Account Spatial Autocorrelation Research Articles

Non-Iterative Multiscale Estimation for Spatial Autoregressive Geographically Weighted Regression Models

Multiscale estimation for geographically weighted regression (GWR) and the related models has attracted much attention due to their superiority. This kind of estimation method will not only improve the accuracy of the coefficient estimators but also reveal the underlying spatial scale of each explanatory variable. However, most of the existing multiscale estimation approaches are backfitting-based iterative procedures that are very time-consuming. To alleviate the computation complexity, we propose in this paper a non-iterative multiscale estimation method and its simplified scenario for spatial autoregressive geographically weighted regression (SARGWR) models, a kind of important GWR-related model that simultaneously takes into account spatial autocorrelation in the response variable and spatial heterogeneity in the regression relationship. In the proposed multiscale estimation methods, the two-stage least-squares (2SLS) based GWR and the local-linear GWR estimators of the regression coefficients with a shrunk bandwidth size are respectively taken to be the initial estimators to obtain the final multiscale estimators of the coefficients without iteration. A simulation study is conducted to assess the performance of the proposed multiscale estimation methods, and the results show that the proposed methods are much more efficient than the backfitting-based estimation procedure. In addition, the proposed methods can also yield accurate coefficient estimators and such variable-specific optimal bandwidth sizes that correctly reflect the underlying spatial scales of the explanatory variables. A real-life example is further provided to demonstrate the applicability of the proposed multiscale estimation methods.

Interactions between ecosystem services and land use in France: A spatial statistical analysis

The provision of ecosystem services (ESs) is driven by land use and biophysical conditions and is thus intrinsically linked to space. Large-scale ES models, developed to inform policy makers on ES drivers, do not usually consider spatial autocorrelation that could be inherent to the distribution of these ESs or to the modeling process. The objective of this study is to estimate the drivers of ecosystem services in France using statistical models and show how taking into account spatial autocorrelation improves the predictive quality of these models. We study six regulating ESs (habitat quality index, water retention index, topsoil organic matter, carbon storage, soil erosion control, and nitrogen oxide deposition velocity) and three provisioning ESs (crop production, grazing livestock density, and timber removal). For each of these ESs, we estimated and compared five spatial statistical models to investigate the best specification (using statistical tests and goodness-of-fit metrics). Our results show that (1) taking into account spatial autocorrelation improves the predictive accuracy of all ES models (ΔR2 ranging from 0.13 to 0.58); (2) land use and biophysical variables (weather and soil texture) are significant drivers of most ESs; (3) forest was the most balanced land use for provision of a diversity of ESs compared to other land uses (agriculture, pasture, urban, and others); (4) Urban area is the worst land use for provision of most ESs. Our findings imply that further studies need to consider spatial autocorrelation of ESs in land use change and optimization scenario simulations.

Spatial trends and projections of chronic malnutrition among children under 5 years of age in Ethiopia from 2011 to 2019: a geographically weighted regression analysis

IntroductionUndernutrition is a serious global health issue, and stunting is a key indicator of children's nutritional status which results from long-term deprivation of basic needs. Ethiopia, the largest and most populous country in Sub-Saharan Africa, has the greatest rate of stunting among children under the age of five, yet the problem is unevenly distributed across the country. Thus, we investigate spatial heterogeneity and explore spatial projection of stunting among under-five children. Further, spatial predictors of stunting were assessed using geospatial regression models.MethodsThe Ethiopia Demographic and Health Surveys (EDHS) data from 2011, 2016, and 2019 were examined using a geostatistical technique that took into account spatial autocorrelation. Ordinary kriging was used to interpolate stunting data, and Kulldorff spatial scan statistics were used to identify spatial clusters with high and low stunting prevalence. In spatial regression modeling, the ordinary least square (OLS) model was employed to investigate spatial predictors of stunting and to examine local spatial variations geographically weighted regression (GWR) and multiscale geographically weighted regression (MGWR) models were employed.ResultsOverall, stunting prevalence was decreased from 44.42% [95%, CI: 0.425–0.444] in 2011 to 36.77% [95%, CI: 0.349–0.375] in 2019. Across three waves of EDHS, clusters with a high prevalence of stunting in children under 5 years were consistently observed in northern Ethiopia stretching in Tigray, Amhara, Afar, and Benishangul-Gumuz. Another area of very high stunting incidence was observed in the Southern parts of Ethiopia and the Somali region of Ethiopia. Our spatial regression analysis revealed that the observed geographical variation of under-five stunting significantly correlated with poor sanitation, poor wealth index, inadequate diet, residency, and mothers' education.ConclusionsIn Ethiopia, substantial progress has been made in decreasing stunting among children under the age of 5 years; although disparities varied in some areas and districts between surveys, the pattern generally remained constant over time. These findings suggest a need for region and district-specific policies where priority should be given to children in areas where most likely to exhibit high-risk stunting.

