Abstract: Ecological influences on health outcomes are associated with the spatial stratification of health. However, the majority of studies that seek to understand these ecological influences utilise aspatial methods. **Geographically** **weighted** **regression** (GWR) is a spatial statistics tool that expands standard **regression** by allowing for spatial variance in parameters. This study contributes to the urban health literature, by employing GWR to uncover geographic variation in Limiting Long Term Illness (LLTI) and area level effects at the small area level in a relatively small, urban environment. Using GWR it was found that each of the three contextual covariates, area level deprivation scores, the percentage of the population aged 75 years plus and the percentage of residences of white ethnicity for each LSOA exhibited a non-stationary relationship with LLTI across space. Multicollinearity among the predictor variables was found not to be a problem. Within an international policy context, this research indicates that even at the city level, a “one-size fits all” policy strategy is not the most appropriate approach to address health outcomes. City “wide” health polices need to be spatially adaptive, based on the contextual characteristics of each area.

Show more
15 Read more

The global modeling techniques, such as the ordinary least squares **regression** (OLS), linear and other non- linear models cannot detect spatial variation and rela- tionships within geographic entities. As a result, intrinsic relationships may be obscured and spatial association between variables in a region is concealed. Such incom- plete information (derived from global statistics), when adopted for addressing policy issues, may be counter- productive. To strengthen this weakness, statistical ge- ographers ([8] Brunsdon et al., 1996 and [1] Fothering- ham et al., 2002) recently came up with **geographically** **weighted** **regression** (GWR)—a technique designed to explore spatial non-stationarity or heterogeneity in geo- graphic dataset. Spatial non-stationarity is a scenario in which global statistical models cannot explain the rela- tionship between sets of variables ([8] Brunsdon et al., 1996).

Show more
12 Read more

The purpose of this paper is to analyze the spatially varying impacts of some classical regressors on per capita household income in Spanish provinces. The authors model this distribution following both a traditional global **regression** and a local analysis with **Geographically** **Weighted** **Regression** (GWR). Several specifications are compared, being the adaptive bisquare weighting function the more efficient in terms of goodness-of-fit. We test for global and local spatial instability using some F-tests and other statistical measures. We find some evidence of spatial instability in the distribution of this variable in relation to some explanatory variables, which cannot be totally solved by spatial dependence specifications. GWR has revealed as a better specification to model per capita household income. It highlights some facets of the relationship completely hidden in the global results and forces us to ask about questions we would otherwise not have asked. Moreover, the application of GWR can also be of help to further exercises of micro-data spatial prediction.

Show more
29 Read more

22 Read more

Land cover is of fundamental importance to many environmental applications and serves as critical baseline information for many large scale models e.g. in developing future scenarios of land use and climate change. Although there is an ongoing movement towards the development of higher resolution global land cover maps, medium resolution land cover products (e.g. GLC2000 and MODIS) are still very useful for modelling and assessment purposes. However, the current land cover products are not accurate enough for many applications so we need to develop approaches that can take existing land covers maps and produce a better overall product in a hybrid approach. This paper uses **geographically** **weighted** **regression** (GWR) and crowdsourced validation data from Geo-Wiki to create two hybrid global land cover maps that use medium resolution land cover products as an input. Two different methods were used: a) the GWR was used to determine the best land cover product at each location; b) the GWR was only used to determine the best land cover at those locations where all three land cover maps disagree, using the agreement of the land cover maps to determine land cover at the other cells. The results show that the hybrid land cover map developed using the first method resulted in a lower overall disagreement than the individual global land cover maps. The hybrid map produced by the second method was also better when compared to the GLC2000 and GlobCover but worse or similar in performance to the MODIS land cover product depending upon the metrics considered. The reason for this may be due to the use of the GLC2000 in the development of GlobCover, which may have resulted in areas where both maps agree with one another but not with MODIS, and where MODIS may in fact better represent land cover in those situations. These results serve to demonstrate that spatial analysis methods can be used to improve medium resolution global land cover information with existing products.

