Search

The generalized Ridge penalty is a powerful tool for dealing with multicollinearity and high‐dimensionality in regression problems. The generalized Ridge regression can be derived as the mean of a posterior distribution with a Normal prior and a given covariance matrix. The covariance matrix controls the structure of the coefficients, which depends on the particular application. For example, it is appropriate to assume that the coefficients have a spatial structure when the covariates are spatially correlated. This study proposes an Expectation‐Maximization algorithm for estimating generalized Ridge parameters whose covariance structure depends on specific parameters. We focus on three cases: diagonal (when the covariance matrix is diagonal with constant elements), Matérn, and conditional autoregressive covariances. A simulation study is conducted to evaluate the performance of the proposed method, and then the method is applied to predict ocean wave heights using wind conditions. [ABSTRACT FROM AUTHOR]

We developed spatial Bayesian hierarchical models to assess potential climate change impacts on suitable habitat for five important tree species in the Pacific northwestern United States (California, Oregon, and Washington). Individual‐species models were fit with presence–absence data from forest inventory field plots and spatial relationships were specified through a conditional autoregressive model. This modeling approach allowed us to visualize uncertainty in response curves, map current and future prediction uncertainty, and provide interval estimates for change. Upward elevational or northward latitudinal shifts in climatically suitable habitat were projected for all species. Climate change impacts were the most damaging for noble fir (Abies procera), for which 79%–100% of the current range was projected to become climatically unsuitable by the 2080s. Although coastal Douglas‐fir (Pseudotsuga menziesii var. menziesii) has been projected by others to gain habitat in Canada, within our study area we projected a net loss of climatically suitable habitat (ca. 8000–31,400 km2) under three of four future climate scenarios. A net loss in habitat was also projected for Oregon white oak (Quercus garryana) under three of four scenarios, with 40%–60% of the current range becoming unsuitable. Although there was no net loss of habitat for forest land blue oak under any scenario, other factors like competition may inhibit blue oak (Quercus douglasii) and white oak from occupying areas projected to increase in climatic suitability. Additionally, between 13% and 32% of blue oak's current range was projected to become unsuitable; some of these areas aligned with dieback following the 2012–2015 California drought, which our data set predates. Unlike the other four species, we projected a 17%–25% increase in climatically suitable habitat for California black oak (Quercus kelloggii), although 1%–20% of the current range was still projected to become unsuitable. Our findings indicate that, although some species will face more pressure in tracking climatically suitable habitat than others, climate change will impact the location of suitable habitat for many species. [ABSTRACT FROM AUTHOR]

With the advent of technology for data gathering and storage, opportunistic citizen science data are proliferating. Species distribution models (SDMs) aim to use species occurrence or abundance for ecological insights, prediction and management. We analysed a massive opportunistic dataset with over 100,000 records of incidental shipboard observations of marine mammals. Our overall goal was to create maps of species density from massive opportunistic data by using spatial regression for count data with an effort offset. We illustrate the method with two marine mammals in the Gulf of Alaska and Bering Sea.We counted the total number of animals in 11,424 hexagons based on presence‐only data. To decrease bias, we first estimated a spatial density surface for ship‐days, which was our proxy variable for effort. We used spatial considerations to create pseudo‐absences, and left some hexagons as missing values. Next, we created SDMs that used modelled effort to create pseudo‐absences, and included the effort surface as an offset in a second stage analysis of two example species, northern fur seals and Steller sea lions.For both effort and species counts, we used spatial count regression with random effects that had a multivariate normal distribution with a conditional autoregressive (CAR) covariance matrix, providing 2.5 million Markov chain Monte Carlo (MCMC) samples (1,000 were retained) from the posterior distribution. We used a novel MCMC scheme that maintained sparse precision matrices for observed and missing data when batch sampling from the multivariate normal distribution. We also used a truncated normal distribution to stabilize estimates, and used a look‐up table for sampling the autocorrelation parameter. These innovations allowed us to draw several million samples in just a few hours.From the posterior distributions of the SDMs, we computed two functions of interest. We normalized the SDMs and then applied an overall abundance estimate obtained from the literature to derive spatially explicit abundance estimates, especially within subsetted areas. We also created 'certain hotspots' that scaled local abundance by standard deviation and using thresholds. Hexagons with values above a threshold were deemed as hotspots with enough evidence to be certain about them. [ABSTRACT FROM AUTHOR]

