An Experiment to Model Spatial Diffusion Process with Nearest Neighbor Analysis and Regression Estimation

Abstract

Spatial diffusion processes can be seen in many geographic phenomena that spread or migrate across space and over time. Studies of these processes were mostly done with verbal description until Hägerstrand (1966) started to approach it with quantitative models. A variety of attempts were made to continue this effort, but only with various degrees of success. Recognizing the critical role that distances between geographic objects or events play in a spatial diffusion process, we experimented with a new approach that uses these distances to detect and distinguish different types of spatial diffusion processes. Our approach is a two-step process that first calculates nearest neighbor ratios in a point process at each time step and then applies regression curve estimation to observe how these ratios change over time. We first report the results from applying this method to three spatio-temporal data sets which show the feasibility of our approach. We then report results of randomly simulated spatial diffusion processes to see if our approach is effective for the purpose of distinguishing different types of spatial diffusion processes. With only extreme cases as exceptions, our experiment found that using estimated regression curves of nearest neighbor ratios over time is usable in classifying spatial diffusion processes to either contagious/expansion or hierarchical/relocation diffusion processes.

Spatial diffusion of Zika fever epidemics in the Municipality of Salvador-Bahia, Brazil, in 2015-2016: does Zika fever have the same spread pattern as Dengue and Chikungunya fever epidemics?

“…The diffusion through expansion model was identified by Barreto et al (2008) 17 in relation to the first Dengue epidemic in Salvador in 1995, during the emergency period of this arbovirus. Lee et al (2004) 24 identified the same pattern concerning the spatial diffusion of Dengue fever between 2003 and 2008 in Taiwan.…”

“…The Rs are presented as a function of time and modeled with a set of regression curves to find the one that best fits the distribution. The results were interpreted according to Lee et al (2014) 24 . Their approach indicates that the processes of diffusion through contagion and expansion are better adjusted using an inverse curve, and the hierarchical and relocation processes are better modeled using a cubic curve.…”

“…The spatial correlograms presented similar configurations. The NNI analysis technique appeared to be the most robust method of analysis as it was based on a statistical approach that used daily information, was modeled using regression curves, and could be compared to other analyses previously simulated by Lee et al (2008) 24 .…”

Spatial diffusion of the 2015–2016 Zika, dengue and chikungunya epidemics in Rio de Janeiro Municipality, Brazil

“…The point pattern data were analysed by the sequential kernel maps [20] and nearest-neighbour analysis regression [21]. The area data were analysed by global autocorrelation correlogram using Moran's I autocorrelation [22] and local autocorrelation by analysing changes in the local indicators of spatial association (LISA) over time [23].…”

A geo-computational algorithm for exploring the structure of diffusion progression in time and space

“…Point pattern analysis can be classified into distance-based or density-based techniques 1 . Distance-based techniques, such as nearest neighbor analysis, use information on the spacing of points to define a pattern 14 , 15 . Density-based techniques, such as quadrat analysis and kernel density estimation, rely on various characteristics of the frequency distribution of the observed numbers of points in regularly defined sub-regions in the study area 16 , 17 .…”