Uncertainty in the effects of the modifiable areal unit problem under different levels of spatial autocorrelation: a simulation study

ABSTRACT

The objective of this paper is to investigate uncertainties surrounding relationships between spatial autocorrelation (SA) and the modifiable areal unit problem (MAUP) with an extensive simulation experiment. Especially, this paper aims to explore how differently the MAUP behaves for the level of SA focusing on how the initial level of SA at the finest spatial scale makes a significant difference to the MAUP effects on the sample statistics such as means, variances, and Moran coefficients (MCs). The simulation experiment utilizes a random spatial aggregation (RSA) procedure and adopts Moran spatial eigenvectors to simulate different SA levels. The main findings are as follows. First, there are no substantive MAUP effects for means. However, the initial level of SA plays a role for the zoning effect, especially when extreme positive SA is present. Second, there is a clear and strong scale effect for the variances. However, the initial SA level plays a non-negligible role in how this scale effect deploys. Third, the initial SA level plays a crucial role in the nature and extent of the MAUP effects on MCs. A regression analysis confirms that the initial SA level makes a substantial difference to the variability of the MAUP effects.     

空间自相关的可塑性面积单元问题效应

可塑性面积单元问题(modifiable areal unit problem,MAUP) 效应是对空间数据分析结果产生不确定性影响的主要原因之一,在空间自相关分析中也不例外.本文分别利用网格模拟数据和中国人均GDP实例数据为数据源,以全局Moran's I 系数来探究空间自相关统计中的MAUP效应,分析结果表明,变量的空间自相关程度依赖于空间的粒度大小与单元的划分方法,但空间单元的变化与自相关性并不存在某种函数关系.因此,在进行空间自相关研究时必须选择合适的地理单元的粒度大小和分区.最后本文给出一种基于地统计内插方法来降低MAUP对空间自相关分析影响.     

Changes in the residential segregation of immigrants in Sweden from 1990 to 2012: Using a multi-scalar segregation measure that accounts for the modifiable areal unit problem

In this paper, the levels of residential segregation of immigrants in Sweden during the years 1990, 1997, 2005, and 2012 are calculated. This paper applies a novel method for calculating segregation that is multi-scalar and addresses the modifiable areal unit problem (MAUP). The level of segregation is evaluated for each populated location by identifying the population that includes the k-nearest neighbours. The share of immigrants in this assessment population is then compared to the share in the reference population that comprises the K-nearest neighbours. One of the strengths of this method is the possibility to modify the reference population, thus making it possible to measure the difference in the results due to the size of the reference population. This study demonstrates that the results can considerably differ depending on which reference population is used. Furthermore, this study indicates that using different reference areas can produce completely different trends over time, such as decreasing or increasing segregation. The results demonstrate a general increase in segregation between 1990 and 1997, followed by a more complex pattern from 1997 to 2012. The segregation values are presented for all populated locations in Sweden, and population-weighted means are calculated for the whole of Sweden, in addition to the Stockholm, Malmö, and Gothenburg metropolitan areas.     

Evaluating representation and scale error in the maximal covering location problem using GIS and intelligent areal interpolation

A common problem in location-allocation modeling is the error associated with the representation and scale of demand. Numerous researchers have investigated aggregation errors associated with using different scaled data, and more recently, error associated with the geographic representation of model objects has also been studied. For covering problems, the validity of using polygon centroid representations of demand has been questioned by researchers, but the alternative has been to assume that demand is uniformly distributed within areal units. The spatial heterogeneity of demand within areal units thus has been modeled using one of two extremes – demand is completely concentrated at one location or demand is uniformly distributed. This article proposes using intelligent areal interpolation and geographic information systems to model the spatial heterogeneity of demand within spatial units when solving the maximal covering location problem. The results are compared against representations that assume demand is either concentrated at centroids or uniformly distributed. Using measures of scale and representation error, preliminary results from the test study indicate that for smaller scale data, representation has a substantial impact on model error whereas at larger scales, model error is not that different for the alternative representations of the distribution of demand within areal units.     

