*! version 1.1.1

Title

itvalpctile -- Executes estimation of interval-valued percentiles (quantiles) for interval-valued data.

Syntax

itvalpctile
lower
upper
[if] [in]
[, cover(real) pl(real) ph(real) np(real) conditional(varname) location(real)]

Description

itvalpctile executes estimation of percentiles (quantiles) for interval-valued data based on
Beresteanu and Sasaki (2021).
It applies to interval-valued survey and questionnaire responses.
The command takes the lower bound (lower) and the upper bound (upper) of the intervals.
It returns interval-valued percentiles (and their valid confidence sets if lower and upper are continuous).
The command can also compute conditional interval-valued percentiles and their confidence sets by calling the option conditional.

Options

cover(real) sets the nominal probability that the confidence sets cover the true percentiles. The default value is cover(.95).

pl(real) sets the lowest percent at which the interval-valued percentile is reported. The default value is pl(10).

ph(real) sets the highest percent at which the interval-valued percentile is reported. The default value is ph(90).

np(real) sets the number of percent points at which the interval-valued percentile is reported. The default value is np(9).

conditional(varname) sets a conditioning variables with which the conditional interval-valued percentiles are estimated. Not calling this option tells the command to estimate the unconditional interval-valued percentiles.

location(real) sets the location of the conditioning variable at which the conditional interval-valued percentiles are estimated. Not calling this option results in using the mean value of the conditioning variable as the location.

Examples

. use "CHTdata_extract10percent.dta"

(lower lower bound, upper upper bound, v1 discrete conditioning variable, v2 continuous conditioning variable)

Estimation of interval-valued percentiles at the percent points 10, 20, 30, 40, 50, 60, 70, 80 and 90:

. itvalpctile lower upper

Estimation of interval-valued percentiles at the percent points 25, 30, 35, 40, 45, 50, 55, 60, 65, 70 and 75:

. itvalpctile lower upper, pl(25) ph(75) np(11)

Estimation of interval-valued percentiles with 90% confidence sets:

. itvalpctile lower upper, cover(0.90)

Estimation of conditional interval-valued percentiles given v2=0.05 for a "continuous" variable v2:

. itvalpctile lower upper, conditional(v2) location(0.05)

Estimation of conditional interval-valued percentiles given v1=40 for a "discrete" variable v1:

. itvalpctile lower upper if v1 == 40

Stored results

itvalpctile stores the following in r():

Scalars

r(N) observations

Macros

r(cmd) itvalpctile

Matrices

r(percent) vector of percents

r(lower) vector lower bounds

r(upper) vector upper bounds

r(CSlower) vector lower bounds of confidence set

r(CSupper) vector upper bounds of confidence set

Reference

Beresteanu, A. and Y. Sasaki. 2021. Quantile Regression with Interval Data.
Econometric Reviews (Special Issue Honoring Cheng Hsiao), 40 (6): 562-583.
Link to Paper.

Authors

Arie Beresteanu, University of Pittsburgh, Pittsburgh, PA.

Yuya Sasaki, Vanderbilt University, Nashville, TN.