空间自回归模型的局部影响分析和运用

由于空间数据的相依特性，使得通常的删除点诊断异常值的方法不适合采用。为了寻找数据中的异常点和影响点，采用局部影响分析技术，通过引入扰动的方法来发现影响点，最后通过实例说明局部影响分析技术能够有效地发现模型中可能的影响点，并且能够揭示更多的细节信息。     

图解Bootstrap方法用于空间相关性Moran检验的有效性

因为区域间经济收敛、外商直接投资和知识溢出等领域的空间经济计量研究依赖于空间关系的存在,所以进行空间相关性Moran’s I检验是关键。然而,已有空间相关性Moran’s I检验理论受到众多假设条件限制。利用＂名义水平—实际水平＂图和＂名义水平—功效＂图,解析非对称Wild Bootstrap方法用于空间相关性Moran’s I检验的有限样本性质,发现即使模型不满足经典的分布假设条件,与渐近检验相比,Bootstrap方法也能够有效地检验研究对象间的空间相关性。     

Investigating emergent nested geographic structure in consumer purchases: a Bayesian dynamic multi-scale spatiotemporal modeling approach

Spatial modeling of consumer response data has gained increased interest recently in the marketing literature. In this paper, we extend the (spatial) multi-scale model by incorporating both spatial and temporal dimensions in the dynamic multi-scale spatiotemporal modeling approach. Our empirical application with a US company’s catalog purchase data for the period 1997–2001 reveals a nested geographic market structure that spans geopolitical boundaries such as state borders. This structure identifies spatial clusters of consumers who exhibit similar spatiotemporal behavior, thus pointing to the importance of emergent geographic structure, emergent nested structure and dynamic patterns in multi-resolution methods. The multi-scale model also has better performance in estimation and prediction compared with several spatial and spatiotemporal models and uses a scalable and computationally efficient Markov chain Monte Carlo method that makes it suitable for analyzing large spatiotemporal consumer purchase datasets.KEYWORDS: Clustering, dynamic linear models, empirical Bayes methods, Markov chain Monte Carlo methods, multi-scale modeling, spatial models     

空间数据分析的发展

空间统计学是研究空间问题的一门学科,它是应用数学快速发展的一个分支。尽管传统的数据分析中有许多很好的方法,但却不能完全地套用于空间数据的分析。空间模型的估计不仅与各种回归形式的假设有关,而且还与空间相关、空间异质的特性有关。从空间模型及推断、适应性估计、非参数回归、空间不相关性检验几个方面研究了空间数据分析方法的发展以及未来的趋势。     

BAYESIAN PREDICTION FOR SPATIAL GENERALISED LINEAR MIXED MODELS WITH CLOSED SKEW NORMAL LATENT VARIABLES

Spatial generalised linear mixed models are used commonly for modelling non‐Gaussian discrete spatial responses. In these models, the spatial correlation structure of data is modelled by spatial latent variables. Most users are satisfied with using a normal distribution for these variables, but in many applications it is unclear whether or not the normal assumption holds. This assumption is relaxed in the present work, using a closed skew normal distribution for the spatial latent variables, which is more flexible and includes normal and skew normal distributions. The parameter estimates and spatial predictions are calculated using the Markov Chain Monte Carlo method. Finally, the performance of the proposed model is analysed via two simulation studies, followed by a case study in which practical aspects are dealt with. The proposed model appears to give a smaller cross‐validation mean square error of the spatial prediction than the normal prior in modelling the temperature data set.     

Likelihood Inference for Spatial Generalized Linear Mixed Models

Spatial modeling is widely used in environmental sciences, biology, and epidemiology. Generalized linear mixed models are employed to account for spatial variations of point-referenced data called spatial generalized linear mixed models (SGLMMs). Frequentist analysis of these type of data is computationally difficult. On the other hand, the advent of the Markov chain Monte Carlo algorithm has made the Bayesian analysis of SGLMM computationally convenient. Recent introduction of the method of data cloning, which leads to maximum likelihood estimate, has made frequentist analysis of mixed models also equally computationally convenient. Recently, the data cloning was employed to estimate model parameters in SGLMMs, however, the prediction of spatial random effects and kriging are also very important. In this article, we propose a frequentist approach based on data cloning to predict (and provide prediction intervals) spatial random effects and kriging. We illustrate this approach using a real dataset and also by a simulation study.     

