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Modelling count, bounded and skewed continuous outcomes in physical activity research: beyond linear regression models.

Published version
Peer-reviewed

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Abstract

BACKGROUND: Inference using standard linear regression models (LMs) relies on assumptions that are rarely satisfied in practice. Substantial departures, if not addressed, have serious impacts on any inference and conclusions; potentially rendering them invalid and misleading. Count, bounded and skewed outcomes, common in physical activity research, can substantially violate LM assumptions. A common approach to handle these is to transform the outcome and apply a LM. However, a transformation may not suffice. METHODS: In this paper, we introduce the generalized linear model (GLM), a generalization of the LM, as an approach for the appropriate modelling of count and non-normally distributed (i.e., bounded and skewed) outcomes. Using data from a study of physical activity among older adults, we demonstrate appropriate methods to analyse count, bounded and skewed outcomes. RESULTS: We show how fitting an LM when inappropriate, especially for the type of outcomes commonly encountered in physical activity research, substantially impacts the analysis, inference, and conclusions compared to a GLM. CONCLUSIONS: GLMs which more appropriately model non-normally distributed response variables should be considered as more suitable approaches for managing count, bounded and skewed outcomes rather than simply relying on transformations. We recommend that physical activity researchers add the GLM to their statistical toolboxes and become aware of situations when GLMs are a better method than traditional approaches for modeling count, bounded and skewed outcomes.

Description

Acknowledgements: Not applicable.

Keywords

Bounded data, Count data, Generalized linear model, Linear regression model, Physical activity, Skewed data, Transformations

Journal Title

Int J Behav Nutr Phys Act

Conference Name

Journal ISSN

1479-5868
1479-5868

Volume Title

Publisher

Springer Science and Business Media LLC
Sponsorship
Health Medical Research Fund (Hong Kong) (HKU741511H)