Testing for Network and Spatial Autocorrelation

TL;DR

This paper introduces a new statistical test for detecting autocorrelation in categorical variables and emphasizes its applicability in both spatial and network data contexts, addressing gaps in existing methods.

Contribution

The paper presents a novel, unified test for autocorrelation in categorical data and highlights its relevance for spatial and network analysis, improving upon existing ad hoc methods.

Findings

Proposed a new test for autocorrelation in categorical variables.

Demonstrated the test's applicability in spatial and network data.

Highlighted the limitations of existing methods for categorical autocorrelation.

Abstract

Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in continuous variables. In this paper we propose two contributions to the literature on tests for autocorrelation. First, we propose a new test for autocorrelation in categorical variables. While some methods currently exist for assessing spatial autocorrelation in categorical variables, the most popular method is unwieldy, somewhat ad hoc, and fails to provide grounds for a single omnibus test. Second, we discuss the importance of testing for autocorrelation in data sampled from the nodes of a network, motivated by social network applications. We demonstrate that our proposed statistic for categorical variables can both be used in the spatial and network setting.