what does the size() option on bootstrap do?

[William Lisowski]

I apparently do not understand the documentation for the bootstrap command.

. sysuse auto, clear
(1978 automobile data)

. set seed 42

. bootstrap e(N) e(r2), size(30): regress price weight
(running regress on estimation sample)

Bootstrap replications (50)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50

Linear regression                                           Number of obs = 74
                                                            Replications  = 50

      Command: regress price weight
        _bs_1: e(N)
        _bs_2: e(r2)

------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             | coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _bs_1 |         74          .        .       .            .           .
       _bs_2 |   .2901023   .1183702     2.45   0.014      .058101    .5221036
------------------------------------------------------------------------------

.

What I expected was "Number of obs = 30" and _bs_1 to also be 30, with no variation. Instead, bootstrap has apparently used size(_N) which is the default, and given me 74 observations.

Can someone explain to me what effect the size(30) option had?

[Leonardo Guizzetti]

This is confusing, and I recall an earlier thread from some years ago about this behaviour but I cannot find that thread now. The -size()- option is supposed to draw a simple random sample with replacement of size n, where n < _N, ignoring clustering. The resulting statistics are based on the specified size, as demonstrated by examining the noisy output of 2 bootstrap samples.

sysuse auto, clear
set seed 42

tempfile res
bootstrap n=(e(N)) _b, reps(2) noi size(30) saving(`res', replace): regress price weight

use `res', clear
list

Result

. bootstrap n=(e(N)) _b, reps(2) noi size(30) saving(`res', replace): regress price weight
bootstrap: First call to regress with data as is:

. regress price weight

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =     29.42
       Model |   184233937         1   184233937   Prob > F        =    0.0000
    Residual |   450831459        72  6261548.04   R-squared       =    0.2901
-------------+----------------------------------   Adj R-squared   =    0.2802
       Total |   635065396        73  8699525.97   Root MSE        =    2502.3

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      weight |   2.044063   .3768341     5.42   0.000     1.292857    2.795268
       _cons |  -6.707353    1174.43    -0.01   0.995     -2347.89    2334.475
------------------------------------------------------------------------------
(file C:\tmp\ST_3fe4_000001.tmp not found)

Bootstrap replications (2)
. regress price weight

      Source |       SS           df       MS      Number of obs   =        30
-------------+----------------------------------   F(1, 28)        =      5.08
       Model |  21802684.2         1  21802684.2   Prob > F        =    0.0323
    Residual |   120244319        28  4294439.96   R-squared       =    0.1535
-------------+----------------------------------   Adj R-squared   =    0.1233
       Total |   142047003        29  4898172.52   Root MSE        =    2072.3

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      weight |   1.301304   .5775335     2.25   0.032     .1182806    2.484328
       _cons |   1359.267   1738.839     0.78   0.441    -2202.584    4921.118
------------------------------------------------------------------------------
. regress price weight

      Source |       SS           df       MS      Number of obs   =        30
-------------+----------------------------------   F(1, 28)        =     20.14
       Model |   126219603         1   126219603   Prob > F        =    0.0001
    Residual |   175456520        28  6266304.28   R-squared       =    0.4184
-------------+----------------------------------   Adj R-squared   =    0.3976
       Total |   301676123        29  10402624.9   Root MSE        =    2503.3

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      weight |   2.548572   .5678573     4.49   0.000     1.385369    3.711775
       _cons |  -1629.684   1936.397    -0.84   0.407    -5596.213    2336.845
------------------------------------------------------------------------------

Linear regression                                           Number of obs = 74
                                                            Replications  =  2

      Command: regress price weight
      [_eq2]n: e(N)

------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             | coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
_eq1         |
      weight |   2.044063   .8819513     2.32   0.020     .3154698    3.772655
       _cons |  -6.707353   2113.507    -0.00   0.997    -4149.106    4135.691
-------------+----------------------------------------------------------------
_eq2         |
           n |         74          .        .       .            .           .
------------------------------------------------------------------------------

. list
     +-------------------------------+
     | _b_wei~t     _b_cons   _eq2_n |
     |-------------------------------|
  1. | 1.301304    1359.267       30 |
  2. | 2.548572   -1629.684       30 |
     +-------------------------------+

So each bootstrap draws a sample of the requested size and bootstrap correctly saves the statistics for each of those samples (shown in red). The hiccup here, I think, is that it is somehow overwriting that in the estimation table output because it's using the coefficient point estimates and those where estimated on the full sample. I would have expected that number to match the size requested.

[Jared Greathouse]

Perhaps this is the thread you meant? Leonardo Guizzetti

[Leonardo Guizzetti]

Perhaps this is the thread you meant? Leonardo Guizzetti

Honestly, I don't recall at this point. These two threads may also be of interest for how to see bootstrap at work and how to (not) abuse it.

[William Lisowski]

My thanks to Leonardo Guizzetti and Jared Greathouse for their discussion and links. How disconcerting to see my earlier participation in discussions similar to the one I have just started. Clearly not all of my 8700+ (at this time) prior posts here are readily accessible in my memory.

I now (and apparently, for some limited time into the future) understand that "Number of obs = 74" is in fact the number of observations used in the initial regression on the full estimation sample. And I now recall something I once knew, that the "observed coefficient" is in fact the value from that initial regression - the bootstrap process gives us only the estimates of the standard errors of those estimated coefficients; it does not provide new estimates of those coefficients. And this is noticeable in Leonardo's example: the two bootstrapped constants are 1359 and -1629; the "observed constant" is -6, which would be an incongruous melding of the two bootstrap results.

So the "observed coefficient" for e(N) is indeed correctly reported as that from the full estimation sample.