Why does bootstrap give a warning message for non-eclass commands?
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Title
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Resampling and missing values
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Author
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Jeff Pitblado, StataCorp
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When bootstrapping statistics on data with missing values,
bootstrap may
produce misleading or erroneous bias and variance statistics unless the
command is an eclass command that generates
e(sample). To
better explain the problem, here is an example.
Consider the following dataset with one missing value:
. clear
. set obs 10
Number of observations (_N) was 0, now 10.
. set seed 570971
. generate x = uniform()
. generate y = invnormal(uniform())
. replace y = . in 5
(1 real change made, 1 to missing)
. save resample, replace
(file resample.dta not found)
file resample.dta saved
. list
| | x y |
| 1. | .0901624 -.8072783 |
| 2. | .8839354 .0117225 |
| 3. | .423627 .6715007 |
| 4. | .8497756 -.026581 |
| 5. | .4759649 . |
| | |
| 6. | .3587709 -.6098545 |
| 7. | .2387148 -2.177713 |
| 8. | .915678 .6642656 |
| 9. | .4609539 .9534492 |
| 10. | .6992906 -1.15695 |
It is clear in the following output that only 9 values are used to calculate
the sample standard deviation (SD) of y.
. summarize y
| | Variable | | Obs Mean Std. dev. Min Max |
| | | | |
| | y | | 9 -.275271 1.013946 -2.177713 .9534492 |
After using the describe command on the saved bootstrap sample
dataset (sum.dta), we see that _bs_1 contains the bootstrap
observations of r(mean). Similarly, _bs_2 contains the
bootstrap observations of r(N).
. set seed 1423567
. bootstrap r(mean) r(N), reps(5) saving(sum, replace) nowarn: summarize y
(running summarize on estimation sample)
(file sum.dta not found)
Bootstrap replications (5): ..... done
Bootstrap results Number of obs = 10
Replications = 5
Command: summarize y
_bs_1: r(mean)
_bs_2: r(N)
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| | | Observed Bootstrap Normal-based |
| | | coefficient std. err. z P>|z| [95% conf. interval] |
| | | |
| _bs_1 | | -.275271 .1767023 -1.56 0.119 -.6216012 .0710592 |
| _bs_2 | | 9 .83666 10.76 0.000 7.360176 10.63982 |
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.
describe using sum
Contains data bootstrap: summarize
Observations: 5 1 Aug 2023 13:34
Variables: 2
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| Variable Storage Display Value |
| name type format label Variable label |
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| _bs_1 float %9.0g r(mean) |
| _bs_2 float %9.0g r(N) |
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Sorted by:
.
use sum, clear
(bootstrap: summarize)
.
list
| | _bs_1 _bs_2 |
| 1. | -.0924903 10 |
| 2. | .0861323 10 |
| 3. | -.088269 9 |
| 4. | -.4005653 8 |
| 5. | -.0740297 9 |
The above listing of the boostrap data reveals the problem; not all of the
bootstrap samples contained 9 observations. This problem is easily fixed
for this example, since we can drop the observations that have a missing
value from the original dataset before using bootstrap.
. use resample, clear
. drop if y == .
(1 observation deleted)
. list
| | x y |
| 1. | .0901624 -.8072783 |
| 2. | .8839354 .0117225 |
| 3. | .423627 .6715007 |
| 4. | .8497756 -.026581 |
| 5. | .3587709 -.6098545 |
| | |
| 6. | .2387148 -2.177713 |
| 7. | .915678 .6642656 |
| 8. | .4609539 .9534492 |
| 9. | .6992906 -1.15695 |
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set seed 1423567
.
bootstrap r(mean) r(N), reps(5) saving(sum, replace) nowarn: summarize y
(running summarize on estimation sample)
Bootstrap replications (5): ..... done
Bootstrap results Number of obs = 9
Replications = 5
Command: summarize y
_bs_1: r(mean)
_bs_2: r(N)
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| | | Observed Bootstrap Normal-based |
| | | coefficient std. err. z P>|z| [95% conf. interval] |
| | | |
| _bs_1 | | -.275271 .2803826 -0.98 0.326 -.8248108 .2742688 |
| _bs_2 | | 9 . . . . . |
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use sum, clear
(bootstrap: summarize)
.
list
| | _bs_1 _bs_2 |
| 1. | .0178111 9 |
| 2. | -.5203212 9 |
| 3. | .1150261 9 |
| 4. | .092199 9 |
| 5. | -.3069329 9 |
In the examples above, I used the nowarn option on bootstrap
to suppress the warning message it issues when no e(sample) is
available.
bootstrap will not produce a warning message when an estimation
command (eclass) that generates e(sample) is supplied. Here,
e(sample) provides bootstrap with all the information it needs
to keep unused observations out of the bootstrap samples. Similarly, to the
mean of y, it is clear from the following output that only 9
observations are used to estimate the coefficient on the predictor for
simple linear regression. The coefficient is saved in _b[x], and the
number of observations used in the estimation is saved in e(N).
. use resample, clear
. regress y x
| Source | | SS df MS | Number of obs = 9 |
| | | F(1, 7) = 1.60 |
| Model | | 1.53022378 1 1.53022378 | Prob > F = 0.2464 |
| Residual | | 6.69446954 7 .956352791 | R-squared = 0.1861 |
| | | Adj R-squared = 0.0698 |
| Total | | 8.22469332 8 1.02808666 | Root MSE = .97793 |
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| y | | Coefficient Std. err. t P>|t| [95% conf. interval] |
| | | |
| x | | 1.451699 1.147646 1.26 0.246 -1.262054 4.165451 |
| _cons | | -1.069013 .7071156 -1.51 0.174 -2.741075 .6030498 |
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set seed 1423567
.
bootstrap _b[x] e(N), reps(5) saving(reg, replace): regress y x
(running regress on estimation sample)
(file reg.dta not found)
Bootstrap replications (5): ..... done
Linear regression Number of obs = 9
Replications = 5
Command: regress y x
_bs_1: _b[x]
_bs_2: e(N)
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| | | Observed Bootstrap Normal-based |
| | | coefficient std. err. z P>|z| [95% conf. interval] |
| | | |
| _bs_1 | | 1.451699 1.172467 1.24 0.216 -.8462939 3.749691 |
| _bs_2 | | 9 . . . . . |
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.
use reg, clear
(bootstrap: regress)
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list
| | _bs_1 _bs_2 |
| 1. | -.5315873 9 |
| 2. | 2.245691 9 |
| 3. | .9832834 9 |
| 4. | 1.318368 9 |
| 5. | 2.373077 9 |
