Some Developments in Bayesian Hierarchical Linear Regression Modeling

A vital research concern for a personalised recommender system is to target items in the long tail. Studies have shown that sales of the e-commerce platform possess a long-tail character, and niche items in the long tail are challenging to be involved in the recommendation list. Since niche items are defined by the niche market, which is a small market segment, traditional recommendation algorithms focused more on popular items promotion and they do not apply to the niche market. In this article, we aim to find the best users for each niche item and proposed a topic-based hierarchical Bayesian linear regression model for niche item recommendation. We first identify niche items and build niche item subgroups based on descriptive information of items. Moreover, we learn a hierarchical Bayesian linear regression model for each niche item subgroup. Finally, we predict the relevance between users and niche items to provide recommendations. We perform a series of validation experiments on Yahoo Movies dataset and compare the performance of our approach with a set of representative baseline recommender algorithms. The result demonstrates the superior performance of our recommendation approach for niche items.

A Bayesian approach to model the trends and variability in urban stormwater quality associated with catchment and hydrologic parameters

Applying the Hierarchical Bayesian Regression model to weekly aggregated sales history data from 92 retail stores located around Tokyo, I calculated price elasticities by item, week, and store. These elasticities are more stable than figures calculated using the Hierarchical Regression or Bayesian Regression models. Furthermore, using Google Earth, I visualized the calculated price elasticities of these 92 stores over 67 weeks, providing a better understanding about heterogeneity of price elasticities across time and space. Keywords: Price Elasticity, Hierarchical Bayesian Regression Model, Markov Chain Monte Carlo (MCMC) method, Google Earth To cite this document: Hirokazu Tajima, "Calculation and Visualization of Dynamic Price Elasticities", Contemporary Management Research, Vol.9, No.4, pp.389-398, 2013. Permanent link to this document: http://dx.doi.org/10.7903/cmr.11071

BackgroundVaccines constitute a fundamental component of public health interventions, preventing the transmission of numerous diseases. Nevertheless, vaccines remain underutilized in various regions globally, particularly in East African nations, where high mortality rates among children under 5 years of age are predominantly attributable to vaccine‐preventable diseases. Consequently, this investigation is aimed at evaluating children′s vaccination coverage and its associated determinants in East Africa utilizing Bayesian hierarchical modeling based on Demographic and Health Survey (DHS) data (2019–2022).MethodsThis study analyzed nationally representative data from the DHS, a standardized cross‐sectional household survey program that collects health and population data using stratified two‐stage cluster sampling. Data were drawn from surveys conducted between 2019 and 2022 in five East African countries: Ethiopia (2019), Kenya (2022), Mozambique (2022), Rwanda (2019/20), and Tanzania (2022). A Bayesian hierarchical regression model was applied to identify factors influencing vaccination coverage, evaluating four candidate models using leave‐one‐out cross‐validation to select the best fit. Statistical significance was assessed using 95% posterior credible intervals (CrIs) after confirming model convergence.ResultsA total of 15,703 weighted children aged 12–23 months were included, with an overall survey response rate of 97.2%. A substantial proportion of children (73.81%) were only partially immunized, highlighting a critical gap in achieving full vaccination coverage. The Bayesian hierarchical ordinal logistic regression showed that several factors were significantly associated with the odds of being in a higher vaccination category versus a lower one. Children residing in Kenya had 3.10 times higher odds of being in a higher vaccination category compared with those in Ethiopia (AOR = 3.10; 95% CrI: 2.49–3.86). Maternal media exposure (AOR = 1.25, 95% CrI: 1.15, 1.38), maternal education (secondary or above) (AOR = 1.42, 95% CrI: 1.21, 1.67), health facility delivery (AOR = 1.53, 95% CrI: 1.19, 1.96), postnatal care visit (AOR = 1.28, 95% CrI: 1.15, 1.43), skilled birth attendance (AOR = 1.61, 95% CrI: 1.24, 2.079), and antenatal care (ANC) visits (four and above) (AOR = 4.08, 95% CrI: 3.44, 4.84) were all positively associated with higher odds of being in a higher vaccination category.ConclusionsVaccination coverage remains low across East Africa, with significant regional disparities. These results highlight the need for focused interventions in high‐risk areas and addressing key determinants to improve childhood vaccination rates.