Sparsity inducing priors are widely used in Bayesian regression analysis, and seek dimensionality reduction to avoid unnecessarily complex models. An alternative to sparsity induction are discrete mixtures, such as spike and slab priors. These ideas extend to selection of random effects, either i ⁢ i ⁢ d or structured (e.g. spatially structured). In contrast to sparsity induction in mixed models with i ⁢ i ⁢ d random effects, in this paper we apply sparsity priors to spatial regression for area units (lattice data), and to spatial random effects in conditional autoregressive priors. In particular, we consider the use of global-local shrinkage to distinguish areas with average predictor effects from areas where the predictor effect is amplified or diminished because the response-predictor pattern is distinct from that of most areas. The operation and utility of this approach is demonstrated using simulated data, and in a real application to diabetes related deaths in New York counties. [ABSTRACT FROM AUTHOR]

Health departments are seeking new ways to determine when and where limited resources should be allocated to achieve maximum benefit for the population. In this work, we demonstrate how one state health department worked to create relative risk measures of cancer incidence, late-stage cancer incidence and mortality incidence displayed in an easy to read map using spatio-temporal statistical tools. The data included age, sex, cancer type and stage, and ZIP Code Tabulation Area (ZCTA) for every incidence and death from 2004 to 2015. Eight types of cancer were selected for analysis: breast, cervical, colorectal, liver, lung, non-Hodgkin lymphoma (NHL), prostate, and melanoma. The risk maps were designed to illustrate areas of the state where risk for developing or dying from certain cancers was higher than the state average, and to show how trends are evolving over time. A hierarchical Bayesian log-normal Poisson regression model, with effects for ZCTA, time period, and a space-time interaction was implemented. The spatial effects accounted for spatial correlation using an intrinsic conditional auto-regressive model, and the time effects used an autoregressive model. Through the model, we were able to achieve reliable estimates of relative risk per ZCTA and time period, even for small population ZCTAs with few, if any, cases during the time period. Furthermore, we calculated a measure of risk probability for each ZCTA, relative to the state average. Results from two cancers are discussed in this manuscript, but all 24 results are available on the project website. [ABSTRACT FROM AUTHOR]

The term low birth weight refers an event where a newborn baby has a weight that is less than 2500 g. This is an essential indicator while the interest is in public health issues such as infant mortality, maternal complications, and antenatal care, etc. of a country, particularly, for a developing country like Bangladesh. The regional development programs are in the current priority list of Bangladesh government and other policy makers. Many of such regional development programs may need the spatial distribution of relative risk for low birth weight that can be obtained by mapping the risks over small area domains like the districts of Bangladesh. This study aims to find whether is there any spatial dependence among the relative risks of low birth weight for the districts of Bangladesh. This has been investigated using Moran's I statistic and a significant spatial dependence in the relative risks was found. Then, attempt has been made to rediscover the spatial distribution based on the idea of spatial smoothing. A Bayesian hierarchical model is used considering percent received antenatal care and female labor force participation as covariates to smooth the observed relative risks of low birth weight in 64 districts of Bangladesh. Revised spatial distribution taking the spatial dependence under consideration through intrinsic conditional autoregressive model is derived and showed in choropleth map along with its different behaviors. [ABSTRACT FROM AUTHOR]

In the recent decade, walking has been encouraged as an active mode of transportation, which could reduce congestion and air pollution and also improve community health. However, pedestrians are more vulnerable to traffic crashes compared with other road users, especially in developing countries such as Saudi Arabia. This paper examines the association among traffic volume, land-use, socio-demographic and roadway characteristics factors, and the frequency of pedestrian crashes based on macro-level safety analysis using data from Riyadh, the Capital of Saudi Arabia. Two Bayesian spatial Poisson-lognormal models for total and severe pedestrian crashes are developed in this study. The results show that the factors that affect total pedestrian crash occurrence are different from those affecting severe pedestrian crash. Several implications for pedestrian safety policies in Riyadh are suggested based on the results. [ABSTRACT FROM AUTHOR]

