Common permutation methods in animal social network analysis do not control for non-independence

This is the final version. Available on open access from Springer via the DOI in this recordData availability: The R code required to repeat the simulations has been deposited at: https://doi.org/10.5281/zenodo.4903396).The non-independence of social network data is a cause for concern among behavioural ecologists conducting social network analysis. This has led to the adoption of several permutation-based methods for testing common hypotheses. One of the most common types of analysis is nodal regression, where the relationships between node-level network metrics and nodal covariates are analysed using a permutation technique known as node-label permutations. We show that, contrary to accepted wisdom, node-label permutations do not automatically account for the non-independences assumed to exist in network data, because regression-based permutation tests still assume exchangeability of residuals. The same assumption also applies to the quadratic assignment procedure (QAP), a permutation-based method often used for conducting dyadic regression. We highlight that node-label permutations produce the same p-values as equivalent parametric regression models, but that in the presence of non-independence, parametric regression models can also produce accurate effect size estimates. We also note that QAP only controls for a specific type of non-independence between edges that are connected to the same nodes, and that appropriate parametric regression models are also able to account for this type of non-independence. Based on this, we suggest that standard parametric models could be used in the place of permutation-based methods. Moving away from permutation-based methods could have several benefits, including reducing over-reliance on p-values, generating more reliable effect size estimates, and facilitating the adoption of causal inference methods and alternative types of statistical analysis.Engineering and Physical Sciences Research Council (EPSRC)European Research Council (ERC)National Institutes of Health (NIH)Natural Environment Research Council (NERC