We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). BHRMs are popular for modeling complex dependence structures (e.g., Gaussian processes and Gaussian Markov random fields) but can be computationally expensive to run. Cross-validation (CV) is, therefore, not a common practice to evaluate the predictive performance of BHRMs. Our method circumvents the need to rerun computationally costly estimation methods for each cross-validation fold and makes CV more feasible for large BHRMs. We shift the CV problem from probability-based sampling to a familiar and straightforward optimization problem by conditioning on the variance-covariance parameters. Our approximation applies to leave-one-out CV and leave-one-cluster-out CV, the latter of which is more appropriate for models with complex dependencies. In many cases, this produces estimates equivalent to full CV. We provide theoretical results, demonstrate the efficacy of our method on publicly available data and in simulations, and compare the model performance with several competing methods for CV approximation. Code and other supplementary materials available online.

We explore how ideas and practices common in Bayesian modeling can be applied to help assess the quality of 3D protein structural models. The basic premise of our approach is that the evaluation of a Bayesian statistical model's fit may reveal aspects of the quality of a structure when the fitted data is related to protein structural properties. Therefore, we fit a Bayesian hierarchical linear regression model to experimental and theoretical 13 Cα chemical shifts. Then, we propose two complementary approaches for the evaluation of such fitting: (a) in terms of the expected differences between experimental and posterior predicted values; (b) in terms of the leave-one-out cross-validation point-wise predictive accuracy. Finally, we present visualizations that can help interpret these evaluations. The analyses presented in this article are aimed to aid in detecting problematic residues in protein structures. The code developed for this work is available on: https://github.com/BIOS-IMASL/Hierarchical-Bayes-NMR-Validation.

Length of stay (LoS) prediction is deemed important for a medical institution's operational and logistical efficiency. Sound estimates of a patient's stay increase clinical preparedness and reduce aberrations. Various statistical methods and techniques are used to quantify and predict the LoS of a patient based on pre-operative clinical features. This study evaluates and compares the results of Bayesian (simple Bayesian regression and hierarchical Bayesian regression) models and machine learning (ML) regression models against multiple evaluation metrics for the problem of LoS prediction of cardiac patients admitted to Tabba Heart Institute, Karachi, Pakistan (THI) between 2015 and 2020. In addition, the study also presents the use of hierarchical Bayesian regression to account for data variability and skewness without homogenizing the data (by removing outliers). LoS estimates from the hierarchical Bayesian regression model resulted in a root mean squared error (RMSE) and mean absolute error (MAE) of 1.49 and 1.16, respectively. Simple Bayesian regression (without hierarchy) achieved an RMSE and MAE of 3.36 and 2.05, respectively. The average RMSE and MAE of ML models remained at 3.36 and 1.98, respectively.

