Geostatistical Regression Models Research Articles

Covariate-dependent spatio-temporal covariance models

Geostatistical regression models are widely used in environmental and geophysical sciences to characterize the mean and dependence structures for spatio-temporal data. Traditionally, these models account for covariates solely in the mean structure, neglecting their potential impact on the spatio-temporal covariance structure. This paper addresses a significant gap in the literature by proposing a novel covariate-dependent covariance model within the spatio-temporal random-effects model framework. Our approach integrates covariates into the covariance function through a Cholesky-type decomposition, ensuring compliance with the positive-definite condition. We employ maximum likelihood for parameter estimation, complemented by an efficient expectation conditional maximization algorithm. Simulation studies demonstrate the superior performance of our method compared to conventional techniques that ignore covariates in spatial covariances. We further apply our model to a PM2.5 dataset from Taiwan, highlighting wind speed’s pivotal role in influencing the spatio-temporal covariance structure. Additionally, we incorporate wind speed and sunshine duration into the covariance function for analyzing Taiwan ozone data, revealing a more intricate relationship between covariance and these meteorological variables.

Revised EU and WHO air quality thresholds: Where does Europe stand?

One year after the new WHO Global Air Quality Guidelines were published, the European Commission proposed revisions to the Ambient Air Quality Directives, seeking to align European Union air quality standards more closely with WHO recommendations. Here, we employed Bayesian geostatistical regression models to estimate at 1km2 spatial resolution the number of Europeans that would be currently exposed to levels above the new suggested thresholds for the three most harmful pollutants, namely PM2.5, PM10, and NO2. The results have shown that in 2021, 97.6% (95% credible interval: 95.1, 99.2%) of the total European population was exposed to PM2.5 levels exceeding the new WHO annual limit values, while 47.5% (36.2, 59.5%) lived in areas where the revised EU thresholds were exceeded. For PM10, the proportion of people exposed to concentrations above the WHO annual thresholds was estimated at 62.5% (54.0, 70.9%) and at 29.6 (21.9, 37.0%) above the EU values, whereas for NO2, the estimates were at 67.4% (57.9, 75.8%) and 20.2% (13.3, 28.5%), respectively. Our high-resolution model-based predictions are readily available to support policy makers and scientists working toward achieving the ambitious European zero-pollution vision for 2050.

Bayesian geostatistical modelling of high-resolution [formula omitted] exposure in Europe combining data from monitors, satellites and chemical transport models

Bayesian geostatistical regression (GR) models estimate air pollution exposure at high spatial resolution, quantify the prediction uncertainty and provide probabilistic inference on the exceedance of air quality thresholds. However, due to high computational burden, previous GR models have provided gridded ambient nitrogen dioxide (NO2) concentrations at smaller areas of investigation. Here, we applied these models to estimate yearly averaged NO2 concentrations at 1 km2 spatial resolution across 44 European countries, integrating information from in situ monitoring stations, satellites and chemical transport model (CTM) simulations. The tropospheric values of NO2 derived from the ozone monitoring instrument (OMI) onboard the National Aeronautics and Space Administration’s (NASA’s) Aura satellite were converted to near ground NO2 concentration proxies using simulations from the 3-D global CTM (GEOS-Chem) at 0.5° × 0.625°spatial resolution and surface-to-column NO2 ratios. Simulations from the Ensemble of regional CTMs at spatial resolution of 0.1° × 0.1°were extracted from the Copernicus atmosphere monitoring service (CAMS). The contribution of these covariates to the predictive capability of geostatistical models was for the first time evaluated here through a rigorous model selection procedure along with additional continental high-resolution satellite-derived products, including novel data from the pan-European Copernicus land monitoring service (CLMS). The results have shown that the conversion of columnar NO2 values to surface quasi-observations yielded models with slightly better predictive ability and lower uncertainty. Nonetheless, the use of higher resolution CAMS-Ensemble simulations as covariates in GR models granted the most accurate surface NO2 estimates, showing that, in 2016, 16.17 (95% C.I. 6.34–29.96) million people in Europe, representing 2.97% (95% C.I. 1.16% - 5.50%) of the total population, were exposed to levels above the EU directive and WHO air quality guidelines threshold for NO2. Our estimates are readily available to policy makers and scientists assessing the burden of disease attributable to NO2 in 2016.

