Geographically Weighted Regression in Advanced Spatial Analysis and Modeling

The main purpose of this study is to run a Geographically Weighted Regression (GWR) on the City of Calgary Census Data using Geographical Weighted Regression. The data available for study is the Census Tract data set for the City of Calgary provided in a geodatabase format. The dataset is similar to the first and fifth Assignments. However, the previous assignments involved the calculation of a simple linear regression and spatial regression which outputs global parameter rather than local. Therefore, in this study, the objective is to fit a GWR model to the Census data using "Average Income" as the dependent variable so as to allow local parameter to estimate the model. The "Geographically Weighted Regression 3" software package is used to compute the global weighted regression model. This paper includes many statistical techniques applied to obtain the final model. It also compares the results obtained from the linear regression model and spatial regression model  with the Geographically Weighted Regression model.

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Spatial Regression in Advanced Spatial analysis and Modeling

Introduction

The main purpose of this study is to explore the process of model selection and spatial regression using S-Plus and its Spatial module. The data available for study is the Census Tract data set for the City of Calgary provided both in GeoDatabase and S-Plus data frame. The dataset is similar to our first Assignment but with an addition of two columns for X and Y to represent Easting and Northing respectively. The previous assignment involved the calculation of a simple linear regression without considering spatial autocorrelation into account. Therefore, in this study, we will fit a regression model to the Census data using ‘Average Income’ as the dependent variable by considering spatial autocorrelation in the regression model. The S-Plus command line was used to compute a Simultaneous Autoregressive (SAR) model so as to describe the relationship between ‘Average Income’ and the other independent variables. This paper includes many statistical techniques applied to obtain the spatial regression model. It also attempts to compare the results obtained from the simple linear regression (in Assignment 1) with the model obtained in this study.

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Variograms, Trend removal and Universal Kriging in Advanced Spatial Analysis and Modeling

Introduction

The main objectives of this study are i) to learn how to use ArcGis‟s GeoStatistical Analyst to examine spatial structure and to interpolate surfaces using GeoStatistical techniques, and ii) to explore GeoStatistical technique using S-Plus (variograms, trend removal, Universal Kriging). The data available for this study include a GeoDatabase that contains a random spot heights feature class for an area in the northwest of the City of Calgary and the City Limits for the City of Calgary. Additionally, a 25m Digital Elevation Model (DEM) for the same area is also included. In this study, we are interpolating the random spot heights surface so as to predict the elevation of the surrounding areas. The software packages used for interpolation are ArcGis and S-Plus. ArcGis is used for Ordinary Kriging interpolation and S-Plus for Universal Kriging. This study aims at evaluating the results performed by two software packages. It also highlights the strengths and weakness of the software packages used for the analysis. This study includes many maps, figures, tables and command lines created in Arcgis and S-Plus; however, the end product of this study is to match the Ordinary Kriging performed in ArcGis and Universal Kriging performed in S-Plus and to understand how different software packages perform the interpolation.

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Interpolation and Trend Surface Analysis in Advanced Spatial Analysis and Modeling

Introduction

'In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points. Surface interpolation functions make predictions from sample measurements for all locations in a raster dataset whether or not a measurement has been taken at the location. There is a variety of ways to derive a prediction for each location; each method is referred to as a model. With each model, there are different assumptions made of the data, and certain models are more applicable for specific data. The Interpolation tools are
generally divided into deterministic and geostatistical methods' (ArcGis 2004). In this study IDW is used as the deterministic interpolator and Global Polynomial interpolation as geostatistical interpolator.

'Trend surface analysis is a method used for the analysis of change over space which attempts to decompose each observation on a spatially distributed variable into acomponent associated with any regional trends present in the data and a component associated with purely local effects. This separation into two components is accomplished by fitting a best-fit surface of a previously specified type using standard regression techniques' (Unwin, 1975). In this study, our main objective is to interpolate the average income for the City of Calgary using ArcGis and calculate a First and Second Order Trend Surface using S-Plus.

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Point Pattern Analysis in Advanced Spatial Analysis and Modeling

Introduction

The analysis of point data in space, in order to obtain patterns in the points that inform something about the underlying process that generated the points, is often termed as point pattern analysis (Fotheringham et al. 2000). The objective in learning more about spatial patterns is to assess spatial dependence so that we may ultimately correct our statistical analyses based upon dependent spatial data and to learn whether geographic phenomena cluster in space. The need of the quantitative measures of spatial pattern is because it is simply not sufficient to rely on one’s visual interpretation of a map (Rogerson 2006, 224). Point pattern analysis is particularly popular in the fields of biology (Diggle, 1983 in Fotheringham et al., 2000), epidemiology (Diggle et al. in Fotheringham et al., 2000) and the analysis of crime patterns (Bailey and Gatrell, 1995 in Fotheringham et al., 2000). This study focuses on the spatial pattern of the Park centers in the residential areas of Calgary.

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