Inter- and Intra-Regional Disparities in Russia: Factors of Uneven Economic Growth

Despite the growing body of literature on the dependence of economic growth from different factors, the reasons for uneven growth remain unclear. Within the country, regions have different growth rates in their diverse parts. It is unclear why the same factor could influence municipalities differently. To reveal this reason, we used hierarchical linear modeling with spatial dependence, which allows us to decompose variation into regional and municipal scales and take into account spatial autocorrelation. We conducted our research on data for 2239 municipalities within 85 Russian regions in 2019. Our model incorporates 20 factors of economic growth, with 7 at the municipal scale. Cross-interaction estimates established that factors attributed to the regional level determined the relationship between dependent variables (growth rate of production, growth rate of social benefits, and taxable income) at the municipal level and predictors. The influence of initial level, investments in fixed assets, employment on municipal growth varies greatly depending on such regional determinants as economic structure, innovation, human capital, and inequality. This paper adds to the existing literature on uneven economic growth at a smaller scale (municipality) and at the same time helps to rethink inter- and intra-regional disparities.

Assessing above-ground biomass-functional diversity relationships in temperate forests in northern Mexico

BackgroundStudies on the relationship between biodiversity and ecosystem productivity have suggested that species richness and functional diversity are the main drivers of ecosystem processes. Several patterns on this relationship have been found, including positive, unimodal, negative, and neutral trends, keeping the issue controversial. In this study, taxonomic diversity and functional diversity as drivers of above-ground biomass (AGB) were compared, and the mechanisms that influence biomass production were investigated by testing the complementarity and the mass-ratio hypotheses.MethodsUsing data from 414 permanent sample plots, covering 23% of temperate forest in the Sierra Madre Oriental (México), we estimated the above-gound biomass (AGB), taxonomic and functional diversity indices, as well as community weighted mean values (CWM) for three functional traits (maximum height, leaf size and wood density) for trees ≥7.5 cm DBH, in managed and unmanaged stands. To compare taxonomic diversity differences between managed and unmanaged stands we carried out a rarefaction analysis. Furthermore, we evaluated the relationship between AGB and taxonomic and functional diversity metrics, as well as CWM traits throught spatial autoregressive models.ResultsWe found a hump-shaped relationship between AGB and species richness in managed and unmanaged forests. CMW of maximum height was the most important predictor of AGB in both stands, which suggested that the mechanism underlaying the AGB-diversity relationship is the dominance of some highly productive species, supporting the mass-ratio hypothesis. Above-ground biomass was significantly correlated with three of the five functional diversity metrics, CWM maximum height and species richness. Our results show the importance of taking into account spatial autocorrelation in the construction of predictive models to avoid spurious patterns in the AGB-diversity relationship.ConclusionSpecies richness, maximum height, functional richness, functional dispersion and RaoQ indices relate with above-ground biomass production in temperate mixed-species and uneven-aged forests of northern Mexico. These forests show a hump-shaped AGB-species richness relationship. Functional diversity explains better AGB production than classical taxonomic diversity. Community weighted mean traits provide key information to explain stand biomass in these forests, where maximum tree height seems to be a more suitable trait for understanding the biomass accumulation process in these ecosystems. Although the impact of forest management on biodiversity is still debated, it has not changed the AGB-diversity relationships in the forests of the Sierra Madre Occidental, Mexico.