The near-shore ocean ecosystem is influenced by catchment runoff. The Great Barrier Reef has been experiencing significant water quality deterioration over the past 150 years, due in part to agricultural intensification and urban settlement in adjacent catchments (Thorburn et al., 2013). There is a need for us to understand the influences of catchment characteristics on stream water quality, with an aim to mitigate and manage the water quality issue in the terrestrial stream runoff derived from the adjacent Great Barrier Reef catchments. The event-based water quality monitoring data set from the Paddock to Reef Integrated Monitoring Program across six Natural Management Regions provides a potential opportunity to develop a data-driven understanding of catchment characteristics affecting water quality at the catchment scale. This requires a robust and reliable modelling tool to relate the monitoring data to anthropogenic and natural processes. In this study, monitoring data of Total Suspended Solids (TSS) and dissolved Oxidised Nitrogen (NOX) from 32 sites across the Great Barrier Reef catchments are selected as case study constituents due to the high risk they pose to reef health when exported from catchments to the receiving marine environment. Also, these two constituents have distinct biogeochemical processes in catchments. Specifically, TSS is typically conserved (although mobilized and deposited) while travelling through river systems; while NOX can be potentially processed and removed from the system altogether. A Bayesian hierarchical linear modelling framework is adopted, due to its ability to borrow strength among sites, allowing information to be transferred across space, and due to its ability to provide uncertainty of the predictions. The Bayesian hierarchical linear regression model in this study is developed to evaluate the significance of various catchment characteristics (e.g., land uses, catchment topography and geology) on spatial variation in water quality. The main findings of this study are listed as follows, • Sites located in the Burdekin and Fitzroy Natural Management Regions tend to have greater TSS concentrations, illustrated by the modelled site-specific spatial random effects (deviation from the overall average concentration). Additionally, grazing and dry land agriculture land uses are positively correlated with the spatial random effect on TSS. The complexity of interaction between different catchment characteristics (e.g., land use and topography) can potentially result in a negative spatial random effect on TSS, which is reduced in the relatively steeper Great Barrier Reef catchments with a denser stream network. • Sugar cane is one of the most significant NOX contributors according to the modelling results, likely partially due to the excessive application of fertilizers; however, conservation land use has limited effect on NOX removal, indicating denitrification process alone may not be sufficient to remove NOX. The modelling results demonstrate different land management strategies are required for the purpose of reducing different constituents. This work will provide scientific insights for water quality management at the catchment scale.

Ghana might not meet the SDGs target 3.2 of reducing neonatal mortality to 12 deaths per 1000 live births by 2030. Identifying core determinants of neonatal deaths provide policy guidelines and a framework aimed at mitigating the effect of neonatal deaths. Most studies have identified household and individual-level factors that contribute to neonatal mortality. However, there are relatively few studies that have rigorously assessed geospatial covariates and spatiotemporal variations of neonatal deaths in Ghana. This study focuses on modeling and mapping of spatiotemporal variations in the risk of neonatal mortality in Ghana using Bayesian Hierarchical Spatiotemporal models. This study used data from the Ghana Demographic and Health Surveys (GDHS) conducted in 1993, 1998, 2003, 2008, and 2014. We employed Bayesian Hierarchical Spatiotemporal regression models to identify geospatial correlates and spatiotemporal variations in the risk of neonatal mortality. The estimated weighted crude neonatal mortality rate for the period under consideration was 33.2 neonatal deaths per 1000 live births. The results obtained from Moran’s I statistics and CAR model showed the existence of spatial clustering of neonatal mortality. The map of smooth relative risk identified Ashanti region as the most consistent hot-spot region for the entire period under consideration. Small body size babies contributed significantly to an increased risk of neonatal mortality at the regional level [Posterior Mean: 0.003 (95% CrI: 0.00,0.01)]. Hot spot GDHS clusters exhibiting high risk of neonatal mortality were identified by LISA cluster map. Rural residents, small body size babies, parity, and aridity contributed significantly to a higher risk of neonatal mortality at the GDHS cluster level. The findings provide actionable and insightful information to prioritize and distribute the scarce health resources equitably to tackle the menace of neonatal mortality. The regions and GDHS clusters with excess risk of neonatal mortality should receive optimum attention and interventions to reduce the neonatal mortality rate.

ObjectivesThis study aimed to analyze any reported antibiotic use for children aged <5 years with fever, diarrhea or cough with fast or difficult breathing (outcome) from low-income and middle-income countries (LMICs) during 2005–2017 by user characteristics: rural/urban residence, maternal education, household wealth, and healthcare source visited. MethodsBased on 132 demographic and health surveys and multiple indicator cluster surveys from 73 LMICs, the outcome by user characteristics for all country-years was estimated using a hierarchical Bayesian linear regression model. ResultsAcross LMICs during 2005–2017, the greatest relative increases in the outcome occurred in rural areas, poorest quintiles and least educated populations, particularly in low-income countries and South-East Asia. In low-income countries, rural areas had a 72% relative increase from 17.8% (Uncertainty Interval (UI): 5.2%–44.9%) in 2005 to 30.6% (11.7%–62.1%) in 2017, compared to a 29% relative increase in urban areas from 27.1% (8.7%–58.2%) in 2005 to 34.9% (13.3%–67.3%) in 2017. Despite these increases, the outcome was consistently highest in urban areas, wealthiest quintiles, and populations with the highest maternal education. ConclusionThese estimates suggest that the increasing reported antibiotic use for sick children aged <5 years in LMICs during 2005–2017 was driven by gains among groups often underserved by formal health services.

