Local linear spatial quantile regression

High-Dimensional Spatial Quantile Function-on-Scalar Regression

This article develops a novel spatial quantile function-on-scalar regression model, which studies the conditional spatial distribution of a high-dimensional functional response given scalar predictors. With the strength of both quantile regression and copula modeling, we are able to explicitly characterize the conditional distribution of the functional or image response on the whole spatial domain. Our method provides a comprehensive understanding of the effect of scalar covariates on functional responses across different quantile levels and also gives a practical way to generate new images for given covariate values. Theoretically, we establish the minimax rates of convergence for estimating coefficient functions under both fixed and random designs. We further develop an efficient primal-dual algorithm to handle high-dimensional image data. Simulations and real data analysis are conducted to examine the finite-sample performance.

Spatial heterogeneity analysis of macro-level crashes using geographically weighted Poisson quantile regression

In recent years, globally quantile-based model (e.g. quantile regression) and spatially conditional mean models (e.g. geographically weighted regression) have been widely and commonly employed in macro-level safety analysis. The former ones assume that the model coefficients are fixed over space, while the latter ones only represent the entire distribution of variable effects by a single concentrated trend. However, the influence of crash related factors on the distribution of crash frequency is observed to vary over space and across different quantiles. Therefore, a geographically weighted Poisson quantile regression (GWPQR) model is employed to investigate the spatial heterogeneity of variable effects crossing different quantiles. Five categories, including exposure, socio-economic, transportation, network and land use were selected to estimate the spatial effects on crash frequency. In the case study, vehicle related crashes collected in New York City were used to validate the predicted performance of the proposed models. The results show that the GWPQR outperforms the NB, QR and GWNBR for modeling the skewed distribution, reconstructing the crash distribution and capturing the unobserved spatial heterogeneity. Additionally, the significant coefficients are further used to classify all 21 variables into key, important and general parts. Then we discuss how these factors affects the regional crashes over space and distribution of crash frequency. This study confirms that the influencing factors have varying effects on different quantiles of distribution and on different regions, which could be helpful to provide support for making safety countermeasures and policies at urban regional level.

Asymmetric and Spatial Non-Stationary Effects of Particulate Air Pollution on Urban Housing Prices in Chinese Cities

Fine particulate matter(PM2.5) pollution will affect people’s well-being and cause economic losses. It is of great value to study the impact of PM2.5 on the real estate market. While previous studies have examined the effects of PM2.5 pollution on urban housing prices, there has been little in-depth research on these effects, which are spatially heterogeneous at different conditional quantiles. To address this issue, this study employs quantile regression (QR) and geographically weighted quantile regression (GWQR) models to obtain a full account of asymmetric and spatial non-stationary effects of PM2.5 pollution on urban housing prices through 286 Chinese prefecture-level cities for 2005–2013. Considerable differences in the data distributions and spatial characteristics of PM2.5 pollution and urban housing prices are found, indicating the presence of asymmetric and spatial non-stationary effects. The quantile regression results show that the negative influences of PM2.5 pollution on urban housing prices are stronger at higher quantiles and become more pronounced with time. Furthermore, the spatial relationship between PM2.5 pollution and urban housing prices is spatial non-stationary at most quantiles for the study period. A negative correlation gradually dominates in most of the study areas. At higher quantiles, PM2.5 pollution is always negatively correlated with urban housing prices in eastern coastal areas and is stable over time. Based on these findings, we call for more targeted approaches to regional real estate development and environmental protection policies.

Spatially Modeling the Effects of Meteorological Drivers of PM2.5 in the Eastern United States via a Local Linear Penalized Quantile Regression Estimator

Fine particulate matter (PM_2.5) poses a significant risk to human health, with long-term exposure being linked to conditions such as asthma, chronic bronchitis, lung cancer, atherosclerosis, etc. In order to improve current pollution control strategies and to better shape public policy, the development of a more comprehensive understanding of this air pollutant is necessary. To this end, this work attempts to quantify the relationship between certain meteorological drivers and the levels of PM_2.5. It is expected that the set of important meteorological drivers will vary both spatially and within the conditional distribution of PM_2.5 levels. To account for these characteristics, a new local linear penalized quantile regression methodology is developed. The proposed estimator uniquely selects the set of important drivers at every spatial location and for each quantile of the conditional distribution of PM_2.5 levels. The performance of the proposed methodology is illustrated through simulation, and it is then used to determine the association between several meteorological drivers and PM_2.5 over the Eastern United States (US). This analysis suggests that the primary drivers throughout much of the Eastern US tend to differ based on season and geographic location, with similarities existing between "typical" and "high" PM_2.5 levels.

