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Is multivariable quantile regression interpreted the same way as a multivariable linear regression would be interpreted? For example, would I say something like "the coefficient represents the quantile (?) change in the response variable for a one unit change in the predictor variable while holding other predictors in the model constant"?

Thank you in advance.

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    $\begingroup$ Yes, that is right. Instead of 'quantile change' you can also say 'change in the b-quantile of the response' (and b is the probability behind the quantile). $\endgroup$ – Michael M Aug 4 '15 at 19:38
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Petscher and Logan has written a very good paper on interpretation of quantile regression (http://onlinelibrary.wiley.com/doi/10.1111/cdev.12190/abstract).

To quote the authors, it is apparently misleading to interpret the regression coefficients of quantile regression in the same way as one would with linear regression results.

Instead the quantile coefficients for a given independent variable X in a certain quantile should be read as the gap between the mean of X for the quantile, compared to instances of X above 1 SD on the mean of X.

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