Spatial Spline Research Articles

SpconfShiny: An R Shiny application for calculating the spatial scale of smoothing splines for point data.

Epidemiological analyses of environmental exposures often benefit from including spatial splines in models to account for confounding by spatial location. Understanding how the number of splines relates to physical spatial differences is not always intuitive and can be context-dependent. To address this, we developed a R Shiny application, spconfShiny, that provides a user-friendly platform to calculate an effective bandwidth metric that quantifies the relationship between spatial splines and the range of implied spatial smoothing. spconfShiny can be accessed at https://g2aging.shinyapps.io/spconfShiny/. We illustrate the procedure to compute the effective bandwidth and demonstrate its use for different numbers of spatial splines across England, India, Ireland, Northern Ireland, and the United States. Using spconfShiny, we show the effective bandwidth increases with the size of the region and decreases with the number of splines. Including 10 splines on a 10km grid corresponds to effective bandwidths of 92.2km in Ireland and 927.7km in the United States.

Income inequality and depressive symptoms among Chinese adults: a quasi-experimental study

ObjectiveThere is a lack of causal evidence on the impact of income inequality on depressive symptoms. The impact of China's Targeted Poverty Alleviation (TPA) policy on depressive symptoms is also unclear. Using a quasi-experimental design, this study aims to investigate the causal effects of TPA and income inequality on depressive symptoms among Chinese adults. Study designThis is a population-based study. MethodsThree waves (2012, 2016, and 2018) of the China Family Panel Studies (CFPS), a nationally representative sample of China, were included in this study. We performed difference-in-difference (DID) models to assess the effect of TPA and income inequality on depressive symptoms. We further conducted the mixed effect models to examine the impact of income inequality on depressive symptoms. The study considered a range of spatial factors and spatial splines to address spatial autocorrelations. ResultsThis study included valid measures of depressive symptoms (Center for Epidemiologic Studies Depression Scale [CES-D-8] score) from 14,442 adults of CFPS. The DID results indicated that at the provincial level, the CES-D-8 score of the TPA treatment group was on average 0.570 (95% confidence interval [CI]: 0.358–0.783) less than the control group. Furthermore, a 0.1 increase in Gini index would lead to a 0.256 (95% CI: 0.064–0.448) increase in CES-D-8 score. The mixed effect model showed that income inequality was a risk factor for depressive symptoms at the provincial level (excess risk = 5.602% [95% CI: 3.047%–8.219%]). ConclusionsOur findings suggest that income inequality adversely affects mental health, but China's Targeted Poverty Alleviation improves the mental health of the Chinese population.

Shorebird Monitoring Using Spatially Explicit Occupancy and Abundance

Loss of habitat and human disturbance are major factors in the worldwide decline of shorebird populations, including that of the threatened migratory piping plover (Charadrius melodus). From 2013 to 2018, we conducted land-based surveys of the shorebird community every other week during the peak piping plover season (September to March). We assessed the ability of a thin plate spline occupancy model to identify hotspot locations on Whiskey Island, Louisiana, for the piping plover and four additional shorebird species (Wilson’s plover (Charadrius wilsonia), snowy plover (Charadrius nivosus), American oystercatcher (Haematopus palliatus), and red knot (Calidris canutus)). By fitting single-species occupancy models with geographic thin plate spline parameters, hotspot priority regions for conserving piping plovers and the multispecies shorebird assemblage were identified on the island. The occupancy environmental covariate, distance to the coastline, was weakly fitting, where the spatially explicit models were heavily dependent on the spatial spline parameter for distribution estimation. Additionally, the detectability parameters for Julian date and tide stage affected model estimations, resulting in seemingly inflated estimates compared to assuming perfect detection. The models predicted species distributions, biodiversity, high-use habitats for conservation, and multispecies conservation areas using a thin-plate spline for spatially explicit estimation without significant landscape variables, demonstrating the applicability of this modeling approach for defining areas on a landscape that are more heavily used by a species or multiple species.