Towards the hedonic modelling and determinants of real estates price in Morocco

In this paper, we propose a new approach to modeling a real estate price index in Morocco, based on the hedonic regression approach. The basic idea of this paper is to verify the importance of the characteristics of the real estate in the real estate price. Thus, based on data from the three major cities of the capital region of Morocco (RABAT Region), we estimated a hedonic model that takes into account spatial autocorrelation. The results obtained through this modeling generally confirm that the surface area and location of the real estate (land, house, villa and apartment) have a significant influence on the price of real estate.

Variance partitioning and spatial eigenvector analyses with large macroecological datasets

Macroecological data are usually structured in space, so taking into account spatial autocorrelation in regression and correlation analyses is essential for a better understanding of patterns and processes. Many methods are available to deal with spatial autocorrelation, but there are some difficulties when one is dealing with huge geographical extents and fine-scale data. So, we propose a relatively simple and fast computer-intensive approach to deal with Principal Coordinate of Neighbor Matrices (PNCM)/Moran’s Eigenvector Mapping (MEM) analyses for large datasets, using global richness pattern of sharks as a model. We performed a variance partitioning approach by regressing species richness against environmental variables and spatial eigenvectors derived from PCNM. Due to the large number of ocean grid cells (> 9000), we ran the analyses 1000 timesby randomly subsampling each time 50 to 4500 cells and compared the distribution of the variance partitioning components, as well as the slopes of the environmental variables. We also estimated Moran’s I coefficients for regression residuals to check if spatial eigenvectors took into account spatial autocorrelation. Comparing statistics of analyses with different sample sizes, we note that although the environmental component increases linearly, other components (unique space and shared) of the most important variables stabilize with about 1000 cells, whereas all other smaller effects tend to stabilize between 2500 and 3000 cells. Besides that, PCNM eigenvectors were able to control spatial autocorrelation very well. We showed that shark richness patterns are strongly and positively correlated with temperature range, according to the well-known pattern of distribution for the taxon, and strong negatively correlated with oxygen supplies, which are higher in polar zones where ice acts as a barrier to sharks. Our approach clearly shows that it is possible to perform a robust evaluation of global patterns of diversity using eigenvector approaches based on a resampling strategy and allows effective computation of the variance partitioning even when dealing with large datasets.

Improving models of wild boar hunting yield distribution: new insights for predictions at fine spatial resolution

ENETWILD consortium has developed methodologies for modelling wild boar abundance distribution based on hunting yield (HY) data. Although the methodologies reached an acceptable reliability, when models were downscaled to higher spatial resolution the predictions of absolute numbers of hunted animals tended to overprediction. Some important issues such as HY-surface relationship and the spatial autocorrelation of HY data or the accuracy of downscaled predictions were not fully addressed yet due to the complexity of dealing with huge datasets at a European scale. In this report we (i) explored the use of hunted wild boar densities (numbers of hunted wild boar relative to surface) instead of raw counts (numbers of hunted animals) as response variable, and (ii) introduced intrinsic Conditional Auto-Regressive models (iCAR) taking into account spatial autocorrelation. Using simulations and actual wild boar data, these new actions were aimed to produce high resolution predictions (2x2 km grid) with higher accuracy. We assessed model fitting in two different regions in Europe with high quality resolution HY data: Aragón autonomous region (North East Spain, belonging to South Bioregion as defined by ENETWILD) and the whole country of Slovenia (East Bioregion). We found that the marked overprediction, as observed in previous reports when models were downscaled, was now controlled by using hunted wild boar densities as response variable. Additionally, higher accuracy in model predictions was reached when iCAR approach was used to control for spatial autocorrelation. This high accuracy was maintained even when high resolution predictions were aggregated and compared to actual wild boar HY. These approaches should be considered in future models and represent an important step forward to model the distribution of wild boar abundance and other wildlife at high resolution over Europe.

