Stata 15 help for qreg

[R] qreg -- Quantile regression

Syntax

Quantile regression

qreg depvar [indepvars] [if] [in] [weight] [, qreg_options]

Interquantile range regression

iqreg depvar [indepvars] [if] [in] [, iqreg_options]

Simultaneous-quantile regression

sqreg depvar [indepvars] [if] [in] [, sqreg_options]

Bootstrapped quantile regression

bsqreg depvar [indepvars] [if] [in] [, bsqreg_options]

qreg_options Description ------------------------------------------------------------------------- Model quantile(#) estimate # quantile; default is quantile(.5)

SE/Robust vce([vcetype], [vceopts]) technique used to estimate standard errors

Reporting level(#) set confidence level; default is level(95) display_options control columns and column formats, row spacing, line width, display of omitted variables and base and empty cells, and factor-variable labeling

Optimization optimization_options control the optimization process; seldom used wlsiter(#) attempt # weighted least-squares iterations before doing linear programming iterations -------------------------------------------------------------------------

vcetype Description ------------------------------------------------------------------------- iid compute the VCE assuming the residuals are i.i.d. robust compute the robust VCE -------------------------------------------------------------------------

vceopts Description ------------------------------------------------------------------------- denmethod nonparametric density estimation technique bwidth bandwidth method used by the density estimator -------------------------------------------------------------------------

denmethod Description ------------------------------------------------------------------------- fitted use the empirical quantile function using fitted values; the default residual use the empirical residual quantile function kernel[(kernel)] use a nonparametric kernel density estimator; default is epanechnikov -------------------------------------------------------------------------

bwidth Description ------------------------------------------------------------------------- hsheather Hall-Sheather's bandwidth; the default bofinger Bofinger's bandwidth chamberlain Chamberlain's bandwidth -------------------------------------------------------------------------

kernel Description ------------------------------------------------------------------------- epanechnikov Epanechnikov kernel function; the default epan2 alternative Epanechnikov kernel function biweight biweight kernel function cosine cosine trace kernel function gaussian Gaussian kernel function parzen Parzen kernel function rectangle rectangle kernel function triangle triangle kernel function -------------------------------------------------------------------------

iqreg_options Description ------------------------------------------------------------------------- Model quantiles(# #) interquantile range; default is quantiles(.25 .75) reps(#) perform # bootstrap replications; default is reps(20)

Reporting level(#) set confidence level; default is level(95) nodots suppress display of the replication dots display_options control columns and column formats, row spacing, line width, display of omitted variables and base and empty cells, and factor-variable labeling -------------------------------------------------------------------------

sqreg_options Description ------------------------------------------------------------------------- Model quantiles(#[#[# ...]]) estimate # quantiles; default is quantiles(.5) reps(#) perform # bootstrap replications; default is reps(20)

Reporting level(#) set confidence level; default is level(95) nodots suppress display of the replication dots display_options control columns and column formats, row spacing, line width, display of omitted variables and base and empty cells, and factor-variable labeling -------------------------------------------------------------------------

bsqreg_options Description ------------------------------------------------------------------------- Model quantile(#) estimate # quantile; default is quantile(.5) reps(#) perform # bootstrap replications; default is reps(20)

Reporting level(#) set confidence level; default is level(95) display_options control columns and column formats, row spacing, line width, display of omitted variables and base and empty cells, and factor-variable labeling -------------------------------------------------------------------------

indepvars may contain factor variables; see fvvarlist. by, mi estimate, rolling, and statsby are allowed with qreg, iqreg, sqreg, and bsqreg; mfp, nestreg, and stepwise are allowed with qreg; see prefix. qreg allows fweights, iweights, and pweights; see weight. See [R] qreg postestimation for features available after estimation.

Menu

qreg

Statistics > Nonparametric analysis > Quantile regression

iqreg

Statistics > Nonparametric analysis > Interquantile regression

sqreg

Statistics > Nonparametric analysis > Simultaneous-quantile regression

bsqreg

Statistics > Nonparametric analysis > Bootstrapped quantile regression

Description

qreg fits quantile (including median) regression models, also known as least-absolute-value models (LAV or MAD) and minimum L1-norm models. The quantile regression models fit by qreg express the quantiles of the conditional distribution as linear functions of the independent variables.

iqreg estimates interquantile range regressions, regressions of the difference in quantiles. The estimated variance-covariance matrix of the estimators (VCE) is obtained via bootstrapping.

sqreg estimates simultaneous-quantile regression. It produces the same coefficients as qreg for each quantile. Reported standard errors will be similar, but sqreg obtains an estimate of the VCE via bootstrapping, and the VCE includes between-quantile blocks. Thus you can test and construct confidence intervals comparing coefficients describing different quantiles.

bsqreg is equivalent to sqreg with one quantile.

