Multivariate Conditional Autoregressive Model Research Articles

Factors associated with different types of freight crashes: A macro-level analysis

Introduction: Despite evidence showing higher fatality rates in freight-related crashes, there has been limited exploration of their spatial distribution and factors associated with such distribution. This gap in the literature primarily stems from the focus of existing studies on micro-level factors predicting the frequency or severity of injuries in freight crashes. The present study delves into the factors contributing to freight crashes at the neighborhood level, particularly focusing on different types of freight crashes: collisions involving a freight vehicle and a passenger vehicle, crashes between freight vehicles, and freight vehicle–non-motorized crashes. Method: This study analyzes traffic crash data from the urbanized region of Seoul, collected between 2016 and 2019. To effectively deal with spatial autocorrelation and model different types of crashes in a unified framework, a Bayesian multivariate conditional autoregressive model was employed. Results: Findings show substantial differences in the factors associated with various types of freight crashes. The predictors for crashes between freight vehicles diverge significantly from those for freight vehicle–non-motorized crashes. Crashes between freight vehicles are relatively more influenced by road network structure, while freight crashes involving non-motorized users are relatively more affected by the built environment and freight facilities than the other crash types examined. Freight vehicle–passenger vehicle crashes fall into an intermediate category, sharing most predictors with either of the other two types of freight crashes. Conclusions and Practical Applications: The findings of this study offer valuable lessons for transportation practitioners and policymakers. They can guide the formulation of effective land use policies and infrastructure planning, specifically designed to address the unique characteristics of different types of freight crashes.

Are ride-hailing services safer than taxis? A multivariate spatial approach with accommodation of exposure uncertainty

Despite many research efforts on ride-hailing services and taxis, limited studies have compared the safety performance of the two modes. A major challenge is the need for reliable mode-specific exposure data to model their safety outcomes. Moreover, crash frequencies of the two modes by injury severities tend to be spatially and inherently correlated. To fully address these issues, this study proposes a novel multivariate conditional autoregressive model considering measurement errors in mode-specific exposures (MVCARME). More specially, a classical measurement error structure accommodates the uncertainty of estimated mode-specific exposures, and a multivariate spatial specification is adopted to capture potential spatial and inherent correlations. The model estimation is accelerated by an integrated nest Laplace approximation method. The census tracts in the city of Chicago are set as the spatial analysis unit. The mode-specific exposures (vehicle-mile-traveled) in each census tract are estimated by trip assignments using ride-hailing and taxi trip data in 2019. The modeling results indicate that both ride-hailing crashes and taxi crashes are positively associated with transportation factors (e.g., vehicle-mile-traveled, mode-specific vehicle-mile-traveled, and traffic signal numbers), land use factors (i.e., number of educational and alcohol-related sites), and demographic factors (e.g., median household income, transit ratio, and walk ratio). By comparison, the proposed model outperforms the others (i.e., negative binomial models and multivariate conditional autoregressive model) by yielding the lowest deviance information criterion (DIC), Watanabe-Akaike information criterion (WAIC), mean absolute error (MAE), and root-mean-square error (RMSE). According to the results of t-tests, ride-hailing services are found to be prone to a higher risk of minor injury crashes compared with taxis, despite no significant difference between the risks of severe injury crashes. Methodologically, this study adds a robust safety evaluation approach for comparing crash risks of different modes to the literature. At the same time, practically, it provides researchers, practitioners, and policy-makers insights into the safety management of various mobility alternatives.

Multivariate spatial modelling for predicting missing HIV prevalence rates among key populations

Abstract Ending the HIV/AIDS pandemic is among the sustainable development goals for the next decade. To overcome the problem caused by the imbalances between the need for care and the limited resources, we shall improve our understanding of the local HIV epidemics, especially for key populations at high risk of HIV infection. However, HIV prevalence rates for key populations have been difficult to estimate because their HIV surveillance data are very scarce. This paper develops a multivariate spatial model for predicting unknown HIV prevalence rates among key populations. The proposed multivariate conditional auto-regressive model efficiently pools information from neighbouring locations and correlated populations. As the real data analysis illustrates, it provides more accurate predictions than independently fitting the sub-epidemic for each key population. Furthermore, we investigate how different pieces of surveillance data contribute to the prediction and offer practical suggestions for epidemic data collection.