Exploratory analysis of the interrelations between co-located boolean spatial features using network graphs

Visual data mining of spatial data is a challenging task. As exploratory analysis is fundamental, it is beneficial to explore the data using different potential visualisations. In this article, we propose and analyse network graphs as a useful visualisation tool to mine spatial data. Due to their ability to represent complex systems of relationships in a visually insightful and intuitive way, network graphs offer a rich structure that has been recognised in many fields as a powerful visual representation. However, they have not been sufficiently exploited in spatial data mining, where they have principally been used on data that come with an explicit pre-specified network graph structure. This research presents a methodology with which to infer relationship network graphs for large collections of boolean spatial features. The methodology consists of four principal stages: (1) define a co-location model, (2) select the type of co-association of interest, (3) compute statistical diagnostics for these co-associations and (4) construct and visualise a network graph of the statistic from step (3). We illustrate the potential usefulness of the methodology using an example taken from an ecological setting. Specifically, we use network graphs to understand and analyse the potential interactions between potential vector and reservoir species that enable the propagation of leishmaniasis, a disease transmitted by the bite of sandflies.     

The impact of spatial scale: exploring urban butterfly abundance and richness patterns using multi-criteria decision analysis and principal component analysis

ABSTRACT

Modelling changes in biodiversity have become a necessary component of smart urban planning practices. However, concepts such as biodiversity are often evaluated using area-based composite indices, the results of which are heavily reliant on specific parameters chosen. This paper explores the design and implementation of a butterfly biodiversity index by comparing two widely accepted modelling techniques: principal component analysis and spatial multi-criteria decision analysis (MCDA). A high degree of scale dependency has been demonstrated in previous studies exploring the use of area-based composite measures. To evaluate the impact of scale, each model was assessed at two different spatial resolutions. The outcomes were analyzed, mapped and compared using ordinary least squares, geographically weighted regression and global Moran’s I to evaluate relative biodiversity patterns across the City of Toronto, Canada. Findings indicate that the impact of spatial scale was significant, whereby the coarser resolution models were found to be more highly correlated with biodiversity, compared to the finer resolution models. The results of this study contribute to a growing body of literature that explores key conceptual questions regarding the robustness of GIS-based MCDA, the impact of scale in urban ecology studies, and the use of composite indices to manage spatial ecological data.     

The scale effects of the spatial autocorrelation measurement: aggregation level and spatial resolution

The scale effects of the spatial autocorrelation (SA) measurement has been explored for decades. However, the effects of the data aggregation levels and spatial resolution on the SA measurement are often confused. Whether the two types of scale effects are the same is still unclear and requires further investigation. We retrieved the land surface temperature (LST) from Landsat 8 images in 30 capital cities of China. By aggregating the LST images, we observed a decrease in the SA of the LST as the data aggregation level increased; this relationship can be fitted well with a negative logarithmic function. We derived an indicator to measure the scale effects intensity of SA, which was negatively correlated with the spatial complexity of LST. Both aggregating images and the increasing spatial resolution induce weaker SA, but the effect of the former was stronger. The aggregating images negatively affected the SA degree regardless of the spatial resolutions of the original images. The SA degrees of the aggregated images were far below those of the real-life images. This study suggests that the scale effects caused by aggregation levels and spatial resolutions are different, and cautions should be taken when applying relevant conclusions derived from aggregating images.     

栅格数字地形分析中的尺度问题研究方法

栅格数字高程模型（DEM）固有的尺度特征给以栅格DEM为基本输入的数字地形分析带来各种尺度问题。对栅格数字地形分析中涉及的尺度进行梳理,以分辨率和分析窗口为重点,对栅格数字地形分析中的多尺度表达、尺度效应、适宜尺度选择、尺度转换等尺度问题及其相互关系进行阐述;分别介绍各类尺度问题的现有定量研究方法,尤其对尺度效应定量刻画和适宜尺度选择方法,根据不同方法计算定量指标所利用的信息类别进行分类归纳;最后讨论了其中有待进一步开展研究的几方面工作。     