Bayesian hierarchical models are commonly used for modeling spatially correlated areal data. However, choosing appropriate prior distributions for the parameters in these models is necessary and sometimes challenging. In particular, an intrinsic conditional autoregressive (CAR) hierarchical component is often used to account for spatial association. Vague proper prior distributions have frequently been used for this type of model, but this requires the careful selection of suitable hyperparameters. In this paper, we derive several objective priors for the Gaussian hierarchical model with an intrinsic CAR component and discuss their properties. We show that the independence Jeffreys and Jeffreys-rule priors result in improper posterior distributions, while the reference prior results in a proper posterior distribution. We present results from a simulation study that compares frequentist properties of Bayesian procedures that use several competing priors, including the derived reference prior. We demonstrate that using the reference prior results in favorable coverage, interval length, and mean squared error. Finally, we illustrate our methodology with an application to 2012 housing foreclosure rates in the 88 counties of Ohio. [ABSTRACT FROM AUTHOR]

Abstract: Ecological data often exhibit spatial pattern, which can be modeled as autocorrelation. Conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models are network‐based models (also known as graphical models) specifically designed to model spatially autocorrelated data based on neighborhood relationships. We identify and discuss six different types of practical ecological inference using CAR and SAR models, including: (1) model selection, (2) spatial regression, (3) estimation of autocorrelation, (4) estimation of other connectivity parameters, (5) spatial prediction, and (6) spatial smoothing. We compare CAR and SAR models, showing their development and connection to partial correlations. Special cases, such as the intrinsic autoregressive model (IAR), are described. Conditional autoregressive and SAR models depend on weight matrices, whose practical development uses neighborhood definition and row‐standardization. Weight matrices can also include ecological covariates and connectivity structures, which we emphasize, but have been rarely used. Trends in harbor seals (Phoca vitulina) in southeastern Alaska from 463 polygons, some with missing data, are used to illustrate the six inference types. We develop a variety of weight matrices and CAR and SAR spatial regression models are fit using maximum likelihood and Bayesian methods. Profile likelihood graphs illustrate inference for covariance parameters. The same data set is used for both prediction and smoothing, and the relative merits of each are discussed. We show the nonstationary variances and correlations of a CAR model and demonstrate the effect of row‐standardization. We include several take‐home messages for CAR and SAR models, including (1) choosing between CAR and IAR models, (2) modeling ecological effects in the covariance matrix, (3) the appeal of spatial smoothing, and (4) how to handle isolated neighbors. We highlight several reasons why ecologists will want to make use of autoregressive models, both directly and in hierarchical models, and not only in explicit spatial settings, but also for more general connectivity models. [ABSTRACT FROM AUTHOR]

The Current Employment Statistics (CES) survey, administered by the US Bureau of Labor Statistics, publishes total employment estimates for thousands of domains at detailed geographical and industrial levels. Some of these domains do not have adequate sample size for the direct probability sample-based estimates to be reliable. Small area estimation methods are used to integrate information from historical sources and correlated domains to improve estimation efficiency. In this article, we explore alternatives to the Fay-Herriot two-stage hierarchical model that relax distributional and independence assumptions among random effects indexed by domain and month in order to more fully borrow strength to improve the efficiency of published employment estimates. We compare the performances of our alternative models on both synthetic data and in application to estimates from the CES survey. [ABSTRACT FROM AUTHOR]

To assess the importance of variation in observer effort between and within bird atlas projects and demonstrate the use of relatively simple conditional autoregressive ( CAR) models for analyzing grid-based atlas data with varying effort. Pennsylvania and West Virginia, United States of America. We used varying proportions of randomly selected training data to assess whether variations in observer effort can be accounted for using CAR models and whether such models would still be useful for atlases with incomplete data. We then evaluated whether the application of these models influenced our assessment of distribution change between two atlas projects separated by twenty years (Pennsylvania), and tested our modeling methodology on a state bird atlas with incomplete coverage (West Virginia). Conditional Autoregressive models which included observer effort and landscape covariates were able to make robust predictions of species distributions in cases of sparse data coverage. Further, we found that CAR models without landscape covariates performed favorably. These models also account for variation in observer effort between atlas projects and can have a profound effect on the overall assessment of distribution change. Accounting for variation in observer effort in atlas projects is critically important. CAR models provide a useful modeling framework for accounting for variation in observer effort in bird atlas data because they are relatively simple to apply, and quick to run. [ABSTRACT FROM AUTHOR]