Hierarchical clustering with spatial adjacency constraints in heavy-tailed areal data

Some natural phenomena with areal/lattice data structures include extreme values or outliers. In such situations, the assumption of Gaussianity for the random field may not be reasonable, and no Gaussian transformation can be found because they exhibit heavy tails. A non-Gaussian stable random field, which is heavy-tailed, could be a more appropriate choice in these cases. This article introduces a sub-Gaussian α-stable (SGαS) random field for spatial analysis of multivariate areal data using a multivariate conditional autoregressive model. We, specifically, focus on the spatial clustering problem of such areal data. To address it, we develop methods that work based on adjacency constraints. To group the data, we offer an adjacency-constrained hierarchical agglomerative clustering (HAC) technique that considers both spatial and non-spatial attributes existing in the multivariate areal data. The proposed clustering algorithm is developed based on spatial adjacency constraint criteria incorporated into the HAC technique. We employed the developed algorithm to group Luxembourg communes based on simulated areal data from the SGαS distributions and French cities along the Gironde estuary based on the estuary areal dataset. We compare the results of the proposed method with the mentioned adjacency criteria, various dissimilarity, and linkages measures in clustering these two datasets.

A Bayesian Bivariate Model for Spatially Correlated Binary Outcomes

Diseases have been studied separately, but two diseases have inherent dependencies on each other, modelling them separately negates practical reality. The authors’ modelling processes are based on univariate separate regressions, which connect each illness to covariates separately. Therefore, the focus of this article is to estimate the spatial correlation within geographic regions using latent variables. Individual and areal-level information, as well as spatially dependent random effects for each spatial unit, are incorporated into the models developed using a hierarchical structure. Simulation techniques provide to assess the models’ performance using Bayesian computing approaches (INLA and MCMC). The findings show a reasonable performance of the DIC and RMSE values of the proposed latent model. From that, the model can be considered as the best compared to the shared component model, multivariate conditional autoregressive model, and univariate models.

Historic and recent trends in county-level coronary heart disease death rates by race, gender, and age group, United States, 1979-2017.

Given recent slowing of declines in national all-cause, heart disease, and stroke mortality, examining spatiotemporal distributions of coronary heart disease (CHD) death rates and trends can provide data critical to improving the cardiovascular health of populations. This paper documents county-level CHD death rates and trends by age group, race, and gender from 1979 through 2017. Using data from the National Vital Statistics System and a Bayesian multivariate space-time conditional autoregressive model, we estimated county-level age-standardized annual CHD death rates for 1979 through 2017 by age group (35-64 years, 65 years and older), race (white, black, other), and gender (men, women). We then estimated county-level total percent change in CHD death rates during four intervals (1979-1990, 1990-2000, 2000-2010, 2010-2017) using log-linear regression models. For all intervals, national CHD death rates declined for all groups. Prior to 2010, although most counties across age, race, and gender experienced declines, pockets of increasing CHD death rates were observed in the Mississippi Delta, Oklahoma, East Texas, and New Mexico across age groups and gender, and were more prominent among non-white populations than whites. Since 2010, across age, race, and gender, county-level declines in CHD death rates have slowed, with a marked increase in the percent of counties with increasing CHD death rates (e.g. 4.4% and 19.9% for ages 35 and older during 1979-1990 and 2010-2017, respectively). Recent increases were especially prevalent and geographically widespread among ages 35-64 years, with 40.5% of counties (95% CI: 38.4, 43.1) experiencing increases. Spatiotemporal differences in these long term, county-level results can inform responses by the public health community, medical providers, researchers, and communities to address troubling recent trends.

Estimating the burden of the opioid epidemic for adults and adolescents in Ohio counties.

