-, and 6-months post-baseline. Assessments queried about cannabis use behavior, physical and psychological distress via the Rotterdam Symptoms Checklist (RSCL), respiratory symptoms via the American Thoracic Society Questionnaire (ATSQ), and quality of life indices (physical and social functioning, pain interference, sleep quality, fatigue) via the Patient Reported Outcomes Measurement Information System (PROMIS-29). Cannabis use status was categorized based on self-reported past 30-day cannabis use at each assessment as non-use [no use at any assessment], occasional-use [use at 1-2 assessments], or consistent-use [use at 3-4 assessments]. Longitudinal hierarchical linear modeling evaluated associations of cannabis use status with average symptoms and symptom trajectories across all four assessments. One-third (33%) of participants reported past 30-day cannabis use at ≥ 1 assessment. Participants who reported cannabis use (occasional-use and consistent-use) had more severe symptoms overall across assessments. While most cancer symptom trajectories did not differ by cannabis use status, participants who reported consistent cannabis use uniquely showed worsening physical function over time. Cannabis use was associated with greater cancer-related symptom severity over time.

Three-year survival follow-up of patients with gastrointestinal cancer treated during the COVID-19 pandemic in Spain: data from the PANDORA-TTD20 study.

The initial SARS-CoV-2 pandemic wave in Spain in 2020 precipitated significant paradigm shifts in gastrointestinal oncology patient management. This study captures the "Zeitgeist" of this period by analyzing adaptive strategies, treatment modifications, and survival outcomes, leveraging a 3-year follow-up perspective to extract insights from this unprecedented experience. We conducted a multicenter, retrospective cohort study utilizing the RETUD-TTD registry, encompassing 703 patients across 19 Spanish centers in April 2020. We evaluated alterations in clinical practice, therapeutic approaches, coronavirus disease 2019 (COVID-19)-related impacts, and patient survival. A Bayesian hierarchical model was employed to identify potential regional-specific frailties. The peak of the pandemic in April 2020 catalyzed substantial shifts in oncological care delivery. Outpatient consultations decreased by 13%, with a notable selection bias toward cases with more favorable prognostic indicators. Multidisciplinary tumor board discussions were significantly curtailed (eg, mean monthly colorectal cancer cases discussed was reduced from 40 to 23), compromising qualitative care measures. This occurred concurrently with an average of over 3 oncologists per center on medical leave. Contrary to initial concerns, the healthcare system demonstrated remarkable resilience. The majority of patients received standard-of-care therapies with regulatory approval, albeit with regimen modifications in 15% of cases. These adaptations included extended dosing intervals, dose intensity modulations, and transitions to oral formulations while maintaining unexpectedly stable long-term survival outcomes. The Bayesian frailty model detected minimal unmeasured prognostic factors related to geographic location, and the type of pandemic-induced adaptation did not significantly impact survival. The model revealed that coronavirus disease 2019's impact was less pronounced than other core prognostic variables. The decentralized Spanish healthcare system exhibited substantial robustness in managing pre-pandemic diagnosed gastrointestinal malignancies, despite asymmetrical, and occasionally severe organizational disruptions. The insights gleaned from this experience could inform future crisis preparedness strategies and optimize care provision during subsequent public health emergencies.

Application of Hierarchical Bayesian Models for Modeling Economic Costs in the Implementation of New Diagnostic Tests

The COVID-19 pandemic has highlighted the need for reliable and rapid diagnostic tests to control the spread of infection. The introduction of new rapid antigen tests often goes in tandem with the limited data availability, making it challenging to assess their performance at the initial phase of the pandemic. Sensitivity and specificity, the key performance characteristics provided by manufacturers, are typically derived under laboratory conditions and may not accurately reflect the tests' performance in field settings. We use the hierarchical Bayesian model to obtain their realistic estimates in real world conditions and show how it may be used in situations in which new tests with limited history are presented on the market. Proposed methodology allows for the efficient information pooling, thereby improving on the accuracy of parameter estimates for new tests. The results suggest that the application of hierarchical model on the Czech data led to a considerabile reduction in uncertainty associated with the parameter estimates as well as with potential economic cost implied by false positive test results. The model can thus assist in better informed decision-making and financial planning of both the government and corporations.

A Dynamical Interpretation of the Intensification of the Winter North Atlantic Jet Stream in Reanalysis

Abstract Jet streams play an important role in determining weather variability and extremes. A better understanding of the mechanisms driving long-term changes in the jet is essential to successfully anticipate extreme meteorological events. This study analyzes the intensification trend of the North Atlantic jet using the ERA5 reanalysis and investigates the dynamical mechanisms involved. The results highlight the importance of an increase in diabatic heating in the free troposphere below the jet entrance over the Gulf Stream sector. This change in diabatic heating modifies the jet directly and produces a local intensification and a slight poleward shift. A two-dimensional frontal-geostrophic model illustrates this mechanism by considering the enhanced diabatic heating associated with the baroclinic growth of extratropical cyclones. The change in diabatic heating also affects the jet indirectly by increasing the mean baroclinicity and subsequent eddy momentum flux convergence. This indirect mechanism has also an effect downstream, where there is an acceleration of the jet core and reduced westerlies along the flanks, reducing the width of the jet. An idealized warming experiment confirms this mechanism by determining the jet response downstream of an idealized land–sea contrast. Finally, using a single-model ensemble of fully coupled climate simulations, we show that the differences in the evolution of the North Atlantic jet are related to the latitude of the increase in baroclinicity, which has a large spread. What emerges from the model hierarchy is a consistent dynamical chain of mechanisms associated with the intensification trend of the North Atlantic jet stream.