Hedonic Brownian Motion Index for Morocco

In this paper, we propose a new approach to modelling a real estate price index in Morocco, based on the hedonic approach. The basic idea of ​​this paper is to verify the importance of the characteristics of the real estate in the real estate price. Thus, based on data from the three major cities of the capital region of Morocco (RABAT Region), we estimated a hedonic model that takes into account spatial autocorrelation. The results obtained through this modelling generally confirm that the surface area and location of the real estate (land, house, villa and apartment) have a significant influence on the price of real estate. In addition, and because of the static nature of the database, which refers to one year, we have proposed a new approach to building the real estate price index, namely the stochastic Brownian motion approach. The results claim that this index is in perfect agreement with the real estate price index based on the repeat sales approach used and developed by the Central Bank.

Estimation of Error Variance-Covariance Parameters Using Multivariate Geographically Weighted Regression Model

The Multivariate Geographically Weighted Regression (MGWR) model is a development of the Geographically Weighted Regression (GWR) model that takes into account spatial heterogeneity and autocorrelation error factors that are localized at each observation location. The MGWR model is assumed to be an error vector ε that distributed as a multivariate normally with zero vector mean and variance-covariance matrix Σ at each location ui,vi, which Σ is sized qxq for samples at the i-location. In this study, the estimated error variance-covariance parameters is obtained from the MGWR model using Maximum Likelihood Estimation (MLE) and Weighted Least Square (WLS) methods. The selection of the WLS method is based on the weighting function measured from the standard deviation of the distance vector between one observation location and another observation location. This test uses a statistical inference procedure by reducing the MGWR model equation so that the estimated error variance-covariance parameters meet the characteristics of unbiased. This study also provides researchers with an understanding of statistical inference procedures.

House price estimation using an eigenvector spatial filtering approach

PurposeNumerous geo-statistical methods have been developed to analyse the spatial dimension and composition of house prices. Despite these advances, spatial filtering remains an under-researched approach within house price studies. This paper aims to examine the spatial distribution of house prices using an eigenvector spatial filtering (ESF) procedure, to analyse the local variation and spatial heterogeneity.Design/methodology/approachUsing 2,664 sale transactions over the one year period Q3 2017 to Q3 2018, an eigenvector spatial filtering approach is applied to evaluate spatial patterns within the Belfast housing market. This method consists of using geographical coordinates to specify eigenvectors across geographic distance to determine a set of spatial filters. These convey spatial structures representative of different spatial scales and units. The filters are incorporated as predictors into regression analyses to alleviate spatial autocorrelation. This approach is intuitive, given that detection of autocorrelation in specific filters and within the regression residuals can be markers for exclusion or inclusion criteria.FindingsThe findings show both robust and effective estimator consistency and limited spatial dependency – culminating in accurately specified hedonic pricing models. The findings show that the spatial component alone explains 14.6 per cent of the variation in property value, whereas 77.6 per cent of the variation could be attributed to an interaction between the structural characteristics and the local market geography expressed by the filters. This methodological step reduced short-scale spatial dependency and residual autocorrelation resulting in increased model stability and reduced misspecification error.Originality/valueEigenvector-based spatial filtering is a less known but suitable statistical protocol that can be used to analyse house price patterns taking into account spatial autocorrelation at varying (different) spatial scales. This approach arguably provides a more insightful analysis of house prices by removing spatial autocorrelation both objectively and subjectively to produce reliable, yet understandable, regression models, which do not suffer from traditional challenges of serial dependence or spatial mis-specification. This approach offers property researchers and policymakers an intuitive but comprehensible approach for producing accurate price estimation models, which can be readily interpreted.