Modelling the relationship between malaria prevalence as a measure of transmission and mortality across age groups

BackgroundParasite prevalence has been used widely as a measure of malaria transmission, especially in malaria endemic areas. However, its contribution and relationship to malaria mortality across different age groups has not been well investigated. Previous studies in a health and demographic surveillance systems (HDSS) platform in western Kenya quantified the contribution of incidence and entomological inoculation rates (EIR) to mortality. The study assessed the relationship between outcomes of malaria parasitaemia surveys and mortality across age groups.MethodsParasitological data from annual cross-sectional surveys from the Kisumu HDSS between 2007 and 2015 were used to determine malaria parasite prevalence (PP) and clinical malaria (parasites plus reported fever within 24 h or temperature above 37.5 °C). Household surveys and verbal autopsy (VA) were used to obtain data on all-cause and malaria-specific mortality. Bayesian negative binomial geo-statistical regression models were used to investigate the association of PP/clinical malaria with mortality across different age groups. Estimates based on yearly data were compared with those from aggregated data over 4 to 5-year periods, which is the typical period that mortality data are available from national demographic and health surveys.ResultsUsing 5-year aggregated data, associations were established between parasite prevalence and malaria-specific mortality in the whole population (RRmalaria = 1.66; 95% Bayesian Credible Intervals: 1.07–2.54) and children 1–4 years (RRmalaria = 2.29; 1.17–4.29). While clinical malaria was associated with both all-cause and malaria-specific mortality in combined ages (RRall-cause = 1.32; 1.01–1.74); (RRmalaria = 2.50; 1.27–4.81), children 1–4 years (RRall-cause = 1.89; 1.00–3.51); (RRmalaria = 3.37; 1.23–8.93) and in older children 5–14 years (RRall-cause = 3.94; 1.34–11.10); (RRmalaria = 7.56; 1.20–39.54), no association was found among neonates, adults (15–59 years) and the elderly (60+ years). Distance to health facilities, socioeconomic status, elevation and survey year were important factors for all-cause and malaria-specific mortality.ConclusionMalaria parasitaemia from cross-sectional surveys was associated with mortality across age groups over 4 to 5 year periods with clinical malaria more strongly associated with mortality than parasite prevalence. This effect was stronger in children 5–14 years compared to other age-groups. Further analyses of data from other HDSS sites or similar platforms would be useful in investigating the relationship between malaria and mortality across different endemicity levels.

Assessing long-term urban surface water changes using multi-year satellite images: A tale of two cities, Dhaka and Hong Kong

Water is a fundamental component of an urban environment. Management of water resources is important to facilitate a liveable environment and urban sustainability. Several factors affect water resources, including urbanization, climate change and seasons. Moreover, the nature of urban expansion and unsustainable water management practices have been associated with water scarcity, loss of biodiversity and increase of flood risk. Knowledge of the changes in urban surface water in relation to changes in seasons, land covers, anthropogenic activities, and topographical characteristics are important for managing watersheds and urban planning, and developing adaptation strategies to address environmental challenges posed by urbanization. However, existing studies rarely consider all the above factors when monitoring surface water changes in the urban environment. To address this problem, this study uses satellite images from multiple seasons and years, and assess the changes in surface water in relation to changes of several important factors, e.g., seasons, urbanization, land cover and topography. Moreover, this study applies advanced geostatistical tools to assess the local relationship between changes in surface water and the driving factors, and compares the findings in two cities Dhaka (Bangladesh) and Hong Kong with a large contrast in many aspects. First, seasonal influence in the distribution of water area is evaluated. Second, land cover classifications are assigned, and then the contingency matrix and decadal maps are formulated to investigate and evaluate the influence of urbanization on the occurrence and transitions in surface water. Third, an advanced geostatistical regression model is used to investigate the spatially varying relationships for change in surface water in relation to change in other land covers and topography. The investigations confirm that the temporal and seasonal variation, and urbanization induced land cover changes largely affect surface water. In addition, topography influences the nature of the city's expansion, which in turn entails the changes in surface water. The flat terrain of Dhaka facilitates the easy invasion of water bodies and horizontal expansion, in contrast, the steep terrain of Hong Kong prohibits horizontal expansion thus it's surface water is more stable than Dhaka.

Explaining variation in adult Anopheles indoor resting abundance: the relative effects of larval habitat proximity and insecticide-treated bed net use