中国区域经济差异空间分异特征及其机理研究

运用全局空间自相关指数、局部空间自相关指数和空间回归模型,从空间依赖性和异质性的角度分析中国区域经济差异空间分异的过程。研究发现:中国经济发达地区和欠发达地区空间集聚格局日趋显著,且东部和中西部区域分别演变成为经济发达地区和欠发达地区的相对集聚区。造成这一分异现象的成因是各种内生因子和宏观经济环境因子的区域间差异及其循环累积作用、空间自相关性的空间近邻效应及极化——涓滴效应。     

Outliers detection in multivariate spatial linear models

In geostatistics, detecting atypical observations is of special interest due to the changes they can cause in environmental and geological patterns. Several methods for detecting them have been already suggested for the univariate spatial case. However, the problem is more complicated when various variables are observed simultaneously and the spatial correlation among them must be taken into account. The aim of this paper is to detect outliers and influential observations in multivariate spatial linear models. For this purpose, we derive and explore two different methods. First, a multivariate version of the forward search algorithm is given, where locations with outliers are detected in the last steps of the procedure. Next, we derive influence measures to assess the impact of the observations on the multivariate spatial linear model. The procedures are easy to compute and to interpret by means of graphical representations. Finally, an example and a Monte Carlo study illustrate the performance of these methods for identification of outliers in multivariate spatial linear models.     

Testing for Spatial Isotropy Under General Designs

Spatial modeling is typically composed of a specification of a mean function and a model for the correlation structure. A common assumption on the spatial correlation is that it is isotropic. This means that the correlation between any two observations depends only on the distance between those sites and not on their relative orientation. The assumption of isotropy is often made due to a simpler interpretation of correlation behavior and to an easier estimation problem under an assumed isotropy. The assumption of isotropy, however, can have serious deleterious effects when not appropriate. In this paper we formulate a test of isotropy for spatial observations located according to a general class of stochastic designs. Distribution theory of our test statistic is derived and we carry out extensive simulations which verify the efficacy of our approach. We apply our methodology to a data set on longleaf pine trees from an oldgrowth forest in the southern United States.     

Estimation in a semiparametric panel data model with nonstationarity

In this paper, we consider a partially linear panel data model with nonstationarity and certain cross-sectional dependence. Accounting for the explosive feature of the nonstationary time series, we particularly employ Hermite orthogonal functions in this study. Under a general spatial error dependence structure, we then establish some consistent closed-form estimates for both the unknown parameters and the unknown functions for the cases where N and T go jointly to infinity. Rates of convergence and asymptotic normalities are established for the proposed estimators. Both the finite sample performance and the empirical applications show that the proposed estimation methods work well.     

A comparison of centring parameterisations of Gaussian process-based models for Bayesian computation using MCMC

Markov chain Monte Carlo (MCMC) algorithms for Bayesian computation for Gaussian process-based models under default parameterisations are slow to converge due to the presence of spatial- and other-induced dependence structures. The main focus of this paper is to study the effect of the assumed spatial correlation structure on the convergence properties of the Gibbs sampler under the default non-centred parameterisation and a rival centred parameterisation (CP), for the mean structure of a general multi-process Gaussian spatial model. Our investigation finds answers to many pertinent, but as yet unanswered, questions on the choice between the two. Assuming the covariance parameters to be known, we compare the exact rates of convergence of the two by varying the strength of the spatial correlation, the level of covariance tapering, the scale of the spatially varying covariates, the number of data points, the number and the structure of block updating of the spatial effects and the amount of smoothness assumed in a Matérn covariance function. We also study the effects of introducing differing levels of geometric anisotropy in the spatial model. The case of unknown variance parameters is investigated using well-known MCMC convergence diagnostics. A simulation study and a real-data example on modelling air pollution levels in London are used for illustrations. A generic pattern emerges that the CP is preferable in the presence of more spatial correlation or more information obtained through, for example, additional data points or by increased covariate variability.     

Decomposition of Variance for Spatial Cox Processes

Abstract. Spatial Cox point processes is a natural framework for quantifying the various sources of variation governing the spatial distribution of rain forest trees. We introduce a general criterion for variance decomposition for spatial Cox processes and apply it to specific Cox process models with additive or log linear random intensity functions. We moreover consider a new and flexible class of pair correlation function models given in terms of normal variance mixture covariance functions. The proposed methodology is applied to point pattern data sets of locations of tropical rain forest trees.     

A close look at the spatial structure implied by the CAR and SAR models

Modeling spatial interactions that arise in spatially referenced data is commonly done by incorporating the spatial dependence into the covariance structure either explicitly or implicitly via an autoregressive model. In the case of lattice (regional summary) data, two common autoregressive models used are the conditional autoregressive model (CAR) and the simultaneously autoregressive model (SAR). Both of these models produce spatial dependence in the covariance structure as a function of a neighbor matrix W and often a fixed unknown spatial correlation parameter. This paper examines in detail the correlation structures implied by these models as applied to an irregular lattice in an attempt to demonstrate their many counterintuitive or impractical results. A data example is used for illustration where US statewide average SAT verbal scores are modeled and examined for spatial structure using different spatial models.     

