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I want to model the changes in a dependent variable with non-normal distribution (e.g. abundance of micro-organisms) as a function of changes in dichotomous independent variables (e.g. gender, sick or healthy). Is it appropriate to use dichotomous variables as a predictor in a quantile regression analysis?

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There is nothing about quantile regression that makes dichotomous predictors inappropriate.

Often (not in your examples, but often) people dichotomize continuous variables. This is nearly always a mistake, but that's true, regardless of the type of regression.

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  1. The distribution of the outcome is useless. You need to look at residual plots
  2. Linear regression models have limiting normal distributions for regression coefficients, and the mean response as well
  3. The mean-difference is often the natural scale for reporting change
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