Spatial Non-stationarity In Relationship Research Articles

Understanding the spatial non-stationarity in the relationships between malaria incidence and environmental risk factors using Geographically Weighted Random Forest: A case study in Rwanda.

As found in the health studies literature, the levels of climate association between epidemiological diseases have been found to vary across regions. Therefore, it seems reasonable to allow for the possibility that relationships might vary spatially within regions. We implemented the geographically weighted random forest (GWRF) machine learning method to analyze ecological disease patterns caused by spatially non-stationary processes using a malaria incidence dataset for Rwanda. We first compared the geographically weighted regression (WGR), the global random forest (GRF), and the geographically weighted random forest (GWRF) to examine the spatial non-stationarity in the non-linear relationships between malaria incidence and their risk factors. We used the Gaussian areal kriging model to disaggregate the malaria incidence at the local administrative cell level to understand the relationships at a fine scale since the model goodness of fit was not satisfactory to explain malaria incidence due to the limited number of sample values. Our results show that in terms of the coefficients of determination and prediction accuracy, the geographical random forest model performs better than the GWR and the global random forest model. The coefficients of determination of the geographically weighted regression (R2), the global RF (R2), and the GWRF (R2) were 4.74, 0.76, and 0.79, respectively. The GWRF algorithm achieves the best result and reveals that risk factors (rainfall, land surface temperature, elevation, and air temperature) have a strong non-linear relationship with the spatial distribution of malaria incidence rates, which could have implications for supporting local initiatives for malaria elimination in Rwanda.

The Spatial and Social Patterning of Property and Violent Crime in Toronto Neighbourhoods: A Spatial-Quantitative Approach

Criminal activities are often unevenly distributed over space. The literature shows that the occurrence of crime is frequently concentrated in particular neighbourhoods and is related to a variety of socioeconomic and crime opportunity factors. This study explores the broad patterning of property and violent crime among different socio-economic stratums and across space by examining the neighbourhood socioeconomic conditions and individual characteristics of offenders associated with crime in the city of Toronto, which consists of 140 neighbourhoods. Despite being the largest urban centre in Canada, with a fast-growing population, Toronto is under-studied in crime analysis from a spatial perspective. In this study, both property and violent crime data sets from the years 2014 to 2016 and census-based Ontario-Marginalisation index are analysed using spatial and quantitative methods. Spatial techniques such as Local Moran’s I are applied to analyse the spatial distribution of criminal activity while accounting for spatial autocorrelation. Distance-to-crime is measured to explore the spatial behaviour of criminal activity. Ordinary Least Squares (OLS) linear regression is conducted to explore the ways in which individual and neighbourhood demographic characteristics relate to crime rates at the neighbourhood level. Geographically Weighted Regression (GWR) is used to further our understanding of the spatially varying relationships between crime and the independent variables included in the OLS model. Property and violent crime across the three years of the study show a similar distribution of significant crime hot spots in the core, northwest, and east end of the city. The OLS model indicates offender-related demographics (i.e., age, marital status) to be a significant predictor of both types of crime, but in different ways. Neighbourhood contextual variables are measured by the four dimensions of the Ontario-Marginalisation Index. They are significantly associated with violent and property crime in different ways. The GWR is a more suitable model to explain the variations in observed property crime rates across different neighbourhoods. It also identifies spatial non-stationarity in relationships. The study provides implications for crime prevention and security through an enhanced understanding of crime patterns and factors. It points to the need for safe neighbourhoods, to be built not only by the law enforcement sector but by a wide range of social and economic sectors and services.

Prediction of soil cadmium distribution across a typical area of Chengdu Plain, China

A suitable method and appropriate environmental variables are important for accurately predicting heavy metal distribution in soils. However, the classical methods (e.g., ordinary kriging (OK)) have a smoothing effect that results in a tendency to neglect local variability, and the commonly used environmental variables (e.g., terrain factors) are ineffective for improving predictions across plains. Here, variables were derived from the obvious factors affecting soil cadmium (Cd), such as road traffic, and were used as auxiliary variables for a combined method (HASM_RBFNN) that was developed using high accuracy surface modelling (HASM) and radial basis function neural network (RBFNN) model. This combined method was then used to predict soil Cd distribution in a typical area of Chengdu Plain in China, considering the spatial non-stationarity of the relationships between soil Cd and the derived variables based on 339 surface soil samples. The results showed that HASM_RBFNN had lower prediction errors than OK, regression kriging (RK) and HASM_RBFNNs, which didn’t consider the spatial non-stationarity of the soil Cd-derived variables relationships. Furthermore, HASM_RBFNN provided improved detail on local variations. The better performance suggested that the derived environmental variables were effective and HASM_RBFNN was appropriate for improving the prediction of soil Cd distribution across plains.

Assessing the spatial nonstationarity in relationship between local patterns of HIV infections and the covariates in South Africa: A geographically weighted regression analysis

Beyond the structural drivers such as distance from the road, rural/urban divide or demographic profiles, not much is known about the spatial relationship between HIV and social covariates. Spatial relations between social covariates and HIV infection of persons above 15 years were explored and mapped using geographically weighted regression model using data from a national HIV household survey conducted in 2008 and comprising 23 369 individuals from approximately 1000 enumeration areas that were randomly selected from the national census. The maps show spatial non-stationarity in relationship between local patterns of HIV prevalence and the social covariates across South Africa. The high prevalence districts have very homogeneous population defined by the following characteristics: Black origin, unfavorable sex ratio (high proportion of females), low socioeconomic status, being single or low marriage rates, multiple sexual partners and intergenerational sex. Markedly, intergenerational sex compounds the risk of acquiring HIV infection for females in poor districts. Identification of key social drivers of HIV and how they vary from location to location can help to effectively guide and focus intervention programs to areas of particular need.

Mapping the results of local statistics: Using geographically weighted regression.

The application of geographically weighted regression (GWR) - a local spatial statistical technique used to test for spatial nonstationarity - has grown rapidly in the social, health and demographic sciences. GWR is a useful exploratory analytical tool that generates a set of location-specific parameter estimates which can be mapped and analysed to provide information on spatial nonstationarity in relationships between predictors and the outcome variable. A major challenge to GWR users, however, is how best to map these parameter estimates. This paper introduces a simple mapping technique that combines local parameter estimates and local t-values on one map. The resultant map can facilitate the exploration and interpretation of nonstationarity.