This study introduces the network weight matrix as a replacement for the spatial weight matrix to measure the spatial dependence between links of a network. This matrix stems from the concepts of betweenness centrality and vulnerability in network science. The elements of the matrix are a function not simply of proximity, but of network topology, network structure, and demand configuration. The network weight matrix has distinctive characteristics, which are capable of reflecting spatial dependence between traffic links: (1) elements are allowed to have negative and positive values capturing the competitive and complementary nature of links, (2) diagonal elements are not fixed to zero, which takes the self-dependence of a link upon itself into consideration, and (3) elements not only reflect the spatial dependence based on the network structure, but they acknowledge the demand configuration as well. We verify the network weight matrix by modeling traffic flows in a 3 × 3 grid test network with 9 nodes and 24 directed links connecting 72 origin-destination (OD) pairs. Models encompassing the network weight matrix outperform both models without spatial components and models with the spatial weight matrix. The network weight matrix represents a more accurate and defensible spatial dependency between traffic links, and offers the potential to augment traffic flow prediction.

Geographically weighted regression (GWR) is a technique that explores spatial nonstationarity in data-generating processes by allowing regression coefficients to vary spatially. It is a widely applied technique across domains because it is intuitive and conforms to the well-understood framework of regression. An alternative method to GWR that has been suggested is spatial filtering, which it has been argued provides a superior alternative to GWR by producing spatially varying regression coefficients that are not correlated with each other and which display less spatial autocorrelation. It is, therefore, worthwhile to examine these claims by comparing the output from both methods. We do this by using simulated data that represent two sets of spatially varying processes and examining how well both techniques replicate the known local parameter values. The article finds no support that spatial filtering produces local parameter estimates with superior properties. The results indicate that the original spatial filtering specification is prone to overfitting and is generally inferior to GWR, while an alternative specification that minimizes the mean square error (MSE) of coefficient estimates produces results that are similar to GWR. However, since we generally do not know the true coefficients, the MSE minimizing specification is impractical for applied research.

The placement of facilities according to spatial and/or geographic requirements is a popular problem within the domain of location science. Objectives that are typically considered in this class of problems include dispersion, median, center, and covering objectives—and are generally defined in terms of distance or service-related criteria. With few exceptions, the existing models in the literature for these problems only accommodate one type of facility. Furthermore, the literature on these problems does not allow for the possibility of multiple placement zones within which facilities may be placed. Due to the unique placement requirements of different facility types—such as suitable terrain that may be considered for placement and specific placement objectives for each facility type—it is expected that different suitable placement zones for each facility type, or groups of facility types, may differ. In this article, we introduce a novel mathematical treatment for multi-type, multi-zone facility location problems. We derive multi-type, multi-zone extensions to the classical integer-linear programming formulations involving dispersion, centering and maximal covering. The complexity of these formulations leads us to follow a heuristic solution approach, for which a novel multi-type, multi-zone variation of the non-dominated sorting genetic algorithm-II algorithm is proposed and employed to solve practical examples of multi-type, multi-zone facility location problems.

The p-regions is a mixed integer programming (MIP) model for the exhaustive clustering of a set of n geographic areas into p spatially contiguous regions while minimizing measures of intraregional heterogeneity. This is an NP-hard problem that requires a constant research of strategies to increase the size of instances that can be solved using exact optimization techniques. In this article, we explore the benefits of an iterative process that begins by solving the relaxed version of the p-regions that removes the constraints that guarantee the spatial contiguity of the regions. Then, additional constraints are incorporated iteratively to solve spatial discontinuities in the regions. In particular we explore the relationship between the level of spatial autocorrelation of the aggregation variable and the benefits obtained from this iterative process. The results show that high levels of spatial autocorrelation reduce computational times because the spatial patterns tend to create spatially contiguous regions. However, we found that the greatest benefits are obtained in two situations: (1) when ; and (2) when the parameter p is close to the number of clusters in the spatial pattern of the aggregation variable.

The most common indicator used to measure spatial dependence is Moran's I proposed by statistician Patrick A. P. Moran in 1950. The index is simple to use and applies the principle of the Pearson correlation coefficient, although it incorporates a proximity measure between elements. However, Moran's I tends to underestimate real spatial autocorrelation when the number of locations are few. This study aims to present a modified version of Moran's I that can measure real spatial autocorrelation even with small samples and check for spatial dependence.

Zipf's rank-size rule, lognormal distribution, and Gibrat's urban growth models are considered as summarizing fundamental properties of systems of cities. In this article, they are used as statistical benchmarks for comparing the shapes of urban hierarchies and evolutionary trends of seven systems of cities in the world including BRICS, Europe, and United States. In order to provide conclusions that avoid the pitfalls of too small samples or uncontrolled urban definitions, these models are tested on some 20,000 urban units whose geographically significant delineations were harmonized in each country over 50 years between 1960 and 2010. As a result, if the models appear not always statistically valid, their usefulness is confirmed since the observed deviations from empirical data remain limited and can often be interpreted from the geohistorical context of urbanism proper to each world region. Moreover, the article provides new free software which authorizes the reproducibility of our experiments with our data bases as well as with complementary data.

This article presents a method for investigating the spatial distribution of vehicle and pedestrian traffic crashes relative to the volume of vehicle and pedestrian movement in urban areas. This method consists of two phases. First, vehicle and pedestrian traffic volumes on the street network are modeled using a space syntax configurational analysis of the network, land use data, and observed traffic data. Second, crash prediction models are fitted to the traffic crash data, using negative binomial regression models and based on traffic volume estimates and street segment lengths. The method was applied in two areas in Tel Aviv, Israel, which differ in their morphological and traffic characteristics. The case-studies illustrated the method's capability in identifying hazardous locations on the network and examining relative crash risks. The analysis shows that an increase in vehicle or pedestrian traffic volume tends to be associated with a decrease in relative crash risk. Moreover, the spatial patterns of relative crash risks are associated with the design characteristics of urban space: areas characterized by dense street networks encourage more walking, and are generally safer for pedestrians, while those with longer street segments encourage more driving, are less safe for pedestrians, but safer for vehicles.