Quantifying the opioid epidemic at the local level is a challenging problem that has important consequences on resource allocation. Adults and adolescents may exhibit different spatial trends and require different interventions and resources so it is important to examine the problem for each age group. In Ohio, surveillance data are collected at the county level for each age group on measurable outcomes of the opioid epidemic, overdose deaths, and treatment admissions. However, our interest lies in quantifying the unmeasurable construct, representing the burden of the opioid epidemic, which drives rates of the outcomes. We propose jointly modeling adult and adolescent surveillance outcomes through a multivariate spatial factor model. A generalized spatial factor model within each age group quantifies a latent factor related to the number of opioid-associated treatment admissions and deaths. By assuming a multivariate conditional autoregressive model for the spatial factors of adults and adolescents, we allow the adolescent model to borrow strength from the adult model (and vice versa), improving estimation. We also incorporate county-level covariates to help explain spatial heterogeneity in each of the factors. We apply this approach to the state of Ohio and discuss the findings. Our framework provides a coherent approach for synthesizing information across multiple outcomes and age groups to better understand the spatial epidemiology of the opioidepidemic.

Patient- and area-level predictors of prostate cancer among South Carolina veterans: a spatial analysis.

Racial and socio-economic status (SES) disparities exist in prostate cancer (PrCA) incidence and mortality. Less is known regarding how geographical factors, including neighborhood social vulnerability and distance traveled to receive care, affect PrCA risk. The purpose of this research was to use the Veterans Administration Medical System, which provides a unique means for studying PrCA epidemiology among diverse individuals with ostensibly equal access to healthcare, to determine whether area-level characteristics influence PrCA incidence while accounting for individual-level risk factors. From the US Veteran's Health Administration (VHA) electronic medical records (EMR) database from January 1999 to December 2015, we identified 3,736 PrCA patients and 104,017 cancer-free controls from South Carolina (SC). The VHA EMRs were linked to the US census which provided area-level factors. US census data were used to construct the Social Vulnerability Index which is a continuous composite measure of area-level vulnerability and was divided into tertiles for modeling purposes. Data were analyzed using a Bayesian multivariate conditional autoregressive model (CAR) which accounted for individual-level factors, area-level factors, spatial random effects, and autocorrelation, which were used to identify areas of higher- or lower-than-expected PrCA incidence after controlling for risk factors. As expected, after accounting for age (sixfold and 13-fold increases in men 40-50years and > 50years, respectively), race was an important risk factor, with threefold higher odds among Blacks in the fully adjusted model [ORadj 2.98 (2.77, 3.20)]. After accounting for all other factors, residing in a ZIP code tabulated areas (ZCTA) with the greatest level social vulnerability versus the lowest, least vulnerable ZCTA's, increased PrCA risk by 39% [ORadj 1.39 (1.11, 1.75)]. While accounting for known risk factors for PrCA, including age, race, and marital status, we found geographic areas in SC characterized by higher than average social vulnerability with higher rates of incident PrCA among veterans. Outreach for screening, education, and care coordination may be needed for veterans in these areas.

Stagnating National Declines in Stroke Mortality Mask Widespread County-Level Increases, 2010-2016.

Background and Purpose- Recent national and state-level trends show a stalling or reversal of previously declining stroke death rates. These national trends may mask local geographic variation and changes in stroke mortality. We assessed county-level trends in stroke mortality among adults aged 35 to 64 and ≥65 years. Methods- We used data from National Vital Statistics Systems and a Bayesian multivariate space-time conditional autoregressive model to estimate age-standardized annual stroke death rates for 2010 through 2016 among middle-aged adults (35-64 years) and older adults (≥65 years) in US counties. We used log-linear regression models to estimate average annual and total percent change in stroke mortality during the period. Results- Nationally, the annual percent change in stroke mortality from 2010 to 2016 was -0.7% (95% CI, -4.2% to 3.0%) among middle-aged adults and -3.5% (95% CI, -10.7% to 4.3%) among older adults, resulting in 2016 rates of 15.0 per 100 000 and 259.8 per 100 000, respectively. Increasing county-level stroke mortality was more prevalent among middle-aged adults (56.6% of counties) compared with among older adults (26.1% of counties). About half (48.3%) of middle-aged adults, representing 60.2 million individuals, lived in counties in which stroke mortality increased. Conclusions- County-level increases in stroke mortality clarify previously reported national and state-level trends, particularly among middle-aged adults. Roughly 3×as many counties experienced increases in stroke death rates for middle-aged adults compared with older adults. This highlights a need to address stroke prevention and treatment for middle-aged adults while continuing efforts to reduce stroke mortality among the more highly burdened older adults. Efforts to reverse these troubling local trends will likely require joint public health and clinical efforts to develop innovative and integrated approaches for stroke prevention and care, with a focus on community-level characteristics that support stroke-free living for all.