Prediction of Bike‐sharing Trip Counts: Comparing Parametric Spatial Regression Models to a Geographically Weighted XGBoost Algorithm

Regression models are commonly applied in the analysis of transportation data. This research aims at broadening the range of methods used for this task by modeling the spatial distribution of bike‐sharing trips in Cologne, Germany, applying both parametric regression models and a modified machine learning approach while incorporating measures to account for spatial autocorrelation. Independent variables included in the models consist of land use types, elements of the transport system and sociodemographic characteristics. Out of several regression models with different underlying distributions, a Tweedie generalized additive model is chosen by its values for AIC, RMSE, and sMAPE to be compared to an XGBoost model. To consider spatial relationships, spatial splines are included in the Tweedie model, while the estimations of the XGBoost model are modified using a geographically weighted regression. Both methods entail certain advantages: while XGBoost leads to far better values regarding RMSE and sMAPE and therefore to a better model fit, the Tweedie model allows an easier interpretation of the influence of the independent variables including spatial effects.

Long-Term Ambient Air Pollution and Childhood Eczema in the United States.

Long-Term Ambient Air Pollution and Childhood Eczema in the United States.

Disentangling spatial and environmental effects: Flexible methods for community ecology and macroecology

AbstractCommunity ecologists and macroecologists have long sought to evaluate the importance of environmental conditions in determining species distributions, community composition, and diversity across sites. Different methods have been used to estimate species–environment relationships, but their differences to jointly fit and disentangle spatial autocorrelation and structure remain poorly studied. We compared how methods in four broad families of statistical models estimated the contribution of the environment and space to variation in species occurrence and abundance. These methods included redundancy analysis (RDA), generalized linear models (GLMs), generalized additive models (GAMs), and three types of tree‐based machine learning (ML) methods: boosted regression trees (BRT), random forests, and regression trees. The spatial component of the model consisted of Moran's eigenvector maps (MEMs; in RDA, GLM, and ML), smooth spatial splines (in GAM), or tree‐based nonlinear modeling of spatial coordinates (in ML). We simulated typical site‐by‐species data to assess the methods' performance in (1) fitting environmental and spatial models, and (2) partitioning the variation explained by environmental and spatial predictors. We observed marked differences in performance among methods generally caused by their different performances in fitting spatial structures. Generalized linear model and BRT with MEMs were generally the most reliable methods for partitioning the variation explained by environmental and spatial effects across a wide range of simulated scenarios. The remaining methods tended to underestimate pure spatial effects, because of either underfitting of simulated spatial structures or overestimation of environmental effects compared to spatial effects when jointly estimated. Performing variation partitioning on nine different empirical datasets using these methods yielded contrasting results, especially in the estimation of the spatial fraction of variation. Our results suggest that previously overlooked methods for performing variation partitioning, especially tree‐based ML, offer flexible approaches to analyze site‐by‐species matrices. We provide general guidelines on the usefulness of different models under different ecological and sampling scenarios, for species distribution modeling, community ecology, and macroecology.

Online Bayesian learning for mixtures of spatial spline regressions with mixed effects

Classification and clustering methods based on univariate functions have been well developed. Recent work has extended the techniques to the domain of bivariate functions by incorporating the techniques based on mixtures of spatial spline regression with mixed-effects models. An Expectation Maximization (EM) algorithm is implemented to facilitate model inference. In this paper, we further extend the mixtures of spatial spline regression with mixed-effects model under the Bayesian framework to accommodate streaming image data. First, we derive a Markov chain Monte Carlo (MCMC) algorithm as an alternative approach to the EM algorithm to make inference on the model. However, MCMC is not scalable to streaming image data since it requires all observed information to update the posterior distribution of the parameters. To tackle this issue, we propose a sequential Monte Carlo (SMC) algorithm to analyse online fashion image data. The existence of model sufficient statistics improves the efficiency of the proposed online SMC algorithm. Instead of saving all batch data for inference, we only require storage of the model sufficient statistics and every data point is only used once, which is well suited for large-scale stream type data. In addition, the proposed algorithm provides an unbiased estimator of the marginal likelihood as a by-product of the approach, which can be used for model selection. Numerical experiments are used to demonstrate the effectiveness of our method. Our implementation is available at https://github.com/ShufeiGe/Online-Bayesian-learning-for-MMSRm.