Integrating green image with relationship marketing: A moderating role of green image

This study integrates social exchange theory, the biophilia hypothesis, the hierarchy of effects model, and self-congruency theory to examine how relational benefits and green image influence positive emotion, customer loyalty, and customer green behavior (CGB). Data were collected from 314 respondents via an online marketing research firm and analyzed using SmartPLS 4.0. The results show that customers’ perceptions of relational benefits have a direct impact on both customer loyalty and positive emotions. While green image significantly affects customer loyalty, it does not have a direct impact on positive emotions or CGB. However, green image enhances the positive association between customer emotions and CGB, suggesting that customers are more likely to engage in green behavior when they feel a positive emotional connection with a company they perceive as environmentally responsible. These findings suggest that restaurant firms should implement marketing strategies to improve their green image by emphasizing the value of relational benefits. Both theoretical and managerial implications are discussed.

The association between maternal stress and human milk concentrations of cortisol and prolactin.

Psychosocial stress affects the relationship between prolactin (PRL) and cortisol (CORT). The dynamics of PRL and CORT changes under stress in human milk (HM) are largely unknown. We investigated how maternal stress related to recent life changes affects milk CORT and PRL concentrations. The study involved 116 mothers exclusively breastfeeding 5-month-old infants. Maternal psychological stress was evaluated using the Recent Life Changes Questionnaire (RLCQ). Stress response was determined by administering the cold pressor test and measuring CORT in saliva taken during and in milk collected after the test. Hormones concentrations were assayed using the ELISA method. The hierarchical regression models were run to test the association between maternal RLCQ, salivary CORT, and PRL, and CORT in milk. Maternal RLCQ correlated positively with the CORT in saliva, however, no direct association was found between RLCQ and PRL. After controlling for covariates, a positive association was found between salivary and milk CORT. A negative relationship was observed between salivary CORT and milk PRL. The results of the present study indicate that maternal psychological stress may affect the relationship between CORT and PRL in HM. In response to psychological stress, both hormones transported via milk can program infant development in the early postnatal period.

A hierarchical active inference model of spatial alternation tasks and the hippocampal-prefrontal circuit.

Cognitive problem-solving benefits from cognitive maps aiding navigation and planning. Physical space navigation involves hippocampal (HC) allocentric codes, while abstract task space engages medial prefrontal cortex (mPFC) task-specific codes. Previous studies show that challenging tasks, like spatial alternation, require integrating these two types of maps. The disruption of the HC-mPFC circuit impairs performance. We propose a hierarchical active inference model clarifying how this circuit solves spatial interaction tasks by bridging physical and task-space maps. Simulations demonstrate that the model's dual layers develop effective cognitive maps for physical and task space. The model solves spatial alternation tasks through reciprocal interactions between the two layers. Disrupting its communication impairs decision-making, which is consistent with empirical evidence. Additionally, the model adapts to switching between multiple alternation rules, providing a mechanistic explanation of how the HC-mPFC circuit supports spatial alternation tasks and the effects of disruption.

Within-person, longitudinal associations between neighborhood cohesion and adult mental health: A test of bidirectional relations.

There is theory and evidence supporting a relationship between neighborhood cohesion and mental health among adult people. However, most studies have used a cross-sectional design, and longitudinal studies have provided mixed support for this hypothesis. Moreover, while neighborhood cohesion is assumed to be a consistent predictor of mental health, the possibility of a reciprocal relation has been overlooked. The aim of the current study was to investigate the within-person reciprocal associations between neighborhood cohesion and adult mental health. This study used data from Understanding Society: the UK Household Longitudinal Study including waves 1, 3, 6, 9, and 12 (n = 81,895). A short version of Buckner's Neighborhood Cohesion Instrument was used, along with two well-established measures of mental health: the 12-item General Health Questionnaire and the mental component summary score of the 12-item Short-Form Health Survey. Hierarchical Bayesian continuous time dynamic modeling revealed significant reciprocal within-person cross-effects (i.e. deterministic effects) between neighborhood cohesion and adult mental health, a larger standardized effect of mental health on neighborhood cohesion than than vice versa. Moreover, peak standardized cross-lagged effects were found for a time interval of approximately 1 year. Finally, the combined stochastic and deterministic interpretation revealed effects of neighborhood cohesion on mental health that were opposite to what was expected, suggesting a faster dissipation of some initially correlated change. Although neighborhood cohesion has traditionally been conceptualized in terms of its contribution to mental health, there is greater support for the view that mental health precedes neighborhood cohesion rather than the reverse.