Options for qreg

+-------+ ----+ 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.

+-----------+ ----+ SE/Robust +--------------------------------------------------------

vce([vcetype], [vceopts]) specifies the type of VCE to compute and the density estimation method to use in computing the VCE.

vcetype specifies the type of VCE to compute. Available types are iid and robust.

vce(iid), the default, computes the VCE under the assumption that the residuals are independent and identically distributed (i.i.d.).

vce(robust) computes the robust VCE under the assumption that the residual density is continuous and bounded away from 0 and infinity at the specified quantile(); see Koenker (2005, sec. 4.2).

vceopts consists of available denmethod and bwidth options.

denmethod specifies the method to use for the nonparametric density estimator. Available methods are fitted, residual, or kernel[(kernel)], where the optional kernel must be one of the kernel choices listed below.

fitted and residual specify that the nonparametric density estimator use some of the structure imposed by quantile regression. The default fitted uses a function of the fitted values and residual uses a function of the residuals. vce(robust, residual) is not allowed.

kernel() specifies that the nonparametric density estimator use a kernel method. The available kernel functions are epanechnikov, epan2, biweight, cosine, gaussian, parzen, rectangle, and triangle. The default is epanechnikov. See [R] kdensity for the kernel function forms.

bwidth specifies the bandwidth method to use by the nonparametric density estimator. Available methods are hsheather for the Hall-Sheather bandwidth, bofinger for the Bofinger bandwidth, and chamberlain for the Chamberlain bandwidth.

See Koenker (2005, sec. 3.4 and 4.10) for a description of the sparsity estimation techniques and the Hall-Sheather and Bofinger bandwidth formulas. See Chamberlain (1994, eq. 2.2) for the Chamberlain bandwidth.

+-----------+ ----+ Reporting +--------------------------------------------------------

level(#); see [R] estimation options.

display_options: noci, nopvalues, noomitted, vsquish, noemptycells, baselevels, allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt), pformat(%fmt), sformat(%fmt), and nolstretch; see [R] estimation options.

+--------------+ ----+ Optimization +-----------------------------------------------------

optimization_options: iterate(#), [no]log, trace. iterate() specifies the maximum number of iterations; log/nolog specifies whether to show the iteration log; and trace specifies that the iteration log should include the current parameter vector. These options are seldom used.

wlsiter(#) specifies the number of weighted least-squares iterations that will be attempted before the linear programming iterations are started. The default value is 1. If there are convergence problems, increasing this number should help.

Options for iqreg

+-------+ ----+ Model +------------------------------------------------------------

quantiles(# #) specifies the quantiles to be compared. The first number must be less than the second, and both should be between 0 and 1, exclusive. Numbers larger than 1 are interpreted as percentages. Not specifying this option is equivalent to specifying quantiles(.25 .75), meaning the interquantile range.

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.

nodots suppresses display of the replication dots.

display_options: noci, nopvalues, noomitted, vsquish, noemptycells, baselevels, allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt), pformat(%fmt), sformat(%fmt), and nolstretch; see [R] estimation options.

Options for sqreg

+-------+ ----+ Model +------------------------------------------------------------

quantiles(# [# [# ...]]) specifies the quantiles to be estimated and should contain numbers 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.

nodots suppresses display of the replication dots.

display_options: noci, nopvalues, 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(#); [R] estimation options.

display_options: noci, nopvalues, noomitted, vsquish, noemptycells, baselevels, allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt), pformat(%fmt), sformat(%fmt), and nolstretch; see [R] estimation options.

