ABSTRACT
The purpose of this chapter is to introduce the reader to a special case of median regression analysis known as quantile regression. Summarizing behaviors and observations in the education and social sciences has traditionally been captured by three well-known measures of central tendency: the average of the observations, the median value, and the mode. Extensions of these descriptive measures to an inferential process are generally focused on the mean of the distribution. Traditional multiple regression analysis asks the question in the vein of, “How does X (e.g., weight) relate to Y (e.g., height)?” and implicit to this question is that the relationships among phenomena are modeled in terms of the average. Subsequently, regression may be thought of as conditional means model, in that for any given value of an independent variable, we elicit a predicted mean on the dependent variable. Since its theoretical development in 1805 by Adrien-Marie Legendre, conditional means modeling has become a universal method for model-based inferencing.
