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I recently submitted a paper, in which I used quantile regression, to a psychology journal. Although I thought I had already put enough thought in a clear exposition of quantile regression, the reviewers asked for better explanations of the quantile regression technique being only familiar with standard OLS regression.

So, what is the best way to explain quantile regression, in an empirical paper, to non-statisticians?

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    $\begingroup$ I think you need to explain why you chose quantile regression over least squares regression. Were the residuals not normally distributed using least squares regression? $\endgroup$ – Glen May 13 '12 at 6:02
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    $\begingroup$ We chose quantile regression for theoretical reasons. Specifically, we were interested in the whole distribution of the dependent variable. $\endgroup$ – Johannes May 13 '12 at 6:30
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    $\begingroup$ @Johannes, you might find this helpful, and the literature it cites. Also, Glen, non-Normal residuals are no reason to rule out using OLS; see here, for example. $\endgroup$ – guest May 13 '12 at 6:33
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    $\begingroup$ i would say that if the residuals depart significantly from normal least squares may not be a good estimation method due to its sensitivity to outliers. So a robust alternative the OLS is required. $\endgroup$ – Michael R. Chernick May 13 '12 at 12:51
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    $\begingroup$ This is an excellent intro published in 2014 "Quantile regression in the study of developmental sciences" Child Dev 85:861-881. $\endgroup$ – N Brouwer Jan 27 '15 at 19:40
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I would consider stressing the motivation and not the technicalities (just give a reference). In particular:

  • Distribution free: you do not wish to assume the parametric form of the error distribution.
  • Robustness: you suspect your dependent variable might be contaminated.

Recovering the whole (conditional) distribution by itself does not justify quantile regression, since under the Normality assumption, the mean and variance suffice to recover the whole distribution. And the same goes for any other parametric error distribution.

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  • $\begingroup$ I don't get your "the mean and variance suffice to recover the whole distribution". Suppose that my dependent variable is BMI and I am interested in making inference on individuals at the tail of its distribution, how can I exactly use the ordinary regression methods? $\endgroup$ – Davide Nov 8 '13 at 15:08
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Try to build up the intuitiveness through the reviewer's/audience's understanding of simpler statistics.

Why would you use median instead of mean as a measure of central tendency? If you can convey this point, the rest should follow.

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