Spatial modelling of risk premiums for water damage insurance

In this paper, we compare different spatial models for modelling the risk premium for water damage insurance on the level of the policyholder. We evaluate four models that take the spatial variability into account: (1) the Intrinsic Conditional Auto-Regressive (ICAR) model; (2) the Besag, York, Mollier (BYM) model; (3) the independent random effects model; and (4) a spatial spline model. The models are compared on a huge data set from the Norwegian insurance company Gjensidige containing seven million observations of policyholders during the period 2011–2018. While Bayesian methods are most frequently used for inference in Gaussian Markov Random Field models, we take a frequentist approach and estimate the model parameters using Laplace approximated restricted maximum likelihood. Using the R package mgcv, we compare the different models for claim frequency, claim size and combined in a risk premium model in a comprehensive cross-validation study. Practical measures such as the loss ratio lift, double lift and Gini index are used to compare performance. Finally, we also compare mgcv with INLA and show that for reasonable big data sets we get identical estimates at a much lower computational cost.

An efficient geostatistical analysis tool for on-farm experiments targeted at localised treatment

On farm experimentation (OFE) has been a long-standing method for farmers to assess alternative management at scales relevant to their farming practices. Through the use of spatially distributed designs, whether simple strips or other ‘whole-of-block’ trials, OFE can provide information such as which treatment should be recommended at specific locations, and make important contributions to precision agriculture. However, when treatment response data sets become large, such as with tens of thousands of field observations that are readily collected using on-the-go sensors, existing geostatistical systems for analysing such experiments become computationally intensive, if not impossible. To enable farmers, or their consultants, to generate high-resolution treatment response and recommendation maps on their own computers within a reasonable time, we present a fast and adaptive local cokriging tool for non-colocated and non-stationary OFE data. It uses a spatially-varying neighbourhood radius. It has a graphical user interface accessible via QGIS, a free and open source software. The adaptive local cokriging is demonstrated on three OFE examples. It performs indistinguishably from global cokriging on a small data set, but for large data sets, for which global cokriging is impractical, it predicts significantly more accurately than spatial splines or sampling-based cokriging. It outperforms cokriging base on a fixed number of nearest neighbours when this fixed number is not carefully chosen. • We give a spatially-varying local cokriging method for large on-farm experimentation data. • The new method could recommend high-resolution site-specific farming treatment. • Its open source code is accessible via a user-friendly interface of Quantum GIS. • It finishes computation within a reasonable time on farmers’ normal PC. • Its promising spatial prediction accuracy is compared with five other techniques.

Spatial Spline Construction through the Monge Model

The solution to the problem of spatial spline construction by its orthogonal projections on the Monge model is considered in the present paper. Constructively, spatial interpolation of a discrete set of points given on projection planes pi1 and pi2 is performed through planar interpolation of its projections. The initial boundary conditions for spatial spline construction are given in the form of initial derivative vector projections in the initial and the terminal points of the discrete set. The possibility of the solution to the problem of spatial spline construction by planar projections, i.e. reduction of a spatial solution to a planar one, is determined by the projectional properties of the Monge model. An algorithm of construction of a spatial polynomial segment by projectionally defined initial conditions – projections of two points and projections of the initial derivatives in these points – is considered. A solution to a more complex problem – formation of a spatial spline consisting of a number of segments connected under a certain order of smoothness – is proposed on the basis of this algorithm. The validity of the proposed projectional algorithm of spline formation is confirmed on numerical example. The algorithm can be applied in solution to a more general and relevant problem of synthesis of 3D geometric models by their projectional 2D images that is currently lacking complete solution.

Spatial Data Reconstruction via ADMM and Spatial Spline Regression

Reconstructing fine-grained spatial densities from coarse-grained measurements, namely the aggregate observations recorded for each subregion in the spatial field of interest, is a critical problem in many real world applications. In this paper, we propose a novel Constrained Spatial Smoothing (CSS) approach for the problem of spatial data reconstruction. We observe that local continuity exists in many types of spatial data. Based on this observation, our approach performs sparse recovery via a finite element method, while in the meantime enforcing the aggregated observation constraints through an innovative use of the Alternating Direction Method of Multipliers (ADMM) algorithm framework. Furthermore, our approach is able to incorporate external information as a regression add-on to further enhance recovery performance. To evaluate our approach, we study the problem of reconstructing the spatial distribution of cellphone traffic volumes based on aggregate volumes recorded at sparsely scattered base stations. We perform extensive experiments based on a large dataset of Call Detail Records and a geographical and demographical attribute dataset from the city of Milan, and compare our approach with other methods such as Spatial Spline Regression. The evaluation results show that our approach significantly outperforms various baseline approaches. This proves that jointly modeling the underlying spatial continuity and the local features that characterize the heterogeneity of different locations can help improve the performance of spatial recovery.

