Testing pairwise association between spatially autocorrelated variables: a new approach using surrogate lattice data

Area of Science:

• Spatial statistics
• Geostatistics
• Image analysis

Background:

• Traditional statistical tests assume independent observations, a condition often violated by spatial autocorrelation in lattice data and images.
• Autocorrelation, common in remote-sensing and geographical data, complicates standard association tests.
• Analytic derivation of null distributions for test statistics is challenging with autocorrelation.

Purpose of the Study:

• To develop a robust statistical method for testing associations in spatial data affected by autocorrelation.
• To introduce a Monte Carlo simulation approach using surrogate data to address violated independence assumptions.
• To provide a reliable method for analyzing mapped variables from sources like remote-sensing and geographical databases.

Main Methods:

• Generated surrogate spatial data by matching dual-tree complex wavelet spectra to preserve autocorrelation functions of original images.
• Used these surrogates to construct probability distributions for association statistics under the null hypothesis.
• Compared the wavelet-based surrogate method against corrected parametric tests and other surrogate generation techniques.

Main Results:

• The proposed wavelet-based surrogate method demonstrated excellent Type I error control, even with strong and long-range autocorrelation.
• The method proved effective for both actual and synthetic spatial data.
• Outperformed alternative surrogate generation methods in controlling statistical errors.

Conclusions:

• Wavelet-based surrogates are highly suitable for spatial data with autocorrelation across all scales and for anisotropic (direction-dependent) patterns.
• The method shows promise for association tests with lattice binary data and for validating species distribution models.
• A Java implementation for generating wavelet-based surrogates is available online.