BackgroundSpatial determinants of malaria risk within communities are associated with heterogeneity of exposure to vector mosquitoes. The abundance of adult malaria vectors inside people’s houses, where most transmission takes place, should be associated with several factors: proximity of houses to larval habitats, structural characteristics of houses, indoor use of vector control tools containing insecticides, and human behavioural and environmental factors in and near houses. While most previous studies have assessed the association of larval habitat proximity in landscapes with relatively low densities of larval habitats, in this study these relationships were analysed in a region of rural, lowland western Kenya with high larval habitat density.Methods525 houses were sampled for indoor-resting mosquitoes across an 8 by 8 km study area using the pyrethrum spray catch method. A predictive model of larval habitat location in this landscape, previously verified, provided derivations of indices of larval habitat proximity to houses. Using geostatistical regression models, the association of larval habitat proximity, long-lasting insecticidal nets (LLIN) use, house structural characteristics (wall type, roof type), and peridomestic variables (cooking in the house, cattle near the house, number of people sleeping in the house) with mosquito abundance in houses was quantified.ResultsVector abundance was low (mean, 1.1 adult Anopheles per house). Proximity of larval habitats was a strong predictor of Anopheles abundance. Houses without an LLIN had more female Anopheles gambiae s.s., Anopheles arabiensis and Anopheles funestus than houses where some people used an LLIN (rate ratios, 95% CI 0.87, 0.85–0.89; 0.84, 0.82–0.86; 0.38, 0.37–0.40) and houses where everyone used an LLIN (RR, 95% CI 0.49, 0.48–0.50; 0.39, 0.39–0.40; 0.60, 0.58–0.61). Cooking in the house also reduced Anopheles abundance across all species. The number of people sleeping in the house, presence of cattle near the house, and house structure modulated Anopheles abundance, but the effect varied with Anopheles species and sex.ConclusionsVariation in the abundance of indoor-resting Anopheles in rural houses of western Kenya varies with clearly identifiable factors. Results suggest that LLIN use continues to function in reducing vector abundance, and that larval source management in this region could lead to further reductions in malaria risk by reducing the amount of an obligatory resource for mosquitoes near people’s homes.

On estimation and prediction of geostatistical regression models via a corrected Stein's unbiased risk estimator

We consider geostatistical regression models to predict spatial variables of interest, where likelihood‐based methods are used to estimate model parameters. It is known that parameters in the Matérn covariogram cannot be estimated well, even when increasing amounts of data are collected densely in a fixed domain. Although a best linear unbiased predictor has been proposed when model parameters are known, a predictor with estimated parameters is nonlinear and may be not the best in practice. Therefore, we propose an adjusted procedure for the likelihood‐based estimates to improve the predicted ability of the nonlinear spatial predictor. The adjusted parameter estimators based on minimizing a corrected Stein's unbiased risk estimator tend to have less bias than the conventional likelihood‐based estimators, and the resulting spatial predictor is more accurate and more stable. Statistical inference for the proposed method is justified both theoretically and numerically. To verify the practicability of the proposed method, a groundwater data set in Bangladesh is analyzed.

Linking in situ LAI and fine resolution remote sensing data to map reference LAI over cropland and grassland using geostatistical regression method

Leaf Area Index (LAI) is an important parameter of vegetation structure. A number of moderate resolution LAI products have been produced in urgent need of large scale vegetation monitoring. High resolution LAI reference maps are necessary to validate these LAI products. This study used a geostatistical regression (GR) method to estimate LAI reference maps by linking in situ LAI and Landsat TM/ETM+ and SPOT-HRV data over two cropland and two grassland sites. To explore the discrepancies of employing different vegetation indices (VIs) on estimating LAI reference maps, this study established the GR models for different VIs, including difference vegetation index (DVI), normalized difference vegetation index (NDVI), and ratio vegetation index (RVI). To further assess the performance of the GR model, the results from the GR and Reduced Major Axis (RMA) models were compared. The results show that the performance of the GR model varies between the cropland and grassland sites. At the cropland sites, the GR model based on DVI provides the best estimation, while at the grassland sites, the GR model based on DVI performs poorly. Compared to the RMA model, the GR model improves the accuracy of reference LAI maps in terms of root mean square errors (RMSE) and bias.

Ecological Drivers of Mansonella perstans Infection in Uganda and Patterns of Co-endemicity with Lymphatic Filariasis and Malaria.

BackgroundMansonella perstans is a widespread, but relatively unknown human filarial parasite transmitted by Culicoides biting midges. Although it is found in many parts of sub-Saharan Africa, only few studies have been carried out to deepen the understanding of its ecology, epidemiology, and health consequences. Hence, knowledge about ecological drivers of the vector and parasite distribution, integral to develop spatially explicit models for disease prevention, control, and elimination strategies, is limited.MethodologyWe analyzed data from a comprehensive nationwide survey of M. perstans infection conducted in 76 schools across Uganda in 2000–2003, to identify environmental drivers. A suite of Bayesian geostatistical regression models was fitted, and the best fitting model based on the deviance information criterion was utilized to predict M. perstans infection risk for all of Uganda. Additionally, we investigated co-infection rates and co-distribution with Wuchereria bancrofti and Plasmodium spp. infections observed at the same survey by mapping geographically overlapping areas.Principal FindingsSeveral bioclimatic factors were significantly associated with M. perstans infection levels. A spatial Bayesian regression model showed the best fit, with diurnal temperature range, normalized difference vegetation index, and cattle densities identified as significant covariates. This model was employed to predict M. perstans infection risk at non-sampled locations. The level of co-infection with W. bancrofti was low (0.3%), due to limited geographic overlap. However, where the two infections did overlap geographically, a positive association was found.Conclusions/SignificanceThis study presents the first geostatistical risk map for M. perstans in Uganda. We confirmed a widespread distribution of M. perstans, and identified important potential drivers of risk. The results provide new insight about the ecologic preferences of this otherwise poorly known filarial parasite and its Culicoides vector species in Uganda, which might be relevant for other settings in sub-Saharan Africa.

