Skip to content

Research at St Andrews

Multiple regressions: the meaning of multiple regression and the non-problem of collinearity

Research output: Contribution to journalArticle

Abstract

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.
Close

Details

Original languageEnglish
Article number3
Number of pages24
JournalPhilosophy, Theory and Practice in Biology
Volume10
DOIs
StatePublished - 2018

    Research areas

  • Regression, Multiple regression, Collinearity, Ordinary least squares, Linear model, Causal effect, Correlation

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Mixed-species aggregations in arthropods

    Boulay, J., Aubernon, C., Ruxton, G. D., Hédouin, V., Deneubourg, J-L. & Charabidzé, D. 2 Jan 2019 In : Insect Science. 26, 1, p. 2-19

    Research output: Contribution to journalReview article

  2. Dropping to escape: a review of an under-appreciated antipredator defence

    Humphreys, R. K. & Ruxton, G. D. 9 Oct 2018 In : Biological Reviews. Early View

    Research output: Contribution to journalReview article

  3. Natural selection for body shape in resource polymorphic Icelandic Arctic charr

    Franklin, O. D., Skúlason, S., Morrissey, M. B. & Ferguson, M. M. 16 Aug 2018 In : Journal of Evolutionary Biology. Early View, 15 p.

    Research output: Contribution to journalArticle

  4. Why war is a man's game

    Micheletti, A. J. C., Ruxton, G. D. & Gardner, A. 15 Aug 2018 In : Proceedings of the Royal Society B: Biological Sciences. 285, 1884, 8 p., 20180975

    Research output: Contribution to journalArticle

  5. Circular data in biology: advice for effectively implementing statistical procedures

    Landler, L., Ruxton, G. D. & Malkemper, E. P. Aug 2018 In : Behavioral Ecology and Sociobiology. 72, 8, 10 p., 128

    Research output: Contribution to journalArticle

ID: 253120157