Quantile regression and Bayesian cluster detection to identify radon prone areas

Albeit the dominant source of radon in indoor environments is the geology of the territory, many studies have demonstrated that indoor radon concentrations also depend on dwelling-specific characteristics. Following a stepwise analysis, in this study we propose a combined approach to delineate radon prone areas. We first investigate the impact of various building covariates on indoor radon concentrations. To achieve a more complete picture of this association, we exploit the flexible formulation of a Bayesian spatial quantile regression, which is also equipped with parameters that controls the spatial dependence across data. The quantitative knowledge of the influence of each significant building-specific factor on the measured radon levels is employed to predict the radon concentrations that would have been found if the sampled buildings had possessed standard characteristics. Those normalised radon measures should reflect the geogenic radon potential of the underlying ground, which is a quantity directly related to the geological environment. The second stage of the analysis is aimed at identifying radon prone areas, and to this end, we adopt a Bayesian model for spatial cluster detection using as reference unit the building with standard characteristics. The case study is based on a data set of more than 2000 indoor radon measures, available for the Abruzzo region (Central Italy) and collected by the Agency of Environmental Protection of Abruzzo, during several indoor radon monitoring surveys.

Asymptotics of nonparametric L-1 regression models with dependent data

We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence structure that allows for longitudinal data and some spatially correlated data, we establish uniform Bahadur representations for the proposed median quantile estimates. The obtained Bahadur representations provide deep insights into the asymptotic behavior of the estimates. Our main theoretical development is based on studying the modulus of continuity of kernel weighted empirical process through a coupling argument. Progesterone data is used for an illustration.

Progress in Spatial Demography

BACKGROUND

Demography is an inherently spatial science, yet the application of spatial data and methods to demographic research has tended to lag that of other disciplines. In recent years, there has been a surge in interest in adding a spatial perspective to demography. This sharp rise in interest has been driven in part by rapid advances in geospatial data, new technologies, and methods of analysis.

OBJECTIVES

We offer a brief introduction to four of the advanced spatial analytic methods: spatial econometrics, geographically weighted regression, multilevel modeling, and spatial pattern analysis. We look at both the methods used and the insights that can be gained by applying a spatial perspective to demographic processes and outcomes. To help illustrate these substantive insights, we introduce six papers that are included in a Special Collection on Spatial Demography. We close with some predictions for the future, as we anticipate that spatial thinking and the use of geospatial data, technology, and analytical methods will change how many demographers address important demographic research questions.

CONCLUSION

Many important demographic questions can be studied and framed using spatial approaches. This will become even more evident as changes in the volume, source, and form of available demographic data-much of it geocoded-further alter the data landscape, and ultimately the conceptual models and analytical methods used by demographers. This overview provides a brief introduction to a rapidly changing field.

On the functional local linear estimate for spatial regression

Consider Z i  = (X i ,Y i ), i ∈ ℤ N be an F×ℝ-valued measurable strictly stationary spatial process, where F is a semi-metric space. We study the spatial covariation between X i and Y i by using the local linear estimate of the functional spatial regression E[Y i |X i ]. The main result of this work is the establishment of the almost complete convergence for the proposed estimator, under some general conditions. We illustrate our methodology by applying the estimator to climatological data.

Geographically Weighted Quantile Regression (GWQR): An Application to U.S. Mortality Data

In recent years, techniques have been developed to explore spatial non-stationarity and to model the entire distribution of a regressand. The former is mainly addressed by geographically weighted regression (GWR), and the latter by quantile regression (QR). However, little attention has been paid to combining these analytical techniques. The goal of this article is to fill this gap by introducing geographically weighted quantile regression (GWQR). This study briefly reviews GWR and QR, respectively, and then outlines their synergy and a new approach, GWQR. The estimations of GWQR parameters and their standard errors, the cross-validation bandwidth selection criterion, and the non-stationarity test are discussed. We apply GWQR to U.S. county data as an example, with mortality as the dependent variable and five social determinants as explanatory covariates. Maps summarize analytic results at the 5, 25, 50, 75, and 95 percentiles. We found that the associations between mortality and determinants vary not only spatially, but also simultaneously across the distribution of mortality. These new findings provide insights into the mortality literature, and are relevant to public policy and health promotion. Our GWQR approach bridges two important statistical approaches, and facilitates spatial quantile-based statistical analyses.

Bayesian Spatial Quantile Regression

Tropospheric ozone is one of the six criteria pollutants regulated by the United States Environmental Protection Agency under the Clean Air Act and has been linked with several adverse health effects, including mortality. Due to the strong dependence on weather conditions, ozone may be sensitive to climate change and there is great interest in studying the potential effect of climate change on ozone, and how this change may affect public health. In this paper we develop a Bayesian spatial model to predict ozone under different meteorological conditions, and use this model to study spatial and temporal trends and to forecast ozone concentrations under different climate scenarios. We develop a spatial quantile regression model that does not assume normality and allows the covariates to affect the entire conditional distribution, rather than just the mean. The conditional distribution is allowed to vary from site-to-site and is smoothed with a spatial prior. For extremely large datasets our model is computationally infeasible, and we develop an approximate method. We apply the approximate version of our model to summer ozone from 1997-2005 in the Eastern U.S., and use deterministic climate models to project ozone under future climate conditions. Our analysis suggests that holding all other factors fixed, an increase in daily average temperature will lead to the largest increase in ozone in the Industrial Midwest and Northeast.