The importance of scale in spatially varying coefficient modeling

While spatially varying coefficient (SVC) models have attracted considerable attention in applied science, they have been criticized as being unstable. The objective of this study is to show that capturing the "spatial scale" of each data relationship is crucially important to make SVC modeling more stable, and in doing so, adds flexibility. Here, the analytical properties of six SVC models are summarized in terms of their characterization of scale. Models are examined through a series of Monte Carlo simulation experiments to assess the extent to which spatial scale influences model stability and the accuracy of their SVC estimates. The following models are studied: (i) geographically weighted regression (GWR) with a fixed distance or (ii) an adaptive distance bandwidth (GWRa), (iii) flexible bandwidth GWR (FB-GWR) with fixed distance or (iv) adaptive distance bandwidths (FB-GWRa), (v) eigenvector spatial filtering (ESF), and (vi) random effects ESF (RE-ESF). Results reveal that the SVC models designed to capture scale dependencies in local relationships (FB-GWR, FB-GWRa and RE-ESF) most accurately estimate the simulated SVCs, where RE-ESF is the most computationally efficient. Conversely GWR and ESF, where SVC estimates are naively assumed to operate at the same spatial scale for each relationship, perform poorly. Results also confirm that the adaptive bandwidth GWR models (GWRa and FB-GWRa) are superior to their fixed bandwidth counterparts (GWR and FB-GWR)

A Hierarchical and Geographically Weighted Regression Model and Its Backfitting Maximum Likelihood Estimator (Short Paper)

Spatial heterogeneity is a typical and common form of spatial effect. Geographically weighted regression (GWR) and its extensions are important local modeling techniques for exploring spatial heterogeneity. However, when dealing with spatial data sampled at a micro-level but the geographical locations of them are only known at a higher level, GWR-based models encounter several problems, such as difficulty in establishing the bandwidth. Because data with this characteristic exhibit spatial hierarchical structures, such data can be suitably handled using hierarchical linear modeling (HLM). This model calibrates random effects for sample-level variables in each group to address spatial heterogeneity. However, it does not work when exploring spatial heterogeneity in some group-level variables when there is insufficient variance in each group. In this study, we therefore propose a hierarchical and geographically weighted regression (HGWR) model, together with a back-fitting maximum likelihood estimator, that can be applied to examine spatial heterogeneity in the regression relationships of data where observations nest into high-order groupings and share the same or very close coordinates within those groups. The HGWR model divides coefficients into three types: local fixed effects, global fixed effects, and random effects. Results of a simulation experiment show that HGWR distinguishes local fixed effects from others and also global effects from random effects. Spatial heterogeneity is reflected in the estimates of local fixed effects, along with the spatial hierarchical structure. Compared with GWR and HLM, HGWR produces estimates with the lowest deviations of coefficient estimates. Thus, the ability of HGWR to tackle both spatial and group-level heterogeneity simultaneously suggests its potential as a promising data modeling tool for handling the increasingly common occurrence where data, in secure settings for example, remove the specific geographic identifiers of individuals and release their locations only at a group level

The GWmodel R package: Further Topics for Exploring Spatial Heterogeneity using Geographically Weighted Models

In this study, we present a collection of local models, termed geographically weighted (GW) models, that can be found within the GWmodel R package. A GW model suits situations when spatial data are poorly described by the global form, and for some regions the localised fit provides a better description. The approach uses a moving window weighting technique, where a collection of local models are estimated at target locations. Commonly, model parameters or outputs are mapped so that the nature of spatial heterogeneity can be explored and assessed. In particular, we present case studies using: (i) GW summary statistics and a GW principal components analysis; (ii) advanced GW regression fits and diagnostics; (iii) associated Monte Carlo significance tests for non-stationarity; (iv) a GW discriminant analysis; and (v) enhanced kernel bandwidth selection procedures. General Election data sets from the Republic of Ireland and US are used for demonstration. This study is designed to complement a companion GWmodel study, which focuses on basic and robust GW models

Geographically weighted regression with parameter-specific distance metrics

Geographically weighted regression (GWR) is an important local technique to model spatially varying relationships. A single distance metric (Euclidean or non-Euclidean) is generally used to calibrate a standard GWR model. However, variations in spatial relationships within a GWR model might also vary in intensity with respect to location and direction. This assertion has led to extensions of the standard GWR model to mixed (or semiparametric)GWR and to flexible bandwidth GWR models. In this article, we present a strongly related extension in fitting a GWR model with parameter-specific distance metrics (PSDM GWR). As with mixed and flexible bandwidth GWR models, a back-fitting algorithm is used for the calibration of the PSDM GWR model. The value of this new GWR model is demonstrated using a London house price data set as a case study. The results indicate that the PSDM GWR model can clearly improve the model calibration in terms of both goodness of fit and prediction accuracy, in contrast to the model fits when only one metric is singly used. Moreover, the PSDM GWR model provides added value in understanding how a regression model’s relationships may vary at different spatial scales, according to the bandwidths and distance metrics selected. PSDM GWR deals with spatial heterogeneities in data relationships in a general way, although questions remain on its model diagnostics, distance metric specification, and computational efficiency, providing options for further research

