dbs: Stata command for computing double bootstrap confidence intervals
Double bootstrap confidence intervals promise more precise results with a better nominal coverage for many applications. The package is lightweight, easy to use and very similar to the regular standard Stata bootstrap command. Multithreading allows the computation with multiple instances even without Stata-MP for massive speed gain. Please refer to the help file for details.
Installation
. net install dbs, from(https://raw.github.com/fbittmann/dbs/stable) replaceExamples
Setup and minimal example
. sysuse auto, clear
(1978 Automobile Data)
. dbs r(mean) r(p50): summarize mpg, detail
Warning: Because the command invoked does not set e(sample),
dbs has no way to determine which observations are
used incalculating the statistics and so assumes
that all observations are used. Check for missing
values with care.
Bootstrap replications (100 / 20)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
..........
Bootstrap results Number of obs = 74
Reps1 = 100
Reps2 = 20
command: summarize mpg, detail
_bs_1: r(mean)
_bs_2: r(p50)
---------------------------------------------------------------------------------
| Observed Coef. Boot. Std. Err. Bias SFrancia [95% Conf. Interval]
----------+----------------------------------------------------------------------
_bs_1 | 21.2973 0.6301 -0.075 0.963 20.1315 22.8198
_bs_2 | 20.0000 0.9891 0.095 0.561 16.9322 22.4864
---------------------------------------------------------------------------------Bootstrap regression coefficients
. dbs _b[weight] _b[_cons]: regress mpg weight
Bootstrap replications (100 / 20)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
..........
Bootstrap results Number of obs = 74
Reps1 = 100
Reps2 = 20
command: regress mpg weight
_bs_1: _b[weight]
_bs_2: _b[_cons]
---------------------------------------------------------------------------------
| Observed Coef. Boot. Std. Err. Bias SFrancia [95% Conf. Interval]
----------+----------------------------------------------------------------------
_bs_1 | -0.0060 0.0006 -0.000 0.003 -0.0077 -0.0048
_bs_2 | 39.4403 1.9402 0.023 0.001 35.2007 44.9857
---------------------------------------------------------------------------------Multithreading with parallel
. net install parallel, from(https://raw.github.com/gvegayon/parallel/stable/) replace
. mata mata mlib index
. dbs r(mean), reps1(5000) reps2(100) parallel(4): summarize mpg, meanonly
Warning: Because the command invoked does not set e(sample),
dbs has no way to determine which observations are
used incalculating the statistics and so assumes
that all observations are used. Check for missing
values with care.
Since multiple instances work in parallel, no progress visualization is available.
Bootstrap results Number of obs = 74
Reps1 = 5000
Reps2 = 100
command: summarize mpg, meanonly
_bs_1: r(mean)
---------------------------------------------------------------------------------
| Observed Coef. Boot. Std. Err. Bias SFrancia [95% Conf. Interval]
----------+----------------------------------------------------------------------
_bs_1 | 21.2973 0.6727 -0.003 0.000 19.9914 22.7805
---------------------------------------------------------------------------------
Using analytic standard errors
. regress mpg weigh
Source | SS df MS Number of obs = 74
-------------+---------------------------------- F(1, 72) = 134.62
Model | 1591.9902 1 1591.9902 Prob > F = 0.0000
Residual | 851.469256 72 11.8259619 R-squared = 0.6515
-------------+---------------------------------- Adj R-squared = 0.6467
Total | 2443.45946 73 33.4720474 Root MSE = 3.4389
------------------------------------------------------------------------------
mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weight | -.0060087 .0005179 -11.60 0.000 -.0070411 -.0049763
_cons | 39.44028 1.614003 24.44 0.000 36.22283 42.65774
------------------------------------------------------------------------------
. matrix list r(table)
r(table)[9,2]
weight _cons
b -.00600869 39.440284
se .00051788 1.6140031
t -11.60251 24.436312
pvalue 3.798e-18 1.385e-36
ll -.00704106 36.222827
ul -.00497632 42.65774
df 72 72
crit 1.9934636 1.9934636
eform 0 0
. dbs _b[weight] _b[_cons], reps(5000) dots(0) seed(123) analytic(r(table)[2,1] r(table)[2,2]): ///
> regress mpg weigh
Bootstrap results Number of obs = 74
Reps = 5000
Reps (inner) = 0
command: regress mpg weigh
analytic standard error(s) provided (shown in brackets)
_bs_1: _b[weight] [r(table)[2,1]]
_bs_2: _b[_cons] [r(table)[2,2]]
---------------------------------------------------------------------------------
| Observed Bootstrap Shapiro-
| Coef. Std. Err. Bias Francia [95% Conf. Interval]
----------+----------------------------------------------------------------------
_bs_1 | -0.0060 0.0006 -0.000 0.000 -0.0075 -0.0048
_bs_2 | 39.4403 1.9915 -0.008 0.000 34.8924 44.9830
---------------------------------------------------------------------------------Using dbs with cluster or panel data
. clear all
. cap program drop iccres
. program define iccres, rclass
1. syntax [if] [in], id(varlist)
2. mixed vrq `if' `in', nostderr || `id': //No SEs for faster computational speed
3. estat icc
4. return scalar icc = r(icc2)
5. end
.
. webuse fifeschool, clear
(School data from Fife, Scotland)
. gen newid = pid
. keep if pid < 50 //Reduce sample for faster computational speed
(1,981 observations deleted)
. dbs r(icc), reps(100) jackknife seed(123) cluster(pid) idcluster(newid): ///
> iccres, id(newid)
Bootstrap replications (100 / 0)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
..........
Bootstrap results Number of obs = 1454
Reps = 100
Reps (inner) = 0
command: iccres, id(newid)
Jackknife standard errors computed
_bs_1: r(icc)
---------------------------------------------------------------------------------
| Observed Bootstrap Shapiro-
| Coef. Std. Err. Bias Francia [95% Conf. Interval]
----------+----------------------------------------------------------------------
_bs_1 | 0.1009 0.0224 -0.004 0.000 0.0648 0.1690
---------------------------------------------------------------------------------
Citation
Thanks for citing this software as follows:
Bittmann, Felix (2020): dbs: Stata module to compute double bootstrap confidence intervals. Available from: https://github.com/fbittmann/dbs. A preprint is available 10.20944/preprints202302.0213.v1.