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

International Journal of Behavioral Nutrition and Physical Activity

Methodology

Karen E. Lamb¹  Simon R. White²  Muhammad Akram³  Ester Cerin⁴ 

[1] Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, University of Melbourne, Melbourne, Australia;Institute for Physical Activity and Nutrition (IPAN), School of Exercise and Nutrition Sciences, Deakin University, Geelong, Australia;MRC Biostatistics Unit, University of Cambridge, Cambridge, UK;Department of Psychiatry, University of Cambridge, Cambridge, UK;Mary MacKillop Institute for Health Research, Australian Catholic University, Melbourne, Australia;Mary MacKillop Institute for Health Research, Australian Catholic University, Melbourne, Australia;School of Public Health, The University of Hong Kong, Hong Kong, China;

关键词: Count data;    Skewed data;    Bounded data;    Physical activity;    Linear regression model;    Generalized linear model;    Transformations;   

DOI  :  10.1186/s12966-023-01460-y

 received in 2022-05-16, accepted in 2023-04-29,  发布年份 2023

来源: Springer

【 摘 要 】

BackgroundInference 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.MethodsIn 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.ResultsWe 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.ConclusionsGLMs 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.

【 授权许可】

CC BY   
© The Author(s) 2023

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