Geostatistical Analysis Through Spectral Techniques: Some Words of Caution

Tapering is a technique proposed in order to avoid the so-called edge-effects in spectral estimation. Recent literature has emphasised the importance of tapering for spectral methods applied to the analysis of spatial dependence. In this work we show, through applications and an extensive simulation study, that tapering can be very dangerous if it is not used with caution. An interesting aspect of spectral estimation arises in the presence of a nugget effect in the spatial structure.     

Outlier Robust Small‐Area Estimation Under Spatial Correlation

Modern systems of official statistics require the estimation and publication of business statistics for disaggregated domains, for example, industry domains and geographical regions. Outlier robust methods have proven to be useful for small‐area estimation. Recently proposed outlier robust model‐based small‐area methods assume, however, uncorrelated random effects. Spatial dependencies, resulting from similar industry domains or geographic regions, often occur. In this paper, we propose an outlier robust small‐area methodology that allows for the presence of spatial correlation in the data. In particular, we present a robust predictive methodology that incorporates the potential spatial impact from other areas (domains) on the small area (domain) of interest. We further propose two parametric bootstrap methods for estimating the mean‐squared error. Simulations indicate that the proposed methodology may lead to efficiency gains. The paper concludes with an illustrative application by using business data for estimating average labour costs in Italian provinces.     

Spatial Modeling of Habitat Preferences of Biological Species using Markov Random Fields

Spatial modeling has gained interest in ecology during the past two decades, especially in the area of biodiversity, where reliable distribution maps are required. Several methods have been proposed to construct distribution maps, most of them acknowledging the presence of spatial interactions. In many cases, a key problem is the lack of true absence data. We present here a model suitable for use when true absence data are missing. The quality of the estimates obtained from the model is evaluated using ROC curve analysis as well as a quadratic cost function, computed from the false positive and false negative error rates. The model is also tested under random and clustered scattering of the presence records. We also present an application of the model to the construction of distribution maps of two endemic bird species in México.     

空气质量对生活满意度的效应研究——基于序数分层空间自回归Probit模型

在居民生活满意度的相关研究中,除考虑人口学特征外,越来越多的实证同时考虑了微观个体所处的宏观环境,对这类呈嵌套结构的分层数据需构建分层统计模型,但传统的分层统计模型未考虑真实的空间依赖。本文将分层统计模型和空间自回归模型相结合,创新性地构建了四种序数分层空间自回归Probit模型,该类模型能够合理地对因变量为序数且存在空间依赖情况并呈分层结构的数据进行建模,模型可避免忽略真实的空间依赖对模型估计的不利影响,且能够对高层组间的空间效应和低层个体间的空间效应区别对待,更有利于模型的解释。最后,空气质量对居民生活满意度的效应实证研究表明:空气质量确实能够对生活满意度产生影响,居民对空气质量的认识和要求并非孤立地局限于本地,而是对一个区域空气质量的空间综合结果。对比2018年和2016年模型结果可知:空气质量的福利效应无法被其他民生福祉因素所取代,并且随着空气质量相关统计信息的高度开放和广泛传播,居民更加重视空气质量,也形成了更加全局的了解。     

Robust Test for Spatial Error Model: Considering Changes of Spatial Layouts and Distribution Misspecification

This article suggests a robust LM (Lagrange Multiplier) test for spatial error model which not only reduces the influence of spatial lag dependence immensely, but also presents robust changes of spatial layouts and distribution misspecification. Monte Carlo simulation results imply that existing LM tests have serious size and power distortion with the presence of spatial lag dependence, group interaction or nonnormal distribution, but the robust LM test of this article shows well performance.     

区域差异导致经济块状发展的空间机理研究

 本文运用空间计量经济学模型以及修正绝对β收敛回归模型,对中国2003—2007年省域经济发展的集聚性与差异性进行研究发现：中国31个省域之间存在着较强的空间集聚和空间依赖性,虽受到地域限制,但集聚辐射区域有逐步扩大的趋势;固定资产投入、人均实际工资以及城镇化率对于区域经济集聚的发展起到稳健的推动作用,FDI对集聚区域发展的促进作用也越加显著,但是财政投入却在一定层度上遏制了块状经济的发展。另外,修正和传统收敛模型均显示,2003-2007年我国经济整体发展呈现明显的不收敛特性。     

A gm estimation of the location parameters in a spatial linear model

Universal kriging is a form of interpolation that takes into account the local trends in data when minimizing the error associated with the estimator. Under multivariate normality assumptions, the given predictor is the best linear unbiased predictor. but if the underlying distribution is not normal, the estimator will not be unbiased and will be vulnerable to outliers. With spatial data, it is not only the presence of outliers that may spoil the predictions, but also the boundary sites. usually corners, that tend to have high leverage. As an alternative, a weighted one-step generalized M estimator of the location parameters in a spatial linear model is proposed. It is especially recommended in the case of irregularly spaced data.