Variation in disease risk underlying observed disease counts is increasingly a focus for Bayesian spatial modelling, including applications in spatial data mining. Bayesian analysis of spatial data, whether for disease or other types of event, often employs a conditionally autoregressive prior, which can express spatial dependence commonly present in underlying risks or rates. Such conditionally autoregressive priors typically assume a normal density and uniform local smoothing for underlying risks. However, normality assumptions may be affected or distorted by heteroscedasticity or spatial outliers. It is also desirable that spatial disease models represent variation that is not attributable to spatial dependence. A spatial prior representing spatial heteroscedasticity within a model accommodating both spatial and non-spatial variation is therefore proposed. Illustrative applications are to human TB incidence. A simulation example is based on mainland US states, while a real data application considers TB incidence in 326 English local authorities. [ABSTRACT FROM AUTHOR]

Data from the Iowa mumps epidemic of 2006 were collected on a spatial lattice over a regular temporal interval. Without access to a person-to-person contact graph, it is sensible to analyze these data as homogenous within each areal unit and to use the spatial graph to derive a contact structure. The spatio-temporal partition is fine, and the counts of new infections at each location at each time are sparse. Therefore, we propose a spatial compartmental epidemic model with general latent time distributions (spatial PS SEIR) that is capable of smoothing the contact structure, while accounting for spatial heterogeneity in the mixing process between locations. Because the model is an extension of the PS SEIR model, it simultaneously handles non-exponentially distributed latent and infectious time distributions. The analysis within focuses on the progression of the disease over both space and time while assessing the impact of a large proportion of the infected people dispersing at the same time because of spring break and the impact of public awareness on the spread of the mumps epidemic. We found that the effect of spring break increased the mixing rate in the population and that the spatial transmission of the disease spreads across multiple conduits. [ABSTRACT FROM AUTHOR]

Background: Malaria and anaemia contribute substantially to child morbidity and mortality. In this study, we sought to jointly model the residual spatial variation in the likelihood of these two correlated diseases, while controlling for individual-level, household-level and environmental characteristics.Methods: A child-level shared component model was utilised to partition shared and disease-specific district-level spatial effects.Results: The results indicated that the spatial variation in the likelihood of malaria was more prominent compared to that of anaemia, for both the shared and specific spatial components. In addition, approximately 30% of the districts were associated with an increased likelihood of anaemia but a decreased likelihood of malaria. This suggests that there are other drivers of anaemia in children in these districts, which warrants further investigation.Conclusions: The maps of the shared and disease-specific spatial patterns provide a tool to allow for more targeted action in malaria and anaemia control and prevention, as well as for the targeted allocation of limited district health system resources. [ABSTRACT FROM AUTHOR]

Recently, spatial regression models have been attracting a great deal of attention in areas ranging from effect of traffic congestion on accident rates to the analysis of trends in gastric cancer mortality. In this paper, we propose efficient estimators for the regression coefficients of the spatial conditional autoregressive model, when uncertain auxiliary information is available about these coefficients. We provide efficiency comparisons of the proposed estimators based on asymptotic risk analysis and Monte Carlo simulations. We apply the proposed methods to real data on Boston housing prices and illustrate how a bootstrapping approach can be employed to compute prediction errors of the estimators. [ABSTRACT FROM AUTHOR]

The analysis of geographical and temporal variability of binomial data, using generalized additive mixed models, are considered. In this class of models, spatially correlated random effects and temporal components are adopted. The frequentist analysis of these complex models is computationally difficult. Recently developed method of data cloning has overcome the computational challenges of the analysis of mixed models from the frequentist approach. We use data cloning, which yields to maximum likelihood estimation, to propose frequentist analysis of spatiotemporal modeling of odds of disease. The advantages of the data cloning approach are that the prediction and prediction interval of the smoothing odds over space and time are easily obtained. We illustrate this approach using a real dataset of yearly asthma physician visits by children in the province of Manitoba, Canada, during 2000-2010. The performance of the proposed approach is also studied through a simulation study. [ABSTRACT FROM AUTHOR]

Objective priors, especially reference priors, have been studied extensively for spatial data in the last decade. In this paper, we study objective priors for a CAR model. In particular, the properties of the reference prior and the corresponding posterior are studied. Furthermore, we show that the frequentist coverage probabilities of posterior credible intervals depend only on the spatial dependence parameter $$\rho $$, and not on the regression coefficient or the error variance. Based on the simulation study for comparing the reference and Jeffreys priors, the performance of two reference priors is similar and better than the Jeffreys priors. One spatial dataset is used for illustration. [ABSTRACT FROM AUTHOR]

