Location‐Specific Cumulative Distribution Function (LSCDF): An Alternative to Spatial Correlation Analysis

Abstract

Quite often, geographical analysis involves comparing the spatial distributions of two variables or attributes. A typical method isOne of the central themes in geographical analysis is to compare and evaluate the spatial distributions of different phenomena or variables in order to determine if the two phenomena or variables are related to each other. In the physical environment, one may be interested in how the spatial pattern of soil fertility level affects the amount of crop yield in different locations, or how the soil characteristics affect vegetative covers for different regions. In urban analysis, one may be interested if there is an association between income level and the level of education attainment in different parts of the city. In segregation study, the issue quite often is reduced to compare the spatial distribution patterns of different ethnic or racial groups to determine if David WS. Wong is an associate professor of geography at George Mason University.

Segregation as a multiscalar phenomenon and its implications for neighborhood-scale research: the case of South Seattle 1990–2010

“…The utility of aspatial segregation measures thus depends on how meaningful the aggregating unit is. Beginning with Morrill (1991) a rapidly growing literature has proposed new and better mechanisms for incorporating proximate observations into measures of segregation as a means of improving the aggregating unit and consequently the measure of segregation (O’Sullivan & Wong, 2007; Reardon & O’Sullivan, 2004; Wong, 1993, 2003, 2005, 2010; see Wong, Reibel, & Dawkins, 2007 for a recent survey). The measure of spatial segregation that underlies the multi-scale segregation measure employed here was first proposed by Reardon and O’Sullivan (2004).…”

“…Duncan et al (1961) cautioned about the effect of scale on measures of segregation as early as 1961 while the Modifiable Areal Unit Problem (MAUP) addressed by Openshaw and others (Openshaw & Taylor, 1979; Openshaw, 1977) brought the issue of scale and aggregate measurement to a broad audience. These authors and many others were certainly sensitive to the fact that population measures vary with scale, but the issue is regularly addressed as a problem to be solved (through better aggregating units) rather than as a source of information about the processes that affect our units of analysis (O’Sullivan & Wong, 2007; Osth, Malmberg, & Andersson, 2014; Wong, 2010). …”

A Scoping Review on the Multiplicity of Scale in Spatial Analysis

“…The modifiable area unit problem (MAUP) refers to the sensitivity of data and analytics to the spatial units or support upon which they are measured . These effects are traditionally grouped 13 into two categories with one focusing on the sensitivity to changes in zonal boundaries (e.g., Burden & Steel, 2016) and another focusing on the sensitivity to changes in scale, which could include either varying observation scales within a single geographic scale (e.g., Chou, 1991;Mu & Wang, 2008;Burden & Steel, 2016) or varying geographic scales for a fixed observation scale (e.g., Wong, 2001). However, in practice it appears that the scale aspect of the MAUP is more often investigated by the former task of varying observation scales within a single geographic scale (e.g., Kwan & Weber, 2008;Houston, 2014).…”

“…Goovaerts et al, 2005; Zhang & Zhang, 2011;Lloyd, 2012, Lloyd, 2016. Other profiles may alternatively be based on spatial autocorrelation statistics(Zhang & Zhang, 2011), entropy(Appleby, 1996), diversity indices, isolation statistics(Östh et al, 2015), fractal dimension(Lam & Quattrochi, 1992;De Cola, 1994), percentages(Petrović et al, 2018), or cumulative probability distributions(Wong, 2001). These values are often computed as a function of geographic scale metrics, most commonly 'global' distance lags between all observations(Phillips, 1988;Lam & Quattrochi, 1992; Liu & Jezek, 1999; Goovaerts et al, 2005; Zhang & Zhang, 2011) or 'local' aggregates for each observation across distance bands, within a moving window, or based on a population-based number of nearest neighbors for an individual-contextual approach (Wong, 2001; Lloyd, 2012; Östh et al, 2015; Petrović et al, 2018).…”

Comparing spatial patterns

“…Cumulative distribution functions have been proposed for SPC problems because they are able to consider the shape of the underlying empirical distributions (Syrjala, ). Wong () proposes a local cumulative distribution function as a means to use the widely employed cumulative distribution function in a spatially‐local comparison. In analysis of neighbourhoods and their social characteristics, comparisons of both geographic and multivariate demographic characteristics have led to use of self‐organizing maps to link social factors and spatial patterns (Spielman & Thill, ), and an approach which decomposes spatial and thematic properties into separate “map” spaces, which can then be visualized and explored for patterns.…”