Modeling of time-dependent safety performance using anonymized and aggregated smartphone-based dangerous driving event data

Safety performance functions (SPFs) are generally used to relate exposure to the expected number of crashes aggregated over a long time (e.g. a year) by holding all other risk factors constant, and to identify hotspots that have excessive crashes regardless of different time periods. However, it is highly likely that the relationships of exposure, risk factors and crash occurrence can vary across different times of day. This study aims to establish time-dependent SPFs for urban roads by using large-scale dangerous driving event data captured by smartphones in different times of day. Multivariate conditional autoregressive (MVCAR) models are developed to jointly account for spatial and temporal dependence of crash observations. Results of two-sample Kolmogorov-Smirnov tests affirm the heterogeneity of the safety effects of dangerous driving events in different time periods. Time-dependent hotspots are identified using potential for safety improvement (PSI) metric. The assumption here is that due to the change of traffic conditions and environment across different times of day, safety hotspots for different time periods should be different from each other. According to the results of Wilcoxon signed-rank tests, hotspots identified by times of day are found to be mostly different from each other. The findings of this study provide insights into temporal effects of risk factors and can support the development of time-dependent safety countermeasures. Besides, this study also shows the potential of leveraging anonymized and aggregated dangerous driving data to assess traffic safety issues.

Graph-based multivariate conditional autoregressive models

ABSTRACTThe conditional autoregressive model is a routinely used statistical model for areal data that arise from, for instances, epidemiological, socio-economic or ecological studies. Various multivariate conditional autoregressive models have also been extensively studied in the literature and it has been shown that extending from the univariate case to the multivariate case is not trivial. The difficulties lie in many aspects, including validity, interpretability, flexibility and computational feasibility of the model. In this paper, we approach the multivariate modelling from an element-based perspective instead of the traditional vector-based perspective. We focus on the joint adjacency structure of elements and discuss graphical structures for both the spatial and non-spatial domains. We assume that the graph for the spatial domain is generally known and fixed while the graph for the non-spatial domain can be unknown and random. We propose a very general specification for the multivariate conditional modelling and then focus on three special cases, which are linked to well-known models in the literature. Bayesian inference for parameter learning and graph learning is provided for the focused cases, and finally, an example with public health data is illustrated.

Spatiotemporal Heterogeneity in the Distribution of Chikungunya and Zika Virus Case Incidences during their 2014 to 2016 Epidemics in Barranquilla, Colombia.

Chikungunya virus (CHIKV) and Zika virus (ZIKV) have recently emerged as globally important infections. This study aimed to explore the spatiotemporal heterogeneity in the occurrence of CHIKV and ZIKV outbreaks throughout the major international seaport city of Barranquilla, Colombia in 2014 and 2016 and the potential for clustering. Incidence data were fitted using multiple Bayesian Poisson models based on multiple explanatory variables as potential risk factors identified from other studies and options for random effects. A best fit model was used to analyse their case incidence risks and identify any risk factors during their epidemics. Neighbourhoods in the northern region were hotspots for both CHIKV and ZIKV outbreaks. Additional hotspots occurred in the southwestern and some eastern/southeastern areas during their outbreaks containing part of, or immediately adjacent to, the major circular city road with its import/export cargo warehouses and harbour area. Multivariate conditional autoregressive models strongly identified higher socioeconomic strata and living in a neighbourhood near a major road as risk factors for ZIKV case incidences. These findings will help to appropriately focus vector control efforts but also challenge the belief that these infections are driven by social vulnerability and merit further study both in Barranquilla and throughout the world’s tropical and subtropical regions.

