Statistical Modelling 7 (2007), 363–376

Worm plot to diagnose fit in quantile regression

Stef van Buuren
Department of Statistics,
TNO Quality of Life,
P.O. Box 2215,
NL–2301 NE Leiden
The Netherlands
and
Department of Methodology and Statistics,
Faculty of Social Sciences,
University of Utrecht,
The Netherlands
eMail: Stef.vanBuuren@tno.nl

Abstract:

The worm plot is a series of detrended Q-Q plots, split by covariate levels. The worm plot is a diagnostic tool for visualizing how well a statistical model fits the data, for finding locations at which the fit can be improved, and for comparing the fit of different models. This paper shows how the worm plot can be used in conjunction with quantile regression. No parametric distributional assumptions are needed to create the worm plot. We fitted both an LMS and a quantile regression model on Dutch height data. The worm plot shows that the quantile regression model is superior to the LMS model in terms of fit. At the same time, it also contains a warning that the particular quantile model used may actually overfit the data. The resulting quantile curves are wiggly at the extremes, and appear less well suited for drawing growth diagrams. The paper concludes that the worm plot is a natural diagnostic tool for quantile regression.

Keywords:

centiles; growth diagrams; LMS model; P-P plot; Q-Q plot; smoothing

Downloads:

Data and software in zipped archive.

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