Using Geovisual Analytics to investigate the performance of Geographically Weighted Discriminant Analysis

Geographically Weighted Discriminant Analysis (GWDA) is a method for prediction and analysis of categorical spatial data. It is an extension of Linear Discriminant Analysis (LDA) that allows the relationship between the predictor variables and the categories to vary spatially. This is also referred to spatial non-stationarity. If spatial non-stationarity exists, GWDA should model the relationship between the categories and predictor variables more accurately, thus resulting in a lower classification uncertainty and ultimately a higher classification accuracy. The GWDA output also requires interpretation to understand which variables are important in driving the classification in different geographical regions. This research uses interactive visualisations from the field of geovisual analytics to investigate the performance of GWDA in terms of classification accuracy, classification uncertainty and spatial non-stationarity. The methodology is demonstrated in a case study that uses GWDA to examine the relationship between county level voting patterns in the 2004 US presidential election and five socio-economic indicators. This research builds on existing techniques to interpret the GWDA output and provides additional insight into the processes driving the classification. It also demonstrates a practical application of geovisual analytic tools

Combining Geographically Weighted Regression and Geovisual Analytics to investigate temporal variations in house price determinants across London in the period 1980-1998

Hedonic price modelling attempts to uncover information on the determinants of prices - in this case the prices are those of houses in the Greater London area for the period between 1980 and 1998. The determinants of house prices can include house attributes (such as size, type of building, age, etc.), neighbourhood attributes (such as proportion of unemployed people in the neighbourhood or local tax rates) and geographic attributes (such as distance from the city centre or proximity to various amenities) (Orford 1999). Almost all applications of hedonic price models applied to housing are in the form of multiple linear regression models where price is regressed on various attributes. The parameter estimates from the calibration of this type of regression model are assumed to yield information on the relative importance of various attributes in influencing price. One major problem with this approach is that it assumes that the determinants of prices are the same in all parts of the study area. This seems particularly illogical in this type of application where there could easily be local variations in preferences and also in supply and demand relationships. Hence, it seems reasonable to calibrate local hedonic price models rather than global ones – that is, to calibrate a model form which is flexible enough to allow the determinants of house prices to vary spatially. Geographically Weighted Regression (GWR) (Fotheringham et al. 2002) is a statistical technique that allows local calibrations and which yields local estimates of the determinants of house prices. GWR was recently used to investigate spatial variations in house price determinants across London separately for each of the years between 1980 and 1998 (Crespo et al. 2007). The result of the GWR analysis is a set of continuous localised parameter estimate surfaces which describe the geography of the parameter space. These surfaces are typically visualised with a set of univariate choropleth maps for each surface which are used to examine the plausibility of the stationarity assumption of the traditional regression and different possible causes of non-stationarity for each separate parameter (Fotheringham and al. 2002). The downside of these separate univariate visualisations is that multivariate spatial and non-spatial relationships and patterns in the parameter space can not be seen. In an attempt to counter this inadequacy, in a previous study we suggested to treat the result space of one single GWR analysis as a multivariate dataset and visually explore it (Demšar et al. 2007). The goal was to identify spatial and multivariate patterns that the separate univariate mapping could not recognise. In this paper we extend this approach with the temporal dimension: we use Geovisual Analytical exploration to investigate the spatio-temporal dynamics in a time series of GWR hedonic price models. The idea is to merge the time series of GWR result spaces (one space per year) into one single highly-dimensional spatio-temporal dataset, which we then visually explore in an attempt to uncover information about the temporal and spatio-temporal behaviour of parameter estimates of GWR and consequently of underlying geographical processes

Geographically Weighted Spline Nonparametric Regression dengan Fungsi Pembobot Bisquare dan Gaussian Pada Tingkat Pengangguran Terbuka Di Pulau Kalimantan

Geographically weighted spline nonparametric regression merupakan pengembangan regresi nonparametrik untuk data spasial dengan estimator parameter bersifat lokal setiap lokasi pengamatan yang diaplikasikan pada kasus tingkat pengangguran terbuka. Tingkat pengangguran terbuka menjadi alat ukur kualitas kesejahteraan di suatu wilayah yang mengindikasikan besarnya persentase penduduk usia kerja yang aktif secara ekonomi. Tujuan penelitian ini yaitu untuk mengidentifikasi faktor-faktor yang mempengaruhi tingkat pengangguran terbuka 56 Kabupaten/Kota di Kalimantan. Metode yang digunakan adalah geographically weighted spline nonparametric regression dengan pembobot fungsi kernel eksponensial. Model terbaik geographically weighted spline nonparametric regression dengan pembobot fungsi kernel eksponensial pada orde 1 titik knot 1 dengan nilai R-Square sebesar 86,410 persen, nilai AIC sebesar 12,152, nilai RMSE sebesar 0,584 serta nilai CV terkecil adalah fungsi kernel bisquare sebesar 77,175. Adapun faktor-faktor yang berpengaruh signifikan terhadap tingkat pengangguran terbuka yaitu  tingkat partisipan angkatan kerja, jumlah penduduk, indeks pembangunan manusia, harapan lama sekolah dan upah minimum

From SpaceStat to CyberGIS: Twenty Years of Spatial Data Analysis Software

This essay assesses the evolution of the way in which spatial data analytical methods have been incorporated into software tools over the past two decades. It is part retrospective and prospective, going beyond a historical review to outline some ideas about important factors that drove the software development, such as methodological advances, the open source movement and the advent of the internet and cyberinfrastructure. The review highlights activities carried out by the author and his collaborators and uses SpaceStat, GeoDa, PySAL and recent spatial analytical web services developed at the ASU GeoDa Center as illustrative examples. It outlines a vision for a spatial econometrics workbench as an example of the incorporation of spatial analytical functionality in a cyberGIS.