Many population-based surveys have binary responses from a large number of individuals in each household within small areas. One example is the Nepal Living Standards Survey (NLSS II), in which health status binary data (good versus poor) for each individual from sampled households (sub-areas) are available in the sampled wards (small areas). To make an inference for the finite population proportion of individuals in each household, we use the sub-area logistic regression model with reliable auxiliary information. The contribution of this model is twofold. First, we extend an area-level model to a sub-area level model. Second, because there are numerous sub-areas, standard Markov chain Monte Carlo (MCMC) methods to find the joint posterior density are very time-consuming. Therefore, we provide a sampling-based method, the integrated nested normal approximation (INNA), which permits fast computation. Our main goal is to describe this hierarchical Bayesian logistic regression model and to show that the computation is much faster than the exact MCMC method and also reasonably accurate. The performance of our method is studied by using NLSS II data. Our model can borrow strength from both areas and sub-areas to obtain more efficient and precise estimates. The hierarchical structure of our model captures the variation in the binary data reasonably well.

BackgroundThere is a growing trend towards the production of "hospital report-cards" in which hospitals with higher than acceptable mortality rates are identified. Several commentators have advocated for the use of Bayesian hierarchical models in provider profiling. Several researchers have shown that some degree of misclassification will result when hospital report cards are produced. The impact of misclassifying hospital performance can be quantified using different loss functions.MethodsWe propose several families of loss functions for hospital report cards and then develop Bayes rules for these families of loss functions. The resultant Bayes rules minimize the expected loss arising from misclassifying hospital performance. We develop Bayes rules for generalized 1-0 loss functions, generalized absolute error loss functions, and for generalized squared error loss functions. We then illustrate the application of these decision rules on a sample of 19,757 patients hospitalized with an acute myocardial infarction at 163 hospitals.ResultsWe found that the number of hospitals classified as having higher than acceptable mortality is affected by the relative penalty assigned to false negatives compared to false positives. However, the choice of loss function family had a lesser impact upon which hospitals were identified as having higher than acceptable mortality.ConclusionThe design of hospital report cards can be placed in a decision-theoretic framework. This allows researchers to minimize costs arising from the misclassification of hospitals. The choice of loss function can affect the classification of a small number of hospitals.

The purpose of this study was to apply a novel statistical method for variable selection and a model-based approach for filling data gaps in mortality rates associated with foodborne diseases using the WHO Vital Registration mortality dataset. Correlation analysis and elastic net regularization methods were applied to drop redundant variables and to select the most meaningful subset of predictors. Whenever predictor data were missing, multiple imputation was used to fill in plausible values. Cluster analysis was applied to identify similar groups of countries based on the values of the predictors. Finally, a Bayesian hierarchical regression model was fit to the final dataset for predicting mortality rates. From 113 potential predictors, 32 were retained after correlation analysis. Out of these 32 predictors, eight with non-zero coefficients were selected using the elastic net regularization method. Based on the values of these variables, four clusters of countries were identified. The uncertainty of predictions was large for countries within clusters lacking mortality rates, and it was low for a cluster that had mortality rate information. Our results demonstrated that, using Bayesian hierarchical regression models, a data-driven clustering of countries and a meaningful subset of predictors can be used to fill data gaps in foodborne disease mortality.

