Restricted random labeling: testing for between-group interaction after controlling for joint population and within-group spatial structure

Abstract

, "Restricted random labeling: testing for between-group interaction after controlling for joint population and within-group spatial structure" (2015). AbstractStatistical measures of spatial interaction between multiple types of entities are commonly assessed against a null model of either toroidal shift (TS), which controls for spatial structure of individual subpopulations, or random labeling (RL) which controls for spatial structure of the joint population. Neither null model controls for both types of spatial structure simultaneously, although this may sometimes be desirable when more than two subpopulations are present. To address this, we propose a flexible framework for specifying null models that we refer to as restricted random labeling (rRL). Under rRL, a specified subset of individuals is restricted, and other individuals are randomly relabeled. Within this framework two specific null models are proposed for pairwise analysis within populations consisting of three or more subpopulations, to simultaneously control for spatial structure in the joint population and one or the other of the two subpopulations being analyzed. Formulas are presented for calculating expected nearest neighbor counts and co-location quotients within the proposed framework. Differences between TS, RL and rRL are illustrated by application to six types of generating processes in a simulation study, and to empirical datasets of tree species in a forest and crime locations in an urban setting. These examples show that rRL null models are typically stricter than either TS or RL, which often detect "interactions" that are an expected consequence either of the joint population pattern or of individual subpopulation patterns.

The Local Colocation Patterns of Crime and Land-Use Features in Wuhan, China

“…A Monte Carlo simulation was performed to determine the statistical significance of the results [5]. To eliminate the effect of within-category clustering, the statistics were computed under the hypothesis of restricted random labeling [32]. This technique constrained one crime type or one land-use type at a time, repeated the shuffling of other point types, and computed the CLQ in each iteration.…”

Employing a spatio-temporal contingency table for the analysis of cork oak cover change in the Sa Serra region of Sardinia

“…This work developed a new version of Dixon’s index of segregation that accounts for the temporal dimension, edge correction and spatial heterogeneity. Previous works focused on developing the index for species interactions studies 18 , 37 and for different geometric configuration of the points in space 44 , 57 , but not for a time dimension or for local estimations of the index. However, applying Dixon’s index to time opens up a multitude of study areas for its possible application; from land cover/use change to clustering analysis (which may include the field of epidemiology 58 ), to species interaction and distribution analyses 16 .…”

“…In fact, in the presence of three or more classes, null model selection is confounded by the existence of multiple processes (i.e. co-occurrence of strong and weak interactions that make the statistic uninterpretable), including processes that affect the entire joint distribution of the classes (for example, a strong environmental gradient) 44 . Therefore, converting the multi-class case into a bivariate one for spatial segregation comparison removes the risk of having large degrees of freedom in the presence of confounders, and allows a more accurate approximation of the joint population.…”

Where are the dangerous intersections for pedestrians and cyclists: A colocation-based approach

“…By repeating this process many times such as 1,000 runs, we will have a sample distribution of the GCLQA→B. Finally, we compare the distribution of the observed GCLQA→B with the corresponding sample distribution to obtain a test statistic along with a significance level (Leslie and Kronenfeld 2011;Kronenfeld and Leslie 2015;Wang et al 2017).…”

“…trial randomly relabels the category of any other objects by following the frequency distribution of each category (Kronenfeld and Leslie 2015). Take LCLQF 1 →TL as an example (F1 means the first record of fatality crashes and TL denotes traffic light controlled-intersections), each simulation run randomly reassigns the labels of all objects (including fatality crashes and all types of intersections including traffic light controlled-, stop sign controlled-and noncontrolled-intersections) but not object F1, and the number of objects in each category remains the same after the process.…”