Spatial Modeling of Residential Crowding in Alexandria Governorate, Egypt: A Geographically Weighted Regression (GWR) Technique

Abstract

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 residential 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 structural measures particularly social characteristics of household such as higher education and illiteracy. 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 distinctly varies over the study area.

Spatial Predictive Modeling of the Burning of Sugarcane Plots in Northeast Thailand with Selection of Factor Sets Using a GWR Model and Machine Learning Based on an ANN-CA

“…where 𝛽𝛽 0 is the intercept term; 𝛽𝛽 1 to 𝛽𝛽 7 are spatially varying coefficients of the X1 to X7 attributes, respectively; and 𝜀𝜀 𝑖𝑖 is an error at point (longitude, latitude/X-meters, Y-meters) i, (𝑢𝑢 𝑖𝑖 𝑣𝑣) 𝑖𝑖 representing the coordinates of the ith point in study scope [72]. The data acquisition for a service area layer of the cane delivery quota not exceeding 120 km is shown as a red boundary in Figure 6.…”

“…where β 0 is the intercept term; β 1 to β 7 are spatially varying coefficients of the X 1 to X 7 attributes, respectively; and ε i is an error at point (longitude, latitude/X-meters, Y-meters) i, (u i v) i representing the coordinates of the ith point in study scope [72].…”

“…The weighting functions used to estimate the parameters in the GWR model were the Gaussian kernel functions [72], which can be written as Equation (7), below. The GWR model's weighted calculation for this was for an area within the subunit boundary in the analysis of a service area of 120 km in relation to the transport distance for the sugarcane delivered to each plant.…”

“…The application of the GWR model requires the creation of data variables within the scope of the appropriate sub-area units, resulting in lower tolerances and higher decision coefficients [70,71]. The implementation of GWR results should have stand residual and Moran's I index values for the relevant models to be used in the most efficient forecasts [70,[72][73][74][75][76].…”

“…The GWR model was modeled using the ArcGIS pro 2.9 software package, this allows a variety of calibration techniques to be used to identify regression weights and optimize bandwidth parameters. [70,71] In this study, a fixed defined kernel with two square functions (in which bandwidth is determined by reducing the Akaike information criteria (AIC)) [72,73] was used. The reason for this is that the points in the units of spatial analysis used are regular and equal size.…”