Education 231C

Applied Categorical & Nonnormal Data Analysis

Quantile Regression

By now you are familiar with OLS regression, a least squares criterion is not the only way to do regression. We could look at the absolute deviations from some point estimate, say the median. We would be trying to obtain the minimum absolute deviations (MAD).

According to Koenker (2000), quantile regression is a statistical technique intended to estimate and conduct inference about conditional quantile functions. Quantile regression methods offer a mechanism for estimationg the conditional median function in addtion to other conditional quantile functions. Ordinary least squares regression asks the question "How does the conditional mean of Y depend on the covariates X?" Quantile regression asks this question at each quantile of the conditional distribution giving a more complete description of how the conditional distribution of Y given X.

In Stata this can be done using the qreg command. Here are some quantile regressions using the hsb2 dataset.

Note that increasing values greater than the median did not change the coefficients for the median regression.

We need to reload the data because of the changes that were made.

We have been using dummy (indicator) coding for the categorical variable. There are other possible codings that we could use. For this example, I would like to use a coding that compares general with vocational and one that compares the average of general and vocational with academic. We can create the coding using variable characteristics in Stata and apply them to the model using the xi3 command available for ATS via the Internet. In this next series of analyses we will look at models which include an interaction. We will use the variables female and socst and create an interaction fxs. Next, we will take a look at the same model using an alternative coding scheme involving the difference between the groups and the grand median.

Categorical Data Analysis Course

Phil Ender -- 5/15/04