Examples

--------------------------------------------------------------------------- Setup . sysuse auto

Median regression . qreg price weight length foreign

Replay results . qreg

Estimate .25 quantile using the Bofinger bandwidth method . qreg price weight length foreign, quantile(.25) vce(iid, bofinger)

Estimate .75 quantile using the Parzen kernel density estimator and the Chamberlain bandwidth method . qreg price weight length foreign, quantile(.75) vce(iid, kernel(parzen) chamberlain)

Estimate [.25, .75] interquantile range, performing 100 bootstrap replications . iqreg price weight length foreign, quantile(.25 .75) reps(100)

Same as above . iqreg price weight length foreign, reps(100)

Estimate .25, .5, and .75 quantiles simultaneously, performing 100 bootstrap replications . sqreg price weight length foreign, quantile(.25 .5 .75) reps(100)

Median regression with bootstrap standard errors . bsqreg price weight length foreign

Estimate .75 quantile with bootstrap standard errors . bsqreg price weight length foreign, quantile(.75) ---------------------------------------------------------------------------

Stored results

qreg stores the following in e():

Scalars e(N) number of observations e(df_m) model degrees of freedom e(df_r) residual degrees of freedom e(q) quantile requested e(q_v) value of the quantile e(sum_adev) sum of absolute deviations e(sum_rdev) sum of raw deviations e(sum_w) sum of weights e(f_r) density estimate e(sparsity) sparsity estimate e(bwidth) bandwidth e(kbwidth) kernel bandwidth e(rank) rank of e(V) e(convcode) 0 if converged; otherwise, return code for why nonconvergence

Macros e(cmd) qreg e(cmdline) command as typed e(depvar) name of dependent variable e(bwmethod) bandwidth method; hsheather, bofinger, or chamberlain e(denmethod) density estimation method; fitted, residual, or kernel e(kernel) kernel function e(wtype) weight type e(wexp) weight expression e(vce) vcetype specified in vce() e(vcetype) title used to label Std. Err. e(properties) b V e(predict) program used to implement predict e(marginsnotok) predictions disallowed by margins e(asbalanced) factor variables fvset as asbalanced e(asobserved) factor variables fvset as asobserved

Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators

Functions e(sample) marks estimation sample

iqreg stores the following in e():

Scalars e(N) number of observations e(df_r) residual degrees of freedom e(q0) lower quantile requested e(q1) upper quantile requested e(reps) number of replications e(sumrdev0) lower quantile sum of raw deviations e(sumrdev1) upper quantile sum of raw deviations e(sumadev0) lower quantile sum of absolute deviations e(sumadev1) upper quantile sum of absolute deviations e(rank) rank of e(V) e(convcode) 0 if converged; otherwise, return code for why nonconvergence

Macros e(cmd) iqreg e(cmdline) command as typed e(depvar) name of dependent variable e(vcetype) title used to label Std. Err. e(properties) b V e(predict) program used to implement predict e(marginsnotok) predictions disallowed by margins e(asbalanced) factor variables fvset as asbalanced e(asobserved) factor variables fvset as asobserved

Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators

Functions e(sample) marks estimation sample

sqreg stores the following in e():

Scalars e(N) number of observations e(df_r) residual degrees of freedom e(n_q) number of quantiles requested e(q#) the quantiles requested e(reps) number of replications e(sumrdv#) sum of raw deviations for q# e(sumadv#) sum of absolute deviations for q# e(rank) rank of e(V) e(convcode) 0 if converged; otherwise, return code for why nonconvergence

Macros e(cmd) sqreg e(cmdline) command as typed e(depvar) name of dependent variable e(eqnames) names of equations e(vcetype) title used to label Std. Err. e(properties) b V e(predict) program used to implement predict e(marginsnotok) predictions disallowed by margins e(asbalanced) factor variables fvset as asbalanced e(asobserved) factor variables fvset as asobserved

Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators

Functions e(sample) marks estimation sample

bsqreg stores the following in e():

Scalars e(N) number of observations e(df_r) residual degrees of freedom e(q) quantile requested e(q_v) value of the quantile e(reps) number of replications e(sum_adev) sum of absolute deviations e(sum_rdev) sum of raw deviations e(rank) rank of e(V) e(convcode) 0 if converged; otherwise, return code for why nonconvergence

Macros e(cmd) bsqreg e(cmdline) command as typed e(depvar) name of dependent variable e(properties) b V e(predict) program used to implement predict e(marginsnotok) predictions disallowed by margins e(asbalanced) factor variables fvset as asbalanced e(asobserved) factor variables fvset as asobserved

Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators

Functions e(sample) marks estimation sample

References

Chamberlain, G. 1994. Quantile regression, censoring, and the structure of wages. In Advances in Economics Sixth World Congress, ed. Christopher A. Sims, 171-209. Cambridge University Press: Cambridge.

Koenker, R. 2005. Quantile Regression. Cambridge University Press: New York.


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