长江经济带空气质量指数的时空特征及驱动因素分析 ——基于贝叶斯空间计量模型的实证

基于2015年长江经济带126个城市空气质量监测数据,首先利用探索性空间数据分析方法揭示了空气质量指数（AQI）的时空演变特征,然后采用贝叶斯空间滞后模型探讨了长江经济带空气质量指数的社会经济驱动因素。研究结果表明：① 长江经济带年AQI在空间上整体具有东高西低,长江以北高长江以南低的分布特点,具有明显的空间集聚特征。空气污染严重的热点地区主要集中长三角城市群的江苏省、浙北地区、皖北大部分地区以及上海市。空气质量较好的冷点地区则主要集中在云南省、四川的攀枝花以及贵州的大部分地区。② 长江经济带AQI在季节上呈现冬春高、夏秋低的季节变化趋势。总体而言,四季的高值集聚主要分布在鄂皖苏,低值集聚主要分布在云贵地区。③ 贝叶斯空间滞后模型回归结果显示,长江经济带空气质量存在显著的空间溢出效应。此外,模型结果证实了“环境库兹涅兹曲线”假说;FDI回归系数为正,支持了“污染避难所”假说;人口密度、公路客运量均是导致空气污染加剧的重要因素,而第三产业比重和建成区绿化覆盖率增加有利于长江经济带空气质量的改善。     

2000年以来中国对美国直接投资的时空演变

2000年以来,随着中国外向型经济的快速发展,以及中美经贸合作伙伴关系的不断深化,中国 对美国直接投资规模持续扩大,至2012年,美国已成为接收中国对外直接投资最大的国家。利用地理集中指数和空间自相关,以美国50个州和哥伦比亚特区为研究单元,分析2000-2014年中国对美国直接投资的时空演变过程及发展趋势。结果表明：①2000年以来COFDI在美国地域分布的不平衡程度有所下降,整体逐渐趋向均衡;②美国吸收COFDI的区域差异较大,南部地区总量领先但增速较慢,东北部、中西部、西部地区实力平均但增速较快,整体差距逐渐缩小;③在空间分布上,呈现由沿海向内陆,由南部向中西部扩散的趋势,表现为“以点带线,多点成面”的时空演化过程;④总体来看,COFDI的空间分布存在较弱的空间自相关性,集聚程度尚不显著,呈现“集聚--随机分布--离散”的空间形态,局部区域形成“冷、热区”的分化。     

基于地理信息系统的2009-2013年甲型H1N1流感的时空分析

甲型H1N1流感作为一种人群普遍易感的急性传染病,自2009年爆发以来,不仅对人类健康造成了危害,也给全球经济造成了巨大损失。为研究中国大陆地区2009年来甲型H1N1流感疫情的时空分布特征,以中国大陆地区31个省级行政区2009-2013年甲型H1N1流感发病率的时空数据为研究对象,采用空间自相关分析技术和季节性分析方法进行了较为全面的空间和时间分析。结果表明：甲型H1N1流感的发病率在空间上和时间上都具有较强的聚集性。空间上,甲流发病高值热点有从新疆、青海和甘肃等西北部地区逐渐南移至中国东南部沿海省份的趋势,且高发聚集省份有增多的趋势;时间上,每年10月至次年4月是中国甲流的高发时段,且在此期间空间上也存在较强的聚集性。     

1991-2012年大陆台资不同类型制造业的时空格局演化

台商投资可促进大陆产业升级和两岸关系稳定。基于1991—2012年台商对大陆制造业直接投资数据,将大陆台资制造业细分成劳动密集型产业、资金密集型产业、技术密集型产业,分析其时空扩散特征,并用灰色关联方法探讨台资制造业时空格局演化的影响要素。结果表明:1大陆台资制造业行业结构有明显的阶段变化,与岛内产业结构调整密切相关;2大陆台资制造业空间分布表现出集聚与扩散并存,在集聚主导下呈现由南向北、由东向西的扩散态势,并由南部沿海地区的单集聚格局发展为南部与东部沿海地区的双集聚中心,最后演化为东部沿海地区的单集聚中心;3东部沿海地区承接南部沿海地区的三类产业(尤其是技术密集型产业)转移成为高度集聚区,中西部则主要吸引资源型和劳动密集型产业;4不同阶段影响台商对大陆不同类型制造业投资的主导因子不同。