Multiple Regression Is Not Multiple Regressions: The Meaning of Multiple Regression and the Non-Problem of Collinearity

By M. Morrissey, Graeme D. Ruxton. Philosophy, Theory, and Practice in Biology, 2018

121 citations recorded by the source corpus.

Simple regression (regression analysis with a single explanatory variable), and multiple regression (regression models with multiple explanatory variables), typically correspond to very different biological questions. The former use regression lines to describe univariate associations. The latter describe the partial, or direct, effects of multiple variables, conditioned on one another. We suspect that the superficial similarity of simple and multiple regression leads to confusion in their interpretation. A clear understanding of these methods is essential, as they underlie a large range of procedures in common use in biology. Beyond simple and multiple regression in their most basic forms, understanding the key principles of these procedures is critical to understanding, and properly applying, many methods, such as mixed models, generalised models, and causal inference using graphs (including path analysis and its extensions). A simple, but careful, look at the distinction between these two analyses is valuable in its own right, and can also be used to clarify widely-held misconceptions about collinearity (correlations among explanatory variables). There is no general sense in which collinearity is a problem. We suspect that the perception of collinearity as a hindrance to analysis stems from misconceptions about interpretation of multiple regression models, and so we pursue discussions about these misconceptions in this light. In particular, collinearity causes multiple regression coefficients to be less precisely estimated than corresponding simple regression coefficients. This should not be interpreted as a problem, as it is perfectly natural that direct effects should be harder to characterise than univariate associations. Purported solutions to the perceived problems of collinearity are detrimental to most biological analyses.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a68c255c6ef8bab31a4f2d72cce2c4c8737c1930

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Citations in the corpus

Robustness of linear mixed‐effects models to violations of distributional assumptions (2020, background): “Morrissey and Ruxton (2018) also point out that the increased variation in estimates is a simple consequence of the sampling design being inadequate for estimating independent effects of correlated variables.”
A standard protocol for reporting species distribution models (2020, background): “The uncertainty around which environmental predictor represents the true causal mechanism may propagate into ‘inflated’ standard errors (Morrissey and Ruxton 2018).”