qreg - Stata

6 qreg — Quantile regression
display options: noomitted, vsquish, noemptycells, baselevels, allbaselevels, nofvlabel,
fvwrap(#), fvwrapon(style), cformat(% fmt), pformat(% fmt), sformat(% fmt), and
nolstretch; see [R] estimation options.
Options for bsqreg
✄
✄
Model
quantile(#) specifies the quantile to be estimated and should be a number between 0 and 1, exclusive.
Numbers larger than 1 are interpreted as percentages. The default value of 0.5 corresponds to the
median.
reps(#) specifies the number of bootstrap replications to be used to obtain an estimate of the
variance–covariance matrix of the estimators (standard errors). reps(20) is the default and is
arguably too small. reps(100) would perform 100 bootstrap replications. reps(1000) would
perform 1,000 replications.
✄
✄ Reporting
level(#); see [R] estimation options.
display options: noomitted, vsquish, noemptycells, baselevels, allbaselevels, nofvlabel,
fvwrap(#), fvwrapon(style), cformat(% fmt), pformat(% fmt), sformat(% fmt), and
nolstretch; see [R] estimation options.
Remarks and examples
Remarks are presented under the following headings:
Median regression
Quantile regression
Estimated standard errors
Interquantile and simultaneous-quantile regression
What are the parameters?
stata.com
Median regression
qreg fits quantile regression models. The default form is median regression, where the objective is
to estimate the median of the dependent variable, conditional on the values of the independent variables.
This method is similar to ordinary regression, where the objective is to estimate the conditional mean
of the dependent variable. Simply put, median regression finds a line through the data that minimizes
the sum of the absolute residuals rather than the sum of the squares of the residuals, as in ordinary
regression. Equivalently, median regression expresses the median of the conditional distribution of
the dependent variable as a linear function of the conditioning (independent) variables. Cameron and
Trivedi (2010, chap. 7) provide a nice introduction to quantile regression using Stata.