Crime Risk Maps: A Multivariate Spatial Analysis of Crime Data

In crime analyses, maps showing the degree of risk help police departments to make decisions on operational matters, such as where to patrol or how to deploy police officers. This study statistically models spatial crime data for multiple crime types in order to produce joint crime risk maps. To effectively model and map the spatial crime data, we consider two important characteristics of crime occurrences: the spatial dependence between sites, and the dependence between multiple crime types. We reflect both characteristics in the model simultaneously using a generalized multivariate conditional autoregressive model. As a real‐data application, we examine the number of incidents of vehicle theft, larceny, and burglary in 83 census tracts of San Francisco in 2010. Then, we employ a Bayesian approach using a Markov chain Monte Carlo method to estimate the model parameters. Based on the results, we detect the crime hotspots, thus demonstrating the advantage of using a multivariate spatial analysis for crime data.

Analysis Dengue Fever and Malaria Cases using Generalized Multivariate Conditional Autoregressive Model

An important topic in epidemiology is dengue fever. This disease is a mosquito-borne infection found in tropical and sub-tropical regions around the world. Another disease infected by mosquito is malaria. The developed methods still offer a lack information how to accommodate a cross correlation between two diseases for different cities. Hence we will provide a natural framework involving a cross correlation for multivariate spatial effect,i.e generalized multivariate conditional autoregressive model (GMCAR). We also focus on analysing the number of infected cases for two diseases in East Java Indonesia as the response variables. Therefore, in this paper we will propose a multivariate count data modelling with GMCAR to analyse the data. The result shows that the proposed model provides a better performance compare a model without cross correlation.

A multivariate spatial approach to model crash counts by injury severity

Conventional safety models rely on the assumption of independence of crash data, which is frequently violated. This study develops a novel multivariate conditional autoregressive (MVCAR) model to account for the spatial autocorrelation of neighboring sites and the inherent correlation across different crash types. Manhattan, which is the most densely populated urban area of New York City, is used as the study area. Census tracts are used as the basic geographic units to capture crash, transportation, land use, and demo-economic data. The specification of the proposed multivariate model allows for jointly modeling counts of various crash types that are classified according to injury severity. Results of Moran’s I tests show the ability of the MVCAR model to capture the multivariate spatial autocorrelation among different crash types. The MVCAR model is found to outperform the others by presenting the lowest deviance information criterion (DIC) value. It is also found that the unobserved heterogeneity was mostly attributed to spatial factors instead of non-spatial ones and there is a strong shared geographical pattern of risk among different crash types.

The Effects of Traffic Composition on Freeway Crash Frequency by Injury Severity: A Bayesian Multivariate Spatial Modeling Approach

This study sets out to investigate the effects of traffic composition on freeway crash frequency by injury severity. A crash dataset collected from Kaiyang Freeway, China, is adopted for the empirical analysis, where vehicles are divided into five categories and crashes are classified into no injury and injury levels. In consideration of correlated spatial effects between adjacent segments, a Bayesian multivariate conditional autoregressive model is proposed to link no-injury and injury crash frequencies to the risk factors, including the percentages of different vehicle categories, daily vehicle kilometers traveled (DVKT), and roadway geometry. The model estimation results show that, compared to Category 5 vehicles (e.g., heavy truck), larger percentages of Categories 1 (e.g., passenger car) and 3 (e.g., medium truck) vehicles would lead to less no-injury crashes and more injury crashes. DVKT, horizontal curvature, and vertical grade are also found to be associated with no-injury and/or injury crash frequencies. The significant heterogeneous and spatial effects for no-injury and injury crashes justify the applicability of the proposed model. The findings are helpful to understand the relationship between traffic composition and freeway safety and to provide suggestions for designing strategies of vehicle safety improvement.

