On the misuse of residuals in ecology: regression of residuals vs. multiple regression

1. Residuals from linear regressions are used frequently in statistical analysis, often for the purpose of controlling for unwanted effects in multivariable datasets. This paper criticizes the practice, building upon recent critiques. 2. Regression of residuals is often used as an alternative to multiple regression, often with the aim of controlling for confounding variables. When correlations exist between independent variables, as is generally the case with ecological datasets, this procedure leads to biased parameter estimates. Standard multiple regression, by contrast, yields unbiased parameter estimates. 3. In multiple regression parameters are estimated controlling for the effects of the other variables in the model, and thus multiple regression achieves what residual regression claims to do. 4. Several measures of correlation exist that differ in the way that variance is partitioned among independent variables. These can be estimated multiply, or sequentially if reasons exist for estimating effects of variables in a hierarchical manner.