Análisis geoestadístico del coeficiente de corrección por accesibilidad a núcleos de población en las valoraciones urbanísticas en España

Theoretical analysis of territorial economies has relied on the idea of territory as a space of exchange, in which the distribution of rural land prices is based largely on the income of accessibility. This paper draws from this context, and is based on the study of the correction factor for accessibility (u1) to regulated population centers as defined in the Valuations Regulation of the Spanish Land Law. For this, we have used Geographic Information Systems (GIS), developing two methods of spatial interpolation, Kriging and Spline, which allows the attainment of a continuous surface with the obtained values. The results of the study have allowed an analysis of the spatial distribution of added value position confirming the links between regional imbalances and the level of economic development achieved in each area of the territory.

Adaptive predictive principal components for modeling multivariate air pollution.

Air pollution monitoring locations are typically spatially misaligned with locations of participants in a cohort study, so to analyze pollution-health associations, exposures must be predicted at subject locations. For a pollution measure like PM2.5 (fine particulate matter) comprised of multiple chemical components, the predictive principal component analysis (PCA) algorithm derives a low-dimensional representation of component profiles for use in health analyses. Geographic covariates and spatial splines help determine the principal component loadings of the pollution data to give improved prediction accuracy of the principal component scores. While predictive PCA can accommodate pollution data of arbitrary dimension, it is currently limited to a small number of pre-selected geographic covariates. We propose an adaptive predictive PCA algorithm, which automatically identifies a combination of covariates that is most informative in choosing the principal component directions in the pollutant space. We show that adaptive predictive PCA improves the accuracy of multi-pollutant exposure predictions at subject locations.

Small area estimation under a spatially non-linear model

We describe a methodology for small area estimation of counts that assumes an area-level version of a nonparametric generalized linear mixed model with a mean structure defined using spatial splines. The proposed method represents an alternative to other small area estimation methods based on area level spatial models that are designed for both spatially stationary and spatially non-stationary populations. We develop an estimator for the mean squared error of the proposed small area predictor as well as an approach for testing for the presence of spatial structure in the data and evaluate both the proposed small area predictor and its mean squared error estimator via simulations studies. Our empirical results show that when data are spatially non-stationary the proposed small area predictor outperforms other area level estimators in common use and that the proposed mean squared error estimator tracks the actual mean squared error reasonably well, with confidence intervals based on it achieving close to nominal coverage. An application to poverty estimation using household consumer expenditure survey data from 2011–12 collected by the national sample survey office of India is presented.

Is a matrix exponential specification suitable for the modeling of spatial correlation structures?

This paper investigates the adequacy of the matrix exponential spatial specifications (MESS) as an alternative to the widely used spatial autoregressive models (SAR). To provide as complete a picture as possible, we extend the analysis to all the main spatial models governed by matrix exponentials comparing them with their spatial autoregressive counterparts.We propose a new implementation of Bayesian parameter estimation for the MESS model with vague prior distributions, which is shown to be precise and computationally efficient. Our implementations also account for spatially lagged regressors. We further allow for location-specific heterogeneity, which we model by including spatial splines. We conclude by comparing the performances of the different model specifications in applications to a real data set and by running simulations. Both the applications and the simulations suggest that the spatial splines are a flexible and efficient way to account for spatial heterogeneities governed by unknown mechanisms.

The impact of transit-oriented development (TOD) on residential property prices: the case of Box Hill, Melbourne

Transit-oriented design (TOD) – an increase in density around transit stations – has arisen in many of Australia’s capital cities as a way to encourage mass transit ridership as well as to efficiently utilize the increase in foot and vehicle traffic that transit stations create. However, the implementation of TODs in Melbourne has faced strong opposition due to residents’ perception that the disamenities of a TOD will outweigh the benefits resulting in negative impacts on property prices. This research analyzes the relationship between proximity to a TOD and residential home prices. Results indicate that proximity to a TOD is positively related to property prices, even after controlling for neighborhood factors such as street connectivity and overall land use mix. By testing a variety of transformations of distance, we find that the benefits of TOD proximity extend approximately 1250 m from the Box Hill station. From a methodological standpoint, we find that more flexible treatments of distance variables in spatial autoregressive and spline models produce better model fit and lead to results more in line with urban economic theory.

