Examining a Full-Range Relationship Using Quantile Regression

Least squares regression (LSR) is one of the most popular techniques used in exercise science and physical education to examine the response of the mean of an explanatory variable y to changes in the vector of covariates x. A disadvantage of LSR is that the conditional mean employed may not provide the complete picture of the distribution. In the presence of a skewed distribution, for example, the mean is a misleading parameter and, a 90% confidence interval obtained from an LSR estimate is less accurate than an interval estimate obtained using the 5th and 95th percentiles. Furthermore, tail behavior, not the mean, is often of particular interest, e.g., when studying the correlates of obesity or examining the effects of an intervention of sedentary behavior. Quantile regression is an alternate method of estimation proposed by econometricians Koenker and Bassett in 1978. Using percentiles rather than the mean of the response variable, it provides a more complete understanding of how covariates affect the distribution of the response variable in terms of location, scale and shape. This presentation provides an introduction to the quantile regression method as an extension of LSR in the context of exercise science and physical education. After an overview of quantile regression, its applications will be illustrated using the data from the National Health and Nutrition Examination Survey (NHANES). Finally, related software will be introduced and demonstrated.