My dissertation is motivated by the need for improved statistical approaches for understanding differences in cancer risk in rural vs. urban areas. To accomplish this goal, we develop three statistical methods that can be used to model and explain differences in age-adjusted rates between small areas with differing characteristics. These methods allow researchers to draw meaningful inferences from sparse spatial or spatio-temporal datasets at the ZIP code or county levels. Furthermore, they can be used to identify regions that might require public health interventions and to motivate costly data collection efforts at the individual level. The statistical methods we propose in this dissertation can be classified into two categories: estimation and mediation. Chapter 2 focuses on precisely estimating age-adjusted cancer mortality rates for small areas from spatio-temporal datasets with an excessive number of zeros. A large proportion of zeros are often present in datasets involving low-prevalence diseases and in datasets that include rural regions with small population sizes. When stratifying counts for each region and year by age group in the process of estimating age-adjusted rates, the proportion of zeros in the dataset is further inflated. We propose a novel Bayesian hierarchical hurdle model with spatial and temporal random effects for estimating age-adjusted rates in these settings. Via a simulation study and two data examples, we study the performance of this model and make recommendations as to when it should be used over a Bayesian hierarchical Poisson regression model for age-adjusted rates. Chapters 3 and 4 address the goal of mediation. Specifically, Chapter 3 focuses on a method for performing a mediation analysis and Chapter 4 introduces a method for performing a decomposition analysis. Both chapters aim to explain a difference in age-adjusted rates at the ZIP code level based on either a ZIP code-level exposure (mediation) or a fixed characteristic (decomposition). We develop flexible statistical methods that use Bayesian hierarchical models with spatial random effects and a Bayesian version of the g-computation technique from causal inference. Both methods were designed to create counterfactual small area estimates of age-adjusted rates within the analysis and consequently stable estimates of the effects of interest. Through a simulation study, we illustrate a high level of precision and minimal bias in the total, direct, and indirect effects when using our proposed mediation analysis method. We also compare our proposed mediation method to two methods used in the medical literature and show that our method exhibits the best trade-off of bias and variance. To demonstrate the performance of our decomposition method, we perform a data analysis to understand whether park access explains the disparity in age-adjusted colorectal cancer incidence rates in rural vs. urban ZIP codes in Iowa. We illustrate that precise inferences can be made from sparse ZIP code-level datasets when incorporating small area estimation techniques into each analysis.

Climate change is intensifying summertime heat exposure across Europe, with growing implications not only for physical human health but also for population mental well-being. However, heat-health research has focused mainly on the physical outcomes of heat exposure; mental health impacts remain underexplored. In particular, spatially and temporally explicit analyses that capture variation in heat exposure across diverse regions are scarce, limiting the systematic identification and monitoring of vulnerable populations. Switzerland serves as a suitable case study for addressing this gap, given its pronounced warming trends and environmental heterogeneity, while the underlying analytical approach is transferable to other countries and regions. This study investigates the relationship between heat and mental health outcomes in Switzerland by integrating population health survey data with satellite data-based heat metrics in a spatially and temporally explicit framework. The study is grounded in a heat-mental health risk framework linking thermal hazard, spatiotemporal exposure, and demographic vulnerability. Individual-level mental health data from the Swiss Health Survey (a comprehensive national health survey conducted in 2007, 2012, 2017, and 2022) are combined with high-resolution land surface temperature (LST) derived from MODIS Aqua as the primary heat exposure indicator, alongside gridded near-surface air temperature for comparison and benchmarking. The temperature metrics are designed to represent environmental heat load rather than single-day extremes. Mental health is expressed through multiple standardised indices capturing psychological burden, vitality, depressive symptoms, and anxiety. To account for spatiotemporal dependencies, we apply hierarchical Bayesian ordinal regression models that also serve as predictive models for scenario-analysis.Results indicate that higher LST is generally associated with poorer mental health outcomes across Switzerland, with the strongest and most credible associations observed during the exceptionally hot summer of 2022. We also found that LST-based models outperform air-temperature-based models, which indicates the added value of thermal remote sensing in heat-health studies across spatially heterogenous areas. Spatial analyses reveal pronounced regional and urban-rural gradients in both heat exposure and baseline mental health, while demographic factors such as age and biological sex exhibit substantial variation in mental health vulnerability but do not significantly modify the heat-mental health relationship itself.By integrating remote sensing, climatological data, and population health records, this study demonstrates a scalable interdisciplinary approach for assessing climate-sensitive mental health risks across space and time. It provides a foundation for integrating mental health into climate adaption, heat warning systems, and spatially targeted public health planning.