Modelling spatial and temporal variability of water quality from different monitoring stations using mixed effects model theory

Polder-type agricultural catchments within river deltas are specific land formations which management is highly demanding from several aspects. The close contact with the coastal sea may additionally affect the quality of adjacent marine environment. This study uses the case of the Lower Neretva Valley (LNV) to test the efficiency of applying Linear Mixed Effect (LME) theory in modelling spatial and temporal variations of surface and groundwater quality within a polder-type agricultural catchment. The methodology uses linear regressive techniques while taking into account spatial and temporal autocorrelation of residuals. The objective was to assess and model the spatial and temporal variability of the quality of surface- and ground-waters, in order to predict the impact of natural processes and human activities. A dataset of physicochemical properties of surface and groundwater quality of the LNV, recorded monthly in the period 2009–2017, was used to model the spatial and temporal variations of water salinity and nitrate concentrations. The network of water quality monitoring sites covers four polders on five thousand hectares of agricultural land, including the following types of water bodies: river streams, lateral canals, pumping stations, drainage canals and groundwater. The method of data analysis, based on LME theory with correlated spatial and temporal residuals, takes also into account the heteroscedasticity of the variance associated with each type of water quality monitoring station. The two Linear Mixed Effects models proposed for the prediction of electrical conductivity and nitrate concentration in the surface waters and groundwater, proved to be efficient at adequately reproducing the heterogeneity and complexity of the study area. However, the prediction of nitrate concentration in the water was not equally satisfactory of the one of electrical conductivity due to the large variation in nutrient concentrations. To improve spatial prediction, the density of monitoring network should be increased.

Association of endemic goitre and exceptional longevity in Sardinia: evidence from an ecological study.

This study aims to test the hypothesis that a high prevalence of endemic goitre, considered as a proxy measure for subclinically reduced thyroid function in the population, is geographically associated with exceptional longevity. Using historical data available for 377 Sardinian municipalities in the first half of the twentieth century, we performed an ecological study to investigate the geographic distribution of goitre and its spatial association with demographic indicators of population longevity. This analysis was conducted by using both conventional ordinary least square and geographically weighted regression models to take into account spatial autocorrelation and included other longevity-associated factors previously identified in Sardinia. The spatial analysis revealed that the goitre rate (p < 0.0001), the proportion of inhabitants involved in pastoralism (p = 0.016), the terrain inclination (p = 0.008), and the distance from the workplace as a proxy for physical activity (p = 0.023) were consistently associated with population longevity at an aggregated level in the 377 municipalities. Within the limits of an ecological study design, our findings support the existence of a significant association between high goitre prevalence and increased probability to survive into old age. The present study confirms previous results and is consistent with animal studies and epidemiological surveys in other long-lived areas known as Blue Zones. Potential mechanisms underlying this association need to be further investigated.

Spatial autocorrelation and entropy for renewable energy forecasting

In renewable energy forecasting, data are typically collected by geographically distributed sensor networks, which poses several issues. (i) Data represent physical properties that are subject to concept drift, i.e., their characteristics could change over time. To address the concept drift phenomenon, adaptive online learning methods should be considered. (ii) The error distribution is typically non-Gaussian. Therefore, traditional quality performance criteria during training, like the mean-squared error, are less suitable. In the literature, entropy-based criteria have been proposed to deal with this problem. (iii) Spatially-located sensors introduce some form of autocorrelation, that is, values collected by sensors show a correlation strictly due to their relative spatial proximity. Although all these issues have already been investigated in the literature, they have not been investigated in combination. In this paper, we propose a new method which learns artificial neural networks by addressing all these issues. The method performs online adaptive training and enriches the entropy measures with spatial information of the data, in order to take into account spatial autocorrelation. Experimental results on two photovoltaic power production datasets are clearly favorable for entropy-based measures that take into account spatial autocorrelation, also when compared with state-of-the art methods.

Conditionally autoregressive models improve occupancy analyses of autocorrelated data: An example with environmental DNA.