In this paper, generalized additive mixed models are constructed for the analysis of geographical and temporal variability of disease ratios. In this class of models, spatio-temporal models that use conditionally autoregressive smoothing across the spatial dimension and B-spline smoothing over the temporal dimension are considered. The frequentist analysis of these complex models is computationally difficult. On the other hand, the advent of the Markov chain Monte Carlo algorithm has made the Bayesian analysis of complex models computationally convenient. Recently developed data cloning (DC) method provides a frequentist approach to mixed models and equally computationally convenient. We propose to use DC, which yields to maximum likelihood estimation, to conduct frequentist analysis of spatio-temporal modeling of disease ratios. The advantages of DC approach are that the non-estimable parameters are flagged automatically and prediction (and prediction intervals) of the smoothing incidence ratios over space and time are easily obtained. We illustrate this approach using a real dataset of yearly childhood asthma visits to hospital in the province of Manitoba, Canada, during 2000-2010. The performance of the DC approach is also studied through a simulation study. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this article, a generalized linear mixed model (GLMM) based on a frequentist approach is employed to examine spatial trend of asthma data. However, the frequentist analysis of GLMM is computationally difficult. On the other hand, the Bayesian analysis of GLMM has been computationally convenient due to the advent of Markov chain Monte Carlo algorithms. Recently developed data cloning (DC) method, which yields to maximum likelihood estimate, provides frequentist approach to complex mixed models and equally computationally convenient method. We use DC to conduct frequentist analysis of spatial models. The advantages of the DC approach are that the answers are independent of the choice of the priors, non-estimable parameters are flagged automatically, and the possibility of improper posterior distributions is completely avoided. We illustrate this approach using a real dataset of asthma visits to hospital in the province of Manitoba, Canada, during 2000–2010. The performance of the DC approach in our application is also studied through a simulation study. [ABSTRACT FROM PUBLISHER]

This paper develops a novel spatial process using generalized skew-normal/independent distributions when the usual Gaussian process assumptions are questionable and transformation to a Gaussian random field is not appropriate. The proposed model provides flexibility in capturing the effects of skewness and heavy tail behavior of the data while maintaining spatial dependence using a conditional autoregressive structure. We use Bayesian hierarchical methods to fit such models and show the validity of our approach. Furthermore, we use Bayesian model selection criteria to choose appropriate models for a real data set on the dengue fever infection in the state of Rio de Janeiro. [ABSTRACT FROM AUTHOR]

To examine childhood cancer diagnoses in the province of Alberta, Canada during 1983-2004, we construct a generalized additive mixed model for the analysis of geographic and temporal variability of cancer ratios. In this model, spatially correlated random effects and temporal components are adopted. The interaction between space and time is also accommodated. Spatio-temporal models that use conditional autoregressive smoothing across the spatial dimension and B-spline over the temporal dimension are considered. We study the patterns of incidence ratios over time and identify areas with consistently high ratio estimates as areas for potential further investigation. We apply the method of penalized quasi-likelihood to estimate the model parameters. We illustrate this approach using a yearly data set of childhood cancer diagnoses in the province of Alberta, Canada during 1983-2004. [ABSTRACT FROM AUTHOR]

Copyright of Conservation Biology is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Canadian Journal of Statistics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Ecology Letters (2010) 13: 246–264 Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future. [ABSTRACT FROM AUTHOR]

A class of hierarchical Bayesian models is proposed for adverse birth Outcomes such as preterm birth, which are assumed to follow a conditional binomial distribution. The log-odds of an adverse outcome in a particular county, logit(pi), follow a linear model that includes observed covariates and normally-distributed random effects. Spatial dependence between neighboring regions is allowed for by including an intrinsically autoregressive (IAR) prior or an IAR convolution prior in the linear predictor. Temporal dependence is incorporated by including a temporal IAR term also. It is shown that the variance parameters underlying these random effects (IAR, convolution, convolution plus temporal IAR) are identifiable. The Deviance Information Criterion (DIC) is considered as a way to compare spatial hierarchical models. Simulations are performed to test whether the DIC can identify whether binomial outcomes come from a hierarchical model that includes different combinations of random and fixed effects. Having validated the DIC as a means of comparing models, we examine preterm birth and low birth weight counts in the state of Arkansas from 1994-2005. We find that preterm birth and low birth weight have different spatial patterns of risk, and that rates of low birth weight can be fit with a relatively simple model that includes a constant spatial effect for all periods, a linear trend, and three covariates (multiple birth, black mother, smoking). It is also found that the risks of each outcome are increasing over time, even with adjustment for covariates. [ABSTRACT FROM AUTHOR]