Asymptotic theory of generalized information criterion for geostatistical regression model selection

Information criteria, such as Akaike's information criterion and Bayesian information criterion are often applied in model selection. However, their asymptotic behaviors for selecting geostatistical regression models have not been well studied, particularly under the fixed domain asymptotic framework with more and more data observed in a bounded fixed region. In this article, we study the generalized information criterion (GIC) for selecting geostatistical regression models under a more general mixed domain asymptotic framework. Via uniform convergence developments of some statistics, we establish the selection consistency and the asymptotic loss efficiency of GIC under some regularity conditions, regardless of whether the covariance model is correctly or wrongly specified. We further provide specific examples with different types of explanatory variables that satisfy the conditions. For example, in some situations, GIC is selection consistent, even when some spatial covariance parameters cannot be estimated consistently. On the other hand, GIC fails to select the true polynomial order consistently under the fixed domain asymptotic framework. Moreover, the growth rate of the domain and the degree of smoothness of candidate regressors in space are shown to play key roles for model selection.

Canopy damage to conifer plantations within a large mixed-severity wildfire varies with stand age

The 2002 Biscuit Fire burned at mixed-severities encompassing over 200,000 ha of publicly owned forestland, including more than 8300 ha of conifer plantations. We used pre- and post-fire digital aerial photography to examine how the level of canopy damage varied within these plantations in relation to topography, weather, vegetation-cover, and management history, with an emphasis on the age of the plantation. We examined 198 plantations that varied widely in age (5–47 years), size (1.25–47 ha), and landscape context. The average level of canopy damage within the plantations was 77%. Based on Random Forest variable importance values, plantation age was the best predictor of canopy damage. Average annual precipitation, elevation and topographic position were ranked second, third, and fourth, respectively. A model selection procedure, using geo-statistical regression models and Akaike’s information criterion, corroborated the importance of plantation age relative to the other predictors tested and also suggested that the influence of age varied over time. The top ranked regression model indicated that the level of canopy damage reached its maximum around age 15 and stayed relatively high until age 25 before declining.

Attributing the variability of eddy‐covariance CO2 flux measurements across temporal scales using geostatistical regression for a mixed northern hardwood forest

The relationships between terrestrial carbon dioxide flux and its primary environmental drivers are uncertain because the processes controlling CO2 cycling, especially at ecosystem scales, are not well understood. This uncertainty is compounded by the fact that the importance of controlling processes, and therefore environmental drivers, may differ across temporal scales. This paper presents and applies a geostatistical regression (GR) approach that can be used with eddy‐covariance data to investigate the relationships between carbon flux and environmental variables at multiple time scales, ranging from monthly to daily. The approach uses an adaptation of the Bayes Information Criterion to identify an optimal set of environmental variables that are able to explain the observed variability in carbon flux. In addition, GR quantifies the temporal correlation in the portion of the flux signal that cannot be explained by the selected variables and directly accounts for this correlation in the analysis. This GR approach was applied to data from the University of Michigan Biological Station (UMBS) AmeriFlux site to (i) identify the dominant explanatory variables for Net Ecosystem Exchange (NEE), Gross Ecosystem Exchange (GEE), and heterotrophic and autotrophic respiration (Rh+a) at different temporal scales, (ii) evaluate whether environmental variables can be used to isolate the GEE and Rh+a signals from the NEE measurements, and (iii) determine the impact of temporal scale on the inferred relationships between environmental variables and CO2 flux. The results confirm the strong correlation between respiration and temperature and the influence of solar radiation on carbon uptake during the growing season. In addition, results highlight the influence of variables such as precipitation, vapor pressure deficit, and the fraction of photosynthetically active radiation (fPAR) in carbon cycling at UMBS. Many relationships between flux and auxiliary variables are found to be scale‐dependent. Site‐specific and remote‐sensing leaf area index and fPAR data are not found to be interchangeable at finer temporal scales. Results also show that a linear GR model is able to capture what may initially appear to be nonlinear relationships between flux and environmental variables, because this apparent nonlinearity is found to be explained by the covariability among key auxiliary variables. Finally, results indicate that GR can be used to identify variables that partially isolate GEE and Rh+a from the NEE signal at finer temporal scales at UMBS.