Site occupancy-detection models (SODMs) are statistical models widely used for biodiversity surveys where imperfect detection of species occurs. For instance, SODMs are increasingly used to analyse environmental DNA (eDNA) data, taking into account the occurrence of both false-positive and false-negative errors. However, species occurrence data are often characterized by spatial and temporal autocorrelation, which might challenge the use of standard SODMs. Here we reviewed the literature of eDNA biodiversity surveys and found that most of studies do not take into account spatial or temporal autocorrelation. We then demonstrated how the analysis of data with spatial or temporal autocorrelation can be improved by using a conditionally autoregressive SODM, and show its application to environmental DNA data. We tested the autoregressive model on both simulated and real data sets, including chronosequences with different degrees of autocorrelation, and a spatial data set on a virtual landscape. Analyses of simulated data showed that autoregressive SODMs perform better than traditional SODMs in the estimation of key parameters such as true-/false-positive rates and show a better discrimination capacity (e.g., higher true skill statistics). The usefulness of autoregressive SODMs was particularly high in data sets with strong autocorrelation. When applied to real eDNA data sets (eDNA from lake sediment cores and freshwater), autoregressive SODM provided more precise estimation of true-/false-positive rates, resulting in more reasonable inference of occupancy states. Our results suggest that analyses of occurrence data, such as many applications of eDNA, can be largely improved by applying conditionally autoregressive specifications to SODMs.

Accessibility, Local Pollution and Housing Prices. Evidence from Nantes Métropole, France

In this empirical article, we analyze the extent to which accessibility and environmental variables are capitalized in apartment prices in Nantes Metropole, France. Using a sample of 5,590 transactions in 2002, 2006, 2008 from the Perval database, we estimate a spatial hedonic price model that takes into account spatial autocorrelation and spatial heterogeneity. Special attention is also paid to the construction of environmental quality variables (noise exposure , air pollution). We find that apartment prices depend positively on proximity to Nantes city centre but that the public transport network (urban or non-urban) has no significant influence. Noise reduction is valued, but only at low or marginal levels of significance. Last, air quality does not significantly influence apartment prices. These results can be related to good accessibility and environmental quality in Nantes Metropole which probably makes households less sensitive to these issues than in other geographical contexts. This seems to provide little support for sustainable urban mobility plans favoring better accessibility, unless public authorities also target the greater awareness of the use of virtuous modes of transport.

PRM224 - ARE POTENTIALLY AVOIDABLE HOSPITALIZATIONS EXPLAINED BY PRIMARY CARE? BEWARE OF SPATIAL HETEROGENEITY.

Potentially avoidable hospitalizations (PAH) are used as indirect measures of access to primary care. However, the evidence about the impact of primary care utilization on PAH is mixed. This study investigates the associations between PAH and measures of access and utilization of primary care in the French region Occitanie, while adjusting for socio-economic and epidemiologic determinants. We also highlight the importance of taking into account spatial autocorrelation and heterogeneity in ecological analyses of PAH. A retrospective analysis of claims and socio-economic data was performed for the French region Occitanie in 2014. The age- and sex-adjusted potentially avoidable hospitalization rates were modelled at the ZIP code level using spatial regression techniques. The standardized rates of PAH vary from 1 to 14.6 per 1000 inhabitants at the ZIP code level; with a mean annual incidence of 4.85 cases per 1000 inhabitants. Congestive heart failure (47%) and chronic obstructive pulmonary disease (25%) were the most frequent categories of PAH. Results of our spatial models revealed the presence of spatial autocorrelation and spatial heterogeneity, which led to identifying two different zones in the Occitanie region based on socio-economic disparities. Separate spatial lag models were fitted in the two zones. Increased nurse density was associated to lower rates of PAH in both zones, but other primary care indicators differed in the two zones. Utilization of primary care had a more contrasted effect: at least one contact with general practitioners was associated with lower PAH rates in one zone, while increased number of contacts with specialist physicians and nurses were associated with higher PAH rates. This study illustrates the importance of taking into account spatial heterogeneity when assessing and interpreting the role of primary care in geographic variations in PAH, by showing that PAH determinants might differ in different areas.

Patterns of size variation in bees at a continental scale: does Bergmann's rule apply?