Show more
27 Read more

22 Read more

The applications of standard **regression** analysis on spatial data are not appropriate because of the characteristics of the spatial data. Spatial data has two characteristics are spatial dependence and spatial heterogeneity. Modeling spatial data using standard linear **regression** model leads to bias, inconsistency and inefficient results. Several models have been developed to accommodate the characteristics of the spatial data. However, the models generally developed to solve only one problem of the spatial data (e.g., spatial dependence or spatial heterogeneity). Four kinds of spatial econometrics models usually used to accommodate spatial dependence are spatial autoregressive (SAR), spatial lagged exogenous variables (SLX), spatial error model (SEM), and spatial Durbin model (SDM). To accommodate the spatial heterogeneity, **geographically** **weighted** **regression** (GWR) or varying coefficient model (VCM) is usually used. Our research proposed to develop a new model to accommodate two characteristics of the spatial data. The model is developed based on the combination SAR and GWR model. We call the model as Spatial Autoregressive **Geographically** **Weighted** **Regression** (SAR-GWR). We used Instrumental Variables (IV) approach and Two Stage Least Square (TSLS) to estimate the parameters of the model. We have done the simulation study by mean Monte Carlo simulation to check the bias and efficiency of the parameter estimates. SAR-GWR model provides better results with small bias and Root Mean Square Error (RMSE) rather than standard GWR. We also found that our method relative robust to the multicollinearity problem. We also applied SAR-GWR model in modeling prevalence rate of the Tuberculosis (TB + ) disease in Bandung and we found the healthy house index gives serious effect in increasing theprevalence rate of TB + in Bandung City.

Show more
27 Read more

Although various schemes have been developed, rainfall merging is still a complex and important issue. The results of rainfall merging are influenced by the kind of merging scheme, the quality of satellite rainfall data, the density of raingauges and so on. Motivated by this, the objective of this paper is to develop a residual-based method for merging satellite and raingauge rainfall using **geographically** **weighted** **regression** (GWR). Theoretically, this novel method is capable of simultaneously blending various satellite rainfall data with gauge measurements and could describe the non-stationary influences of geographical and terrain factors on rainfall spatial distribution. Using the proposed method, an experimental study on merging the rainfall from CMOROH (Joyce et al., 2004) and gauge measurements was conducted for the Ganjiang River basin, in southeast China. The capability of our merging scheme for constructing daily rainfall fields under different gauge densities is investigated and discussed. The accuracy gain achieved by rainfall merging relative to traditional interpolation merely only raingauge measurements is analysed.

Show more
20 Read more

influence (Gilbert, 2011) & (Robinson, 2011). Spatial **regression** method frequently used is **Geographically** **Weighted** Regresssion (GWR), which is a **regression** method involving the effect of the location into the predictor (Fotheringham, et al., 2002). In the linear **regression** model generated only parameter estimator that apply globally, while in the GWR models generated model parameter estimator that is local to each observation location. Mixed **geographically** **Weighted** **Regression** (MGWR) is a combination of global linear **regression** model with the GWR model. So that the model will be generated MGWR estimator parameters are global and some others are localized in accordance with the location of observations (Purhadi and Yasin, 2012).

Show more
distinctness. One possible solution is to include only the locations of data with similar attributes (i.e., homo- geneity). However, it is difficult to decide the number of groups with different attributes and identify the loca- tions of data in each group. Moreover, the mean value of a non-stationary process is usually a step function [8] or is continuous across space, and it is difficult to find the exact boundary of appropriate locations. The other possi- bility is to use the varying coefficient model [10], allowing the coefficient terms to vary according to locations. Then, the model is a form of local linear models [15] and can be used to explore the dynamic property of spatial data. Based on the concept of the varying coefficient model, **geographically** **weighted** **regression** (GWR) is modified to solve the MAUP [6].

Show more
18 Read more

Constructing mathematical models of processes is a common theme in analytical research in a wide range of disciplines. “Researchers search for variables to identify various dimensions of phenomena and for relationships among the variables to interpret or change the real world.” (Casetti, 1972, P.82). Traditional analytical methods, however, tend to assume constant relationships among variables; that is, models with constant parameters are constructed to describe the relationships between variables. This is usually achievable and acceptable in physical sciences, where the investigated phenomena are determined by certain natural laws, for example, Newton’s law of universal gravitation involves a constant parameter, the gravitational constant. In social and environmental sciences, however, the relationships between variables may not be constant. For example, the relationship between elevation and precipitation may change according to complex geographical phenomena. Traditional global models can mask this non-stationarity in relationships (Fotheringham, 1997, Brunsdon et al., 1999a, Brunsdon et al., 1999b, Farber and Yeates, 2006). Models that allow parameters to vary across geographical space, over time, or according to other contexts are thus useful. Typical forms of such models are **regression** models that have spatially varying coefficients. This thesis focuses on a widely applied model of this type, namely **Geographically** **Weighted** **Regression** (GWR).

