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The marginality principle revisited: Should “higher-order” terms always be accompanied by “lower-order” terms in regression analyses?

Morris, Timothy; Pham, Tra; (2023) The marginality principle revisited: Should “higher-order” terms always be accompanied by “lower-order” terms in regression analyses? Biometrical Journal , 65 (8) , Article 2300069. 10.1002/bimj.202300069. Green open access

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Abstract

The marginality principle guides analysts to avoid omitting lower-order terms from models in which higher-order terms are included as covariates. Lower-order terms are viewed as “marginal” to higher-order terms. We consider how this principle applies to three cases: regression models that may include the ratio of two measured variables; polynomial transformations of a measured variable; and factorial arrangements of defined interventions. For each case, we show that which terms or transformations are considered to be lower-order, and therefore marginal, depends on the scale of measurement, which is frequently arbitrary. Understanding the implications of this point leads to an intuitive understanding of the curse of dimensionality. We conclude that the marginality principle may be useful to analysts in some specific cases but caution against invoking it as a context-free recipe.

Type: Article
Title: The marginality principle revisited: Should “higher-order” terms always be accompanied by “lower-order” terms in regression analyses?
Open access status: An open access version is available from UCL Discovery
DOI: 10.1002/bimj.202300069
Publisher version: https://doi.org/10.1002/bimj.202300069
Language: English
Additional information: © 2023 The Authors. Biometrical Journal published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/).
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Population Health Sciences > Inst of Clinical Trials and Methodology
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Population Health Sciences > Inst of Clinical Trials and Methodology > MRC Clinical Trials Unit at UCL
URI: https://discovery.ucl.ac.uk/id/eprint/10176892
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