Efficient likelihood computations for some multivariate Gaussian Markov random fields

Data collected from spatial locations are often multivariate. Gaussian conditional autoregressive (CAR) models, also known as Gaussian Markov random fields, are frequently used to analyze such continuous data, or as models for the parameters of discrete distributions. Two difficulties in Gaussian maximum likelihood estimation are ensuring that the parameter estimates are allowable values, and computing the likelihood efficiently. It is shown here that, for some commonly-used multivariate CAR models, checking for allowable parameter values can be facilitated, and the likelihood can be computed very quickly.

A Spatio-Temporal Model and Inference Tools for Longitudinal Count Data on Multicolor Cell Growth.

Multicolor cell spatio-temporal image data have become important to investigate organ development and regeneration, malignant growth or immune responses by tracking different cell types both in vivo and in vitro. Statistical modeling of image data from common longitudinal cell experiments poses significant challenges due to the presence of complex spatio-temporal interactions between different cell types and difficulties related to measurement of single cell trajectories. Current analysis methods focus mainly on univariate cases, often not considering the spatio-temporal effects affecting cell growth between different cell populations. In this paper, we propose a conditional spatial autoregressive model to describe multivariate count cell data on the lattice, and develop inference tools. The proposed methodology is computationally tractable and enables researchers to estimate a complete statistical model of multicolor cell growth. Our methodology is applied on real experimental data where we investigate how interactions between cancer cells and fibroblasts affect their growth, which are normally present in the tumor microenvironment. We also compare the performance of our methodology to the multivariate conditional autoregressive (MCAR) model in both simulations and real data applications.

Integrating multiple data sources in species distribution modeling: a framework for data fusion.

The last decade has seen a dramatic increase in the use of species distribution models (SDMs) to characterize patterns of species' occurrence and abundance. Efforts to parameterize SDMs often create a tension between the quality and quantity of data available to fit models. Estimation methods that integrate both standardized and non-standardized data types offer a potential solution to the tradeoff between data quality and quantity. Recently several authors have developed approaches for jointly modeling two sources of data (one of high quality and one of lesser quality). We extend their work by allowing for explicit spatial autocorrelation in occurrence and detection error using a Multivariate Conditional Autoregressive (MVCAR) model and develop three models that share information in a less direct manner resulting in more robust performance when the auxiliary data is of lesser quality. We describe these three new approaches ("Shared," "Correlation," "Covariates") for combining data sources and show their use in a case study of the Brown-headed Nuthatch in the Southeastern U.S. and through simulations. All three of the approaches which used the second data source improved out-of-sample predictions relative to a single data source ("Single"). When information in the second data source is of high quality, the Shared model performs the best, but the Correlation and Covariates model also perform well. When the information quality in the second data source is of lesser quality, the Correlation and Covariates model performed better suggesting they are robust alternatives when little is known about auxiliary data collected opportunistically or through citizen scientists. Methods that allow for both data types to be used will maximize the useful information available for estimating species distributions.

Is Poverty Decentralizing? Quantifying Uncertainty in the Decentralization of Urban Poverty

In this article we argue that the recent focus on the suburbanization of poverty is problematic because of the ambiguities and inconsistencies in defining suburbia. To improve transparency, replicability, and comparability, we suggest that research on the geographical changes to the distribution of poverty should focus on three questions: (1) How centralized is urban poverty? (2) To what extent is it decentralizing? (3) Is it becoming spatially dispersed? With respect to all three questions, the issue of quantifying uncertainty has been underresearched. The main contribution of the article is to provide a practical and robust solution to the problem of inference based on a Bayesian multivariate conditional autoregressive (CAR) model, made accessible via the R software package CARBayes. Our approach can be applied to spatiotemporally autocorrelated data and can estimate both levels of and change in global relative centralization index (RCI), local RCIs, and dissimilarity indexes. We illustrate our method with an application to Scotland's four largest cities. Our results show that poverty was centralized in 2011 in Glasgow, Dundee, and Aberdeen. Poverty in Edinburgh, however, was decentralized: Nonpoor households tend to live closer to the center than poor ones and increasingly so. We also find evidence of statistically significant reductions in centralization of poverty in all four cities. To test whether this change is associated with poverty becoming more dispersed, we estimate changes to evenness and local decentralization of poverty, revealing complex patterns of change.