Introducing the GWmodel R and python packages for modelling spatial heterogeneity

In the very early developments of quantitative geography, statistical techniques were invariably applied at a ‘global’ level, where moments or relationships were assumed constant across the study region (Fotheringham and Brunsdon, 1999). However, the world is not an “average” space but full of variations and as such, statistical techniques need to account for different forms of spatial heterogeneity or non-stationarity (Goodchild, 2004). Consequently, a number of local methods were developed, many of which model non- stationarity relationships via some regression adaptation. Examples include: the expansion method (Casetti, 1972), random coefficient modelling (Swamy et al., 1988), multilevel modelling (Duncan and Jones, 2000) and space varying parameter models (Assunção, 2003). One such localised regression, geographically weighted regression (GWR) (Brunsdon et al., 1996) has become increasingly popular and has been broadly applied in many disciplines outside of its quantitative geography roots. This includes: regional economics, urban and regional analysis, sociology and ecology. There are several toolkits available for applying GWR, such as GWR3.x (Charlton et al., 2007); GWR 4.0 (Nakaya et al., 2009); the GWR toolkit in ArcGIS (ESRI, 2009); the R packages spgwr (Bivand and Yu, 2006) and gwrr (Wheeler, 2011); and STIS (Arbor, 2010). Most focus on the fundamental functions of GWR or some specific issue - for example, gwrr provides tools to diagnose collinearity. As a major extension, we report in this paper the development an integrated framework for handling spatially varying structures, via a wide range of geographically weighted (GW) models, not just GWR. All functions are included in an R package named GWmodel, which is also mirrored with a set of GW modelling tools for ESRI’s ArcGIS written in Python

Hybrid ceramics-based cancer theranostics

Cancer is a major threat to human lives. Early detection and precisely targeted therapy/therapies for cancer is the most effective way to reduce the difficulties (e.g., side effects, low survival rate, etc.) in treating cancer. To enable effective cancer detection and treatment, ceramic biomaterials have been intensively and extensively investigated owing to their good biocompatibility, high bioactivity, suitable biodegradability and other distinctive properties that are required for medical devices in oncology. Through hybridization with other materials and loading of imaging agents and therapeutic agents, nanobioceramics can form multifunctional nanodevices to simultaneously provide diagnostic and therapeutic functions for cancer patients, and these nanodevices are known as hybrid ceramics-based cancer theranostics. In this review, the recent developments of hybrid ceramics-based cancer theranostics, which include the key aspects such as their preparation, biological evaluation and applications, are summarized and discussed. The challenges and future perspectives for the clinical translation of hybrid ceramics-based cancer theranostics are also discussed. It is believed that the potential of hybrid ceramic nanoparticles as cancer theranostics is high and that the future of these theranostics is bright despite the difficulties along the way for their clinical translation

Plasma noise in TianQin time delay interferometry

TianQin is a proposed geocentric space-based gravitational wave observatory mission, which requires time-delay interferometry (TDI) to cancel laser frequency noise. With high demands for precision, solar-wind plasma environment at $\sim 10^5$ km above the Earth may constitute a non-negligible noise source to laser interferometric measurements between satellites, as charged particles perturb the refractivity along light paths. In this paper, we first assess the plasma noises along single links from space-weather models and numerical orbits, and analyze the time and frequency domain characteristics. Particularly, to capture the plasma noise in the entire measurement band of $10^{-4} - 1$ Hz, we have performed additional space-weather magnetohydrodynamic simulations in finer spatial and temporal resolutions and utilized Kolmogorov spectra in high-frequency data generation. Then we evaluate the residual plasma noises of the first- and second-generation TDI combinations. Both analytical and numerical estimations have shown that under normal solar conditions the plasma noise after TDI is less than the secondary noise requirement. Moreover, TDI is shown to exhibit moderate suppression on the plasma noise below $\sim 10^{-2}$ Hz due to noise correlation between different arms, when compared with the secondary noise before and after TDI.Comment: 12 pages, 15 figures, accepted by Phys. Rev.

Package ‘GWmodel’

In GWmodel, we introduce techniques from a particular branch of spatial statis- tics,termed geographically-weighted (GW) models. GW models suit situa- tions when data are not described well by some global model, but where there are spatial re- gions where a suitably localised calibration provides a better description. GWmodel in- cludes functions to calibrate: GW summary statistics, GW principal components analy- sis, GW discriminant analysis and various forms of GW regression; some of which are pro- vided in basic and robust (outlier resistant) forms