Mixtures of spatial spline regressions for clustering and classification

Classification and clustering of functional data arise in many areas of modern research. Currently, techniques for performing such tasks have concentrated on applications to univariate functions. Such techniques can be extended to the domain of classifying and clustering bivariate functions (i.e. surfaces) over rectangular domains. This is achieved by combining the current techniques in spatial spline regression (SSR) with finite mixture models and mixed-effects models. As a result, three novel techniques have been developed: spatial spline mixed models (SSMM) for fitting populations of surfaces, mixtures of SSR (MSSR) for clustering surfaces, and MSSR discriminant analysis (MSSRDA) for classification of surfaces. Through simulations and applications to problems in handwritten character recognition, it is shown that SSMM, MSSR, and MSSRDA are effective in performing their desired tasks. It is also shown that in the context of handwritten character recognition, MSSR and MSSRDA are comparable to established methods, and are able to outperform competing approaches in missing-data situations.

Spatial Spline Regression Models

SummaryWe describe a model for the analysis of data distributed over irregularly shaped spatial domains with complex boundaries, strong concavities and interior holes. Adopting an approach that is typical of functional data analysis, we propose a spatial spline regression model that is computationally efficient, allows for spatially distributed covariate information and can impose various conditions over the boundaries of the domain. Accurate surface estimation is achieved by the use of piecewise linear and quadratic finite elements.

The position control of a spatial binary hyper redundant manipulator through its inverse kinematics

This article is about the position control of a binary hyper redundant manipulator, which is driven by pneumatic on-off actuators. The end platform of the binary hyper redundant manipulator bears a small fine tuning manipulator, which is a continuously actuated six-joint manipulator attached as a versatile error-compensation tool. It is employed to compensate especially the discretization errors. The position control aims to make the end-effector of the fine tuning manipulator track a specified sequence of successive poses as required by the task to be performed. This aim is achieved by solving the inverse kinematics problem of the binary hyper redundant manipulator, i.e. by determining the binary positions of the on-off actuators, so that the end platform of the binary hyper redundant manipulator enters the inverted working volume of the fine tuning manipulator for each specified target pose of the end effector. As to solve the inverse kinematics problem of the binary hyper redundant manipulator, three methods are presented. They are the plain spline fitting method, the extended spline fitting method, and the workspace filling method. The plain spline fitting method is based on forcing the actual backbone curve of the binary hyper redundant manipulator to approximate a spatial reference spline which is specified as the desired backbone curve. In the extended spline fitting method, the result found in the plain spline fitting method is improved by using a genetic algorithm. In the workspace filling method, the workspace of the binary hyper redundant manipulator is filled randomly with a sufficiently large finite number of discrete configurational samples. If it is desired to have a concentration on a particular region of the workspace, then that region is filled by using a genetic algorithm. After the filling stage, the sample closest to the desired configuration is determined by a suitable searching algorithm. The three methods are demonstrated and comparatively discussed by means of several examples.

Solving reachable workspace of some parallel manipulators by computer-aided design variation geometry

To shape the workspace of some novel parallel manipulators (PMs) is significant. A novel computer-aided design (CAD) variation geometry approach is proposed to shape and solve the reachable workspace of some PMs with three to six degrees of freedom (DOFs). Some basic techniques are described for designing the simulation mechanism and solving the reachable workspace. The simulation mechanisms of some PMs with three to six DOFs are created. When varying the driving dimensions of the active legs in the given extent, the simulation mechanisms vary correspondingly, and the position components of the moving platform are solved automatically. By transferring the position solutions into spatial spline curves in the simulation mechanism, all the boundary surfaces of the workspace can be created and visualized dynamically. Comparing with analytic approaches for solving workspace, the CAD variation geometry approach is simple, straightforward, accurate, and repeatable.