Show more
167 Read more

Despite growing research for residential crowding effects on housing market and public health perspectives, relatively little attention has been paid to explore and model spatial patterns of res- idential crowding over space. This paper focuses upon analyzing the spatial relationships between residential crowding and socio-demographic variables in Alexandria neighborhoods, Egypt. Global and local geo-statistical techniques were employed within GIS-based platform to identify spatial variations of residential crowding determinates. The global ordinary least squares (OLS) model assumes homogeneity of relationships between response variable and explanatory variables across the study area. Consequently, it fails to account for heterogeneity of spatial relationships. Local model known as a **geographically** **weighted** **regression** (GWR) was also employed using the same response variable and explanatory variables to capture spatial non-stationary of residential crowding. A comparison of the outputs of both models indicated that OLS explained 74 percent of residential crowding variations while GWR model explained 79 percent. The GWR improved strength of the model and provided a better goodness of fit than OLS. In addition, the findings of this analysis revealed that residential crowding was significantly associated with different struc- tural measures particularly social characteristics of household such as higher education and illi- teracy. Similarly, population size of neighborhood and number of dwelling rooms were found to have direct impacts on residential crowding rate. The spatial relationship of these measures dis- tinctly varies over the study area.

Show more
15 Read more

Nonresponse can undermine the quality of social survey data. Understanding who does/does not respond to surveys is important for those involved in the collection and analysis of these data. Levels of nonresponse are known to vary **geographically**. However, there has been little consideration of how the predictors of survey nonresponse might vary **geographically** within countries. This study examines the possibility of spatial variation in response behavior using regional interactions and **geographically** **weighted** **regression**. Our results suggest that there is geographical variation in response behavior. Relying on “one size fits all” global models in nonresponse modelling might, therefore, be insufficient.

Show more
This study has limitations. First, the lack of data on the latest district demarcations means that this study could not offer insights into outcomes in the recently created districts. Related to the above data limitation is the challenge of using predictors from different measurement occasions. Our preference for predictors measured in the same year was not feasible given the non-availability of data. Nonetheless, the temporal explanation of our results is valid because all predictors used in this study preceded the outcome variable. Second, because of the high correlation between the explanatory variables, we had to use recommended data reduction techniques to reduce the data. Although this approach is rigorous and recommended to address multicolinearity problems, it limited our ability to have more information about the direct connection between speci ﬁ c indicators and our outcome variable. Despite these limitations, the study's strengths are noteworthy. The use of the GWR analytical method improved the study's explanatory po- wer, beyond that offered by traditional **regression** models. In addition, the use of thematic mapping made it possible to highlight geographical disparities in academic achievement in Ghana that have been ignored in many studies.

Show more
11 Read more

where there is usually high fire occurrence (check Fig. 1a). However, these maps are too oversmoothed in capturing lo- cal variations, especially in the logistic GWR model. The trend of the residuals of the logistic model towards cluster- ing did not significantly decrease from the ordinary model to the GWR model according to the Average Nearest Neighbour Distance Analysis (Table 2), and there was only a minor im- provement, especially in the overestimation errors. Although in the GW logistic model there were fewer errors, the spatial distribution was very similar to the ordinary logistic model (Fig. 2). Also, analysis of the linear GW **regression** model residuals revealed similar characteristics to the global OLS model, with a mean value of 0.01 and a SD of 0.51, accept- ably following the shape of the normal curve (Fig. 5b). The Kolmogorov-Smirnov test value was low (0.03) but still sig- nificant (p = 0.000), showing that the normal fit was poor. The residuals fitted properly except for low fire density val- ues according to the normal Q − Q plot (Fig. 5c). However, the scatterplot was more compact along the tendency line and the standardized residual map (Fig. 5d) showed a more dis- persed distribution through the study area in comparison to the OLS model (Fig. 3d), without any evident systematic pat- tern. These analyses indicated a slightly better performance of the GWR model.

Show more
17 Read more

Even though GWR was used as a more robust method for accounting for spatial dependence, the final model explained a relatively small amount of the variation. The relationships identified were complex with **regression** coefficients switching between negative and positive val- ues in different locations, which indicates that while focusing interventions on a particular risk factor might be beneficial in one area, it may actually be detrimental in another area. As with any **regression** method, they cannot prove causality, and other drivers may not have been retained as a result of the deliberately stringent method of covariate selection. The fact that the most important vari- ables occur in blocks greater than half the GWR bandwidth rather than random scattering suggests the regional heterogeneity is real, with demonstrably different factors associated with the spread of bTB in different areas where spread has occurred, and it is this that is perhaps the most important finding of this study.

Show more
14 Read more