Is `Statistix Inferens' Still the Geographical Name for a Wild Goose?

After the recent death of Peter Gould, I decided to look once again at his insightful paper `Is Statistix Inferens the Geographical Name for a Wild Goose?' (Gould 1970) - hence the title for this guest editorial. For those readers who have not seen this article, Gould outlines a number of shortcomings of the common statistical practices of geographers of the day

Quantitative methods I: Reproducible research and quantitative geography.

Reproducible quantitative research is research that has been documented sufficiently rigorously that a third party can replicate any quantitative results that arise. It is argued here that such a goal is desirable for quantitative human geography, particularly as trends in this area suggest a turn towards the creation of algorithms and codes for simulation and the analysis of Big Data. A number of examples of good practice in this area are considered, spanning a time period from the late 1970s to the present day. Following this, practical aspects such as tools that enable research to be made reproducible are discussed, and some beneficial side effects of adopting the practice are identified. The paper concludes by considering some of the challenges faced by quantitative geographers aspiring to publish reproducible research

Assessing the changing flowering date of the common lilac in North America: a random coefficient model approach

A data set consisting of Volunteered geographical information (VGI) and data provided by expert researchers monitoring the first bloom dates of lilacs from 1956 to 2003 is used to investigate changes in the onset of the North American spring. It is argued that care must be taken when analysing data of this kind, with particular focus on the issues of lack of experimental design, and Simpson’s paradox. Approaches used to overcome this issue make use of random coefficient modelling, and bootstrapping approaches. Once the suggested methods have been employed, a gradual advance in the onset of spring is suggested by the results of the analysis. A key lesson learned is that the appropriateness of the model calibration technique used given the process of data collection needs careful consideration

Estimating probability surfaces for geographical point data: An adaptive kernel algorithm

The statistical analysis of spatially referenced information has been acknowledged as an important component of geographical data processing. With the arrival of GIS there has been a need to devise statistical methods that are compatible with, and relevant to, GIS-based methodologies. Here an algorithm is presented which estimates a “risk surface” from a set of point-referenced events. Such a surface may be viewed as an object embedded in three-dimensional space, or as a contour map. In addition to this view, it is possible to incorporate these surfaces into a broader based GIS framework, allowing the mapping of these patterns in conjunction with other data, overlay analysis, and spatial query. The technique is adaptive, in the sense that parameters which control the surface estimation are adjusted over geographic space, allowing for local variations in point pattern characteristics. The paper is concluded with an example based on probabilistic mapping using data taken from Californian Redwood seedling data

Path Estimation from GPS Tracks

The widespread availability of hand-held GPS units has led to a proliferation in data on the tracks of individuals as they walk, drive or otherwise go about journeys. This data has been used in a number of ways - for example the OpenStreetMap project (The OpenStreetMap Foundation 2007). One characteristic of projects such as this is that there will often be several GPS tracks for the same stretch of road. In general, repeatedly measuring something and taking the average of measurements leads to a more accurate result. The question addressed here is “is it possible to ’average’ GPS tracks and if so, does this lead to a better estimate of road location?”

Spatial variations in the average rainfall - altitude relationship in Great Britain: an approach using geographically weighted regression

The relationship between annual rainfall totals and gauge elevation over Great Britain is re-examined using the recently developed technique of geographically weighted regression (GWR). This enables the spatial drift of regression parameters to be identified, estimated and mapped. It is shown that the rate of increase of precipitation with height, or height coefficient, varies from around 4.5 mm:m in the northwest to almost zero in the southeast. There is a particularly rapid change in this value across the English Midlands. The predicted sea level precipitation varies from 1250 mm to less than 600 mm in much the same way

Locally-varying explanations behind the United Kingdom\u27s vote to leave the European Union

Explanations behind area-based (Local Authority-level) voting preference in the 2016 referendum on membership of the European Union are explored using aggregate-level data. Developing local models, special attention is paid to whether variables explain the vote equally well across the country. Variables describing the post-industrial and economic successfulness of Local Authorities most strongly discriminate variation in the vote. To a lesser extent this is the case for variables linked to metropolitan and big city contexts, which assist the Remain vote, those that distinguish more traditional and nativist values, assisting Leave, and those loosely describing material outcomes, again reinforcing Leave. Whilst variables describing economic competitiveness co-vary with voting preference equally well across the country, the importance of secondary variables - those distinguishing metropolitan settings, values and outcomes - does vary by region. For certain variables and in certain areas, the direction of effect on voting preference reverses. For example, whilst levels of European Union migration mostly assist the Remain vote, in parts of the country the opposite effect is observed

Links, comparisons and extensions of the geographically weighted regression model when used as a spatial predictor

In this study, we link and compare the geographically weighted regression (GWR) model with the kriging with an external drift (KED) model of geostatistics. This includes empirical work where models are performance tested with respect to prediction and prediction uncertainty accuracy. In basic forms, GWR and KED (specified with local neighbourhoods) both cater for nonstationary correlations (i.e. the process is heteroskedastic with respect to relationships between the variable of interest and its covariates) and as such, can predict more accurately than models that do not. Furthermore, on specification of an additional heteroskedastic term to the same models (now with respect to a process variance), locallyaccurate measures of prediction uncertainty can result. These heteroskedastic extensions of GWR and KED can be preferred to basic constructions, whose measures of prediction uncertainty are only ever likely to be globallyaccurate. We evaluate both basic and heteroskedastic GWR and KED models using a case study data set, where data relationships are known to vary across space. Here GWR performs well with respect to the more involved KED model and as such, GWR is considered a viable alternative to the more established model in this particular comparison. Our study adds to a growing body of empirical evidence that GWR can be a worthy predictor; complementing its more usual guise as an exploratory technique for investigating relationships in multivariate spatial data sets

Locally-varying explanations behind the United Kingdom\u27s vote to leave the European Union

Explanations behind area-based (Local Authority-level) voting preference in the 2016 referendum on membership of the European Union are explored using aggregate-level data. Developing local models, special attention is paid to whether variables explain the vote equally well across the country. Variables describing the post-industrial and economic successfulness of Local Authorities most strongly discriminate variation in the vote. To a lesser extent this is the case for variables linked to metropolitan and big city contexts, which assist the Remain vote, those that distinguish more traditional and nativist values, assisting Leave, and those loosely describing material outcomes, again reinforcing Leave. Whilst variables describing economic competitiveness co-vary with voting preference equally well across the country, the importance of secondary variables - those distinguishing metropolitan settings, values and outcomes - does vary by region. For certain variables and in certain areas, the direction of effect on voting preference reverses. For example, whilst levels of European Union migration mostly assist the Remain vote, in parts of the country the opposite effect is observed