Approximate Cross-Validated Mean Estimates for Bayesian Hierarchical Regression Models

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.

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

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.

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.

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.

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.

Considering the flexibility and applicability of Bayesian modeling, in this work we revise the main characteristics of two hierarchical models in a regression setting. We study the full probabilistic structure of the models along with the full conditional distribution for each model parameter. Under our hierarchical extensions, we allow the mean of the second stage of the model to have a linear dependency on a set of covariates. The Gibbs sampling algorithms used to obtain samples when fitting the models are fully described and derived. In addition, we consider a case study in which the plant size is characterized as a function of nitrogen soil concentration and a grouping factor (farm).

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.

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.

Female genital mutilation/cutting (FGM/C) is considered a public health and human rights concern, mainly concentrated in Africa, and has been targeted for elimination under the sustainable development goals. Interventions aimed at ending the practice often rely on data from household surveys which employ complex designs leading to outcomes that are not totally independent, thus requiring advanced statistical techniques. Combining data from multiple surveys within robust statistical framework holds promise to provide more precise estimates due to increased sample size, and accurately identify ‘hotspots’ and allow for assessment of changes over time. In this study, rich datasets from six (6) successive waves of the Nigeria Demographic and Health Surveys and Multiple Indicator Cluster Surveys undertaken between 2003 and 2016/17, were combined and analyzed in order to better assess changes in the likelihood and prevalence of FGM/C among 0-14-year old girls in Nigeria. We used Bayesian hierarchical regression models which explicitly accounted for the inherent spatial and temporal autocorrelations within the data while simultaneously adjusting for variations due to different survey methods and the effects of linear and non-linear covariates. Parameters were estimated using Markov chain Mote Carlo techniques and model fit assessments were based on Deviance Information Criterion. Results show that prevalence of FGM/C among 0–14 years old girls in Nigeria varied over time and across geographical locations and peaked in 2008 with a shift from South to North. A girl was more likely to be cut if her mother was cut, supported FGM/C continuation, or had no higher education. The effects of mother’s age, wealth and type of residence (urban-rural) were no longer significant in 2016. These results reflect the gains of interventions over the years, but also echo the belief that FGM/C is a social norm thus requiring tailored all-inclusive interventions for the total abandonment of FGM/C in Nigeria.

Genetic association study is a useful tool to identify the genetic component that is responsible for a disease. The phenomenon that a certain gene expresses in a parent-of-origin manner is referred to as genomic imprinting. When a gene is imprinted, the performance of the disease-association study will be affected. This thesis presents statistical testing methods developed specially for nuclear family data centering around the genetic association studies incorporating imprinting effects. For qualitative diseases with binary outcomes, a class of TDTI* type tests was proposed in a general two-stage framework, where the imprinting effects were examined prior to association testing. On quantitative trait loci, a class of Q-TDTI(c) type tests and another class of Q-MAX(c) type tests were proposed. The proposed testing methods flexibly accommodate families with missing parental genotype and with multiple siblings. The performance of all the methods was verified by simulation studies. It was found that the proposed methods improve the testing power for detecting association in the presence of imprinting. The class of TDTI* tests was applied to a rheumatoid arthritis study data. Also, the class of Q-TDTI(c) tests was applied to analyze the Framingham Heart Study data.
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\nThe human microbiome is the collection of the microbiota, together with their genomes and their habitats throughout the human body. The human microbiome comprises an inalienable part of our genetic landscape and contributes to our metabolic features. Also, current studies have suggested the variety of human microbiome in human diseases. With the high-throughput DNA sequencing, the human microbiome composition can be characterized based on bacterial taxa relative abundance and the phylogenetic constraint. Such taxa data are often high-dimensional overdispersed and contain excessive number of zeros. Taking into account of these characteristics in taxa data, this thesis presents statistical methods to identify associations between covariate/outcome and the human microbiome composition. To assess environmental/biological covariate effect to microbiome composition, an additive logistic normal multinomial regression model was proposed and a group l1 penalized likelihood estimation method was further developed to facilitate selection of covariates and estimation of parameters. To identify microbiome components associated with biological/clinical outcomes, a Bayesian hierarchical regression model with spike and slab prior for variable selection was proposed and a Markov chain Monte Carlo algorithm that combines stochastic variable selection procedure and random walk metropolis-hasting steps was developed for model estimation. Both of the methods were illustrated using simulations as well as a real human gut microbiome dataset from The Penn Gut Microbiome Project.

BackgroundLimitations to accessing delivery care services increase the risks of adverse outcomes during pregnancy and delivery for all pregnant women, particularly among adolescents in LMICs. In order to inform adolescent-specific delivery care initiatives and coverage, we conducted a comprehensive analysis of trends, projections and inequalities in coverage of delivery care services among adolescents at national, urban-rural and socio-economic levels in LMICs.MethodsUsing 224 nationally representative cross-sectional survey data between 2000 and 2019, we estimated the coverage of institutional delivery (INSD) and skilled birth attendants (SBA). Bayesian hierarchical regression models were used to estimate trends, projections and determinants of INSD and SBA.ResultsCoverage of delivery care services among adolescents increased substantially at the national level, as well as in both urban and rural areas in most countries between 2000 and 2018. Of the 54 LMICs, 24 countries reached 80% coverage of both INSD and SBA in 2018, and predictions for 40 countries are set to exceed 80% by 2030. The trends in coverage of INSD and SBA of adult mothers mostly align with those for adolescent mothers. Our findings show that urban-rural and wealth-based inequalities to delivery care remain persistent by 2030. In 2018, urban settings across 54 countries had higher rates of coverage exceeding 80% compared to rural for both INSD (45 urban, 16 rural) and SBA (50 urban, 19 rural). Several factors such as household head age ≥ 46 years, household head being female, access to mass media, lower parity, higher education, higher ANC visits and higher socio-economic status could increase the coverage of INSD and SBA among adolescents and adult women.ConclusionsMore than three-quarters of the LMICs are predicted to achieve 80% coverage of INSD and SBA among adolescent mothers in 2030, although with sustained inequalities.