Body size latitudinal clines have been widley explained by the Bergmann's rule in homeothermic vertebrates. However, there is no general consensus in poikilotherms organisms in particular in insects that represent the large majority of wildlife. Among them, bees are a highly diverse pollinators group with high economic and ecological value. Nevertheless, no comprehensive studies of species assemblages at a phylogenetically larger scale have been carried out even if they could identify the traits and the ecological conditions that generate different patterns of latitudinal size variation. We aimed to test Bergmann's rule for wild bees by assessing relationships between body size and latitude at continental and community levels. We tested our hypotheses for bees showing different life history traits (i.e. sociality and nesting behaviour). We used 142 008 distribution records of 615 bee species at 50 × 50 km (CGRS) grids across the West Palearctic. We then applied generalized least squares fitted linear model (GLS) to assess the relationship between latitude and mean body size of bees, taking into account spatial autocorrelation. For all bee species grouped, mean body size increased with higher latitudes, and so followed Bergmann's rule. However, considering bee genera separately, four genera were consistent with Bergmann's rule, while three showed a converse trend, and three showed no significant cline. All life history traits used here (i.e. solitary, social and parasitic behaviour; ground and stem nesting behaviour) displayed a Bergmann's cline. In general there is a main trend for larger bees in colder habitats, which is likely to be related to their thermoregulatory abilities and partial endothermy, even if a ‘season length effect’ (i.e. shorter foraging season) is a potential driver of the converse Bergmann's cline particularly in bumblebees.

Stunting among children under 3 years of age in Côte d'Ivoire: spatial and temporal variations between 1994 and 2011.

To investigate spatial heterogeneity of stunting prevalence among children in Côte d'Ivoire and examine changes in stunting between 1994 and 2011, to assess the impact of the 2002-2011 civil war that led to temporary partitioning of the country. Data from 1994, 1998 and 2011 Côte d'Ivoire Demographic and Health Surveys (DHS) were analysed using a geostatistical approach taking into account spatial autocorrelation. Stunting data were interpolated using ordinary kriging; spatial clusters with high and low stunting prevalence were identified using Kulldorff spatial scan statistics. Multilevel multivariable logistic regression was then carried out, with year of survey as the main independent variable and an interaction term for time by geographic zone (Abidjan, South, North). Côte d'Ivoire, West Africa. Children aged 0-35 months included in three DHS (n 6709). Overall stunting prevalence was 30·7, 28·7 and 27·8 % in 1994, 1998 and 2011, respectively (P=0·32). Clusters with high prevalence were found in 1994 (in the West region, P<0·001) and 1998 (in the West and North-West regions, P<0·01 and P=0·01, respectively), but not in 2011. Abidjan was included in a cluster with low prevalence in all surveys (P<0·05). Risk of stunting did not change between 1994 and 2011 at national level (adjusted OR; 95 % CI: 1·39; 0·72, 2·64), but decreased in the South (0·74; 0·58, 0·94) and increased from 1998 to 2011 in Abidjan (1·96; 1·06, 3·64). In Côte d'Ivoire, significant changes in stunting prevalence were observed at the sub-national level between 1994 and 2011.

Combining imperfect automated annotations of underwater images with human annotations to obtain precise and unbiased population estimates

Optical methods for surveying populations are becoming increasingly popular. These methods often produce hundreds of thousands to millions of images, making it impractical to analyze all the images manually by human annotators. Computer vision software can rapidly annotate these images, but their error rates are often substantial, vary spatially and are autocorrelated. Hence, population estimates based on the raw computer automated counts can be seriously biased. We evaluated four estimators that combine automated annotations of all the images with manual annotations from a random sample to obtain (approximately) unbiased population estimates, namely: ratio, offset, and linear regression estimators as well as the mean of the manual annotations only. Each of these estimators was applied either globally or locally (i.e., either all data were used or only those near the point in question, to take into account spatial variability and autocorrelation in error rates). We also investigated a simple stratification scheme that splits the images into two strata, based on whether the automated annotator detected no targets or at least one target. The 16 methods resulting from a combination of four estimators, global or local estimation, and one stratum or two strata, were evaluated using simulations and field data. Our results indicated that the probability of a false negative is the key factor determining the best method, regardless of the probability of false positives. Stratification was the most effective method in improving the accuracy and precision of the estimates, provided the false negative rate was not too high. If the probability of false negatives is low, stratified estimation with the local ratio estimator or local regression (essentially geographically weighted regression) is best. If the probability of false negatives is high, no stratification with a simple global linear regression or simply the manual sample mean alone is recommended.