The Effects of Lucid Dreaming and Nightmares on Sleep Quality and Mental Health Outcomes

ABSTRACT Objectives This study aimed to investigate relationships between lucid dreaming and sleep and mental health outcomes within a representative sample of the general population. We also sought to examine how nightmares interact with the relationship between lucid dreaming, sleep, and mental health outcomes. Methods Participants (N = 1332) completed measures of lucid dream frequency, nightmare frequency, anxiety and depressive symptoms, stress, and sleep quality. Hierarchical regression models were conducted, where step-1 examined the direct effect of lucid dreaming on all outcome variables, and step-2 added nightmares into the equation (to examine direct effects of lucid dreaming frequency and nightmares, and the indirect effect of nightmares). Results Step-1 results demonstrated that lucid dreaming positively predicted poor sleep quality, stress, anxiety, and depressive symptoms. Step-2 results revealed that nightmares were the only significant predictor of poor sleep quality, stress, and anxiety symptoms, accounting for all of the variance of lucid dreaming. Nightmares and the interaction of nightmares and lucid dreaming positively predicted depressive symptoms. Conclusions Our results suggest that nightmares alone explain associations between lucid dreaming and poor sleep quality, anxiety symptoms, and stress. However, both nightmares and the combination of nightmares and lucid dreaming are associated with increased depressive symptoms.

Assessing Barriers and Difficulties to Healthcare Access Among Syrian Refugees in Jordan: An Observational Study

(1) Background: Worldwide, refugees may have some difficulties in accessing healthcare services. However, little is known about the factors that may predict the level of accessibility to the public healthcare system in the host countries. (2) Aim: To examine the level of accessibility of Syrian refugees to the public healthcare system in Jordan and further to identify the prediction of socioeconomic factors and barriers to healthcare access. (3) Methods: A cross-sectional study was conducted with a convenient sample of 356 Syrian refugees residing outside camps (Irbid, Ajloun, and Jarash). Data were collected using the Access to Healthcare Services Scale instrument (adopted from the Canadian Community Health Survey), which is composed of 2 sections: the general access scale (8 items) and the difficulties scale (20 items). One-way ANOVA test and independent t-test were used to examine epidemiological correlations among variables, whereas a hierarchical linear regression model was used to examine the predictability of socioeconomic factors and barriers to overall access to the public healthcare system by exploring the incremental impact of additional predictors. (4) Results: the mean age of the 356 participants was 35.22 years old, 56.5% were female, 67.4% were married, most of them 46.1% have secondary education, and non-employed 69.9%. Significant associations were observed among participants with different marital status (p < 0.001), educational level (mean 11.85 vs. 19.85, p < 0.001), working status (15.47 vs. 17.93, p < 0.001), family household number (16.42 vs. 17.0, p < 0.001), and health insurance (none: 15.50 vs. governmental 24.50, p < 0.001). Multivariate analysis revealed that the most important factors that may predict the overall access to healthcare services were: family monthly income (beta −0.19, p < 0.001), household family number (beta 0.17, <0.001), health insurance (beta −0.09, p = 0.047), and barriers (beta −0.43, <0.001), even after adjusting for potential confounding effects: sex, age, educational level, and place of residence. (5) Conclusions: Our findings indicate that socioeconomic factors and barriers may considerably predict overall access to public healthcare in Jordan. It is crucially important, therefore, for the Jordanian government and international organizations to create and develop strategic plans and programs that enhance refugees’ access to health services, positively impacting their health and wellness.

Hierarchical modelling of epibenthic communities on the Scotian Shelf and Gulf of Maine (Atlantic Canada) in support of conservation planning

Identification of ecologically significant units at different spatial scales is essential for management of biodiversity attributes. This case study illustrates a coupled methodological approach to delineate benthic habitats and associated assemblages at different spatial scales. Two complementary analyses were employed based on the occurrences of 99 epibenthic invertebrate species in Atlantic Canada, sampled during depth-stratified random trawl sets. To identify epibenthic assemblage types, isometric feature mapping and partitioning around medoids (ISOPAM) was used in combination with a joint species distribution model (JSDM), which also produced continuous distribution surfaces across the spatial domain. ISOPAM identified nine significantly spatially coherent assemblages (biotopes) at spatial scales of hundreds of meters to hundreds of kilometers, with associated diagnostic species. Those assemblages were closely matched by eight regions of common profile using the JSDM, indicating strong environmental influences on their distributions. These smaller-scale assemblages were grouped into three biophysical units. The results from the JSDM were validated with independent data showing good congruence. This indicates that the spatial units ascribed to identified assemblages are robust and suitable for marine spatial planning and monitoring.