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Worm plot to diagnose fit in quantile regression

Stef van Buuren is Department of Statistics, TNO Quality of Life, The Netherlands and Department of Methodology & Statistics, Faculty of Social Sciences, University of Utrecht, The Netherlands. E-mail: Stef.vanBuuren{at}tno.nl

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.

Key Words: centiles • growth diagrams • LMS model • P-P plot • Q-Q plot • smoothing

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Statistical Modelling, Vol. 7, No. 4, 363-376 (2007)
DOI: 10.1177/1471082X0700700406


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This Article Abstract Free Full Text (Free PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to Saved Citations Download to citation manager Add to My Marked Citations Citing Articles Citing Articles via Google Scholar Citing Articles via Scopus Google Scholar Articles by Buuren, S. v. Search for Related Content Social Bookmarking                         What's this?