Analysis and Geovisualisation of Hector’s Dolphin Abundance and Distribution Patterns in Space and Time

While Hector’s dolphin (Cephalorhynchus hectorii) has been the topic of many research projects within the first Marine Mammal Sanctuary in New Zealand, few long-term analytical abundance and distribution projects in other population strongholds have been conducted. The primary purpose of this thesis project was to test quantitative observations that suggested that this unprotected population of Hector’s dolphin at Te Waewae Bay, on the south coast of the South Island, New Zealand, may be in decline and utilises non-continuous portions of the coastline. Seasonal patterns of distribution and density were extracted from a rich data set collected over 24 consecutive months that provided fine-scale data of encounters with dolphins along four preplanned transects that followed the concave nature of the bay. Monthly data were binned into seasons producing eight seasons of data over the two years. Survey results revealed that Hector’s dolphin in warmer seasons were found in greater densities closer to shore and that in the cooler seasons the range extended outward and across more offshore areas. Individual seasons did not have as strong a pattern as the complete two year data set that indicated hotspots of higher densities of dolphins in the vicinity of freshwater inputs into Te Waewae Bay. To explore individual spatio-temporal movement patterns and how the individual patterns relate to group spatio-temporal patterns, 58 individual Hector’s dolphin movements were extracted from geo-tagged photographic data and then analysed. Visual analysis of movement patterns of individual dolphins were found to vary dramatically, having distribution patterns that exhibited a high degree of site fidelity. Most notable were the twenty one dolphins that remained in relatively small areas on either the east (ten dolphins) or west (eleven dolphins) halves of the bay. This evidence of strong site fidelity may suggest partitioning along as yet unidentified social or environmental parameters. Abundance estimates were calculated from mark-recapture photographic identifications. Calculations using Pollock’s Robust Design were limited to seasonal estimates of the total population of Hector’s dolphins, which ranged from the low in winter 2005 of 380 (CV=13%; 95% CI, 300-500) to the high in summer 2005/2006 of 580 (CV=9%; 95% CI, 480-700). The estimates from these eight seasons correspond to the numbers of dolphins that utilise the bay as their primary homerange and indicate that the population is not yet in a critical decline. However, caution is urged in interpretation because two years of field data is insufficient to calculate robust survival or reproduction rates for such a long lived species. To examine whether statistically quantifiable relationships exist between environmental variables and dolphin distribution patterns, both global (ordinary least squares; OLS) and local regression (geographically weighted regression; GWR) modelling techniques were applied. The local model was a spatially explicit model. The GWR model outperformed the OLS model, revealing statistically significant hotspots directly related to the amount of rain falling four days prior to the surveys being conducted as well as to distance from the main source of freshwater in the bay. The outcomes from this thesis offer a robust baseline of information regarding the population of Hector’s dolphin in Te Waewae Bay, such that management will have the capacity to monitor long term changes in abundance and distribution. This thesis findings have suggested that freshwater input may play a crucial role in Hector’s dolphin distribution in Te Waewae Bay, which when added to previous research results indicating the importance of oceanic frontal zones, water clarity, and depth, suggests that the picture of habitat requirements for Hector’s dolphin is becoming less obscure

A visual analytics framework for spatio-temporal analysis and modelling

To support analysis and modelling of large amounts of spatio-temporal data having the form of spatially referenced time series (TS) of numeric values, we combine interactive visual techniques with computational methods from machine learning and statistics. Clustering methods and interactive techniques are used to group TS by similarity. Statistical methods for TS modelling are then applied to representative TS derived from the groups of similar TS. The framework includes interactive visual interfaces to a library of modelling methods supporting the selection of a suitable method, adjustment of model parameters, and evaluation of the models obtained. The models can be externally stored, communicated, and used for prediction and in further computational analyses. From the visual analytics perspective, the framework suggests a way to externalize spatio-temporal patterns emerging in the mind of the analyst as a result of interactive visual analysis: the patterns are represented in the form of computer-processable and reusable models. From the statistical analysis perspective, the framework demonstrates how TS analysis and modelling can be supported by interactive visual interfaces, particularly, in a case of numerous TS that are hard to analyse individually. From the application perspective, the framework suggests a way to analyse large numbers of spatial TS with the use of well-established statistical methods for TS analysis

Comparing spatial patterns

The second author would like to acknowledge Natural Sciences and Engineering Research Council of Canada for funding this paper.The comparison of spatial patterns is a fundamental task in geography and quantitative spatial modelling. With the growth of data being collected with a geospatial element, we are witnessing an increased interest in analyses requiring spatial pattern comparisons (e.g., model assessment and change analysis). In this paper, we review quantitative techniques for comparing spatial patterns, examining key methodological approaches developed both within and beyond the field of geography. We highlight the key challenges using examples from widely known datasets from the spatial analysis literature. Through these examples, we identify a problematic dichotomy between spatial pattern and process—a widespread issue in the age of big geospatial data. Further, we identify the role of complex topology, the interdependence of spatial configuration and composition, and spatial scale as key (research) challenges. Several areas ripe for geographic research are discussed to establish a consolidated research agenda for spatial pattern comparison grounded in quantitative geography. Hierarchical scaling and the modifiable areal unit problem are highlighted as ideas which can be exploited to identify pattern similarities across spatial and temporal scales. Increased use of “time-aware” comparisons of spatial processes are suggested, which properly account for spatial evolution and pattern formation. Simulation-based inference is identified as particularly promising for integrating spatial pattern comparison into existing modelling frameworks. To date, the literature on spatial pattern comparison has been fragmented, and we hope this work will provide a basis for others to build on in future studies.PostprintPeer reviewe