st: bootstrapping standard errors

 From Thomas Mählmann To Subject st: bootstrapping standard errors Date Fri, 21 May 2004 18:24:28 +0200

```Dear All,

I wrote a small ado.file ("mcar_ordinal_6"), given below,  to get bootstrap
std. err. estimates for the coefficients of a binary logit model with one
categorical variable (given by the dummies x1 - x5) and one continuous
variable Z4. I compare these estimates (obtained by typing: . bootstrap
"mcar_ordinal_6" ....) with the usual bootstrapped logit std. err's
(obtained by typing: . bootstrap "logit Y x1 x2 x3 x4 x5 Z4" _b, reps(1000)
dots).  To my surprise, both ways result in totally different std. err.
estimates (given below)!

What is wrong with my ado.file? Any suggestions?

Thank's a lot
Thomas

program define mcar_ordinal_6, rclass
version 8.2

logit Y x1 x2 x3 x4 x5 Z4
mat beta=e(b)

return scalar x1=beta[1,1]
return scalar x2=beta[1,2]
return scalar x3=beta[1,3]
return scalar x4=beta[1,4]
return scalar x5=beta[1,5]
return scalar Z4=beta[1,6]
return scalar const=beta[1,7]

end

. bootstrap "mcar_ordinal_6" const=r(const) Z4=r(Z4) x1=r(x1) x2=r(x2)
x3=r(x3) x4=r(x4) x
> 5=r(x5) , reps(1000) dots

Bootstrap statistics                              Number of obs    =
12451
Replications     =
1000

----------------------------------------------------------------------------
--
Variable     |  Reps  Observed      Bias  Std. Err. [95% Conf. Interval]
-------------+--------------------------------------------------------------
--
const |   559    5.9239  .2659001  3.056453  -.0796589   11.92746
(N)
|                                       .3723237   11.91934
(P)
|                                        .167534   11.36338
(BC)
Z4 |   973 -.1012986  2.435581  3.419307  -6.811373   6.608775
(N)
|                                      -.1615792   10.09536
(P)
|                                      -2.702652   6.346565
(BC)
x1 |  1000 -3.159859  .0387406  .7028649   -4.53912  -1.780598
(N)
|                                      -4.705648  -1.790577
(P)
|                                      -4.807204  -1.910804
(BC)
x2 |  1000 -3.567799   .221243   .762015  -5.063133  -2.072466
(N)
|                                      -4.854494  -1.469348
(P)
|                                      -5.062595  -2.441963
(BC)
x3 |  1000 -3.020464   .755457  1.099255  -5.177578  -.8633499
(N)
|                                      -4.334947  -.2468368
(P)
|                                      -4.853861  -1.190173
(BC)
x4 |  1000 -1.279128  .4245199   .660478  -2.575211   .0169558
(N)
|                                      -1.876799   .2625169
(P)
|                                      -2.165759  -.2838531
(BC)
x5 |   999  -.365843  .2844974  1.212824   -2.74582   2.014134
(N)
|                                      -.9417797   1.215659
(P)
|                                      -1.233725  -.0630795
(BC)
----------------------------------------------------------------------------
--

. bootstrap "logit Y x1 x2 x3 x4 x5 Z4" _b, reps(1000) dots

Bootstrap statistics                              Number of obs    =
12451
Replications     =
1000

----------------------------------------------------------------------------
--
Variable     |  Reps  Observed      Bias  Std. Err. [95% Conf. Interval]
-------------+--------------------------------------------------------------
--
b_x1 |   618 -3.159859  .4253625  .5268016    -4.1944  -2.125317
(N)
|                                      -3.579062   -1.61639
(P)
|                                       -3.82373  -2.401615
(BC)
b_x2 |   939 -3.567799  -.040688  .6170578  -4.778773  -2.356826
(N)
|                                      -4.897816  -2.479752
(P)
|                                      -4.931322  -2.527777
(BC)
b_x3 |   985 -3.020464 -.0677732  .6212142  -4.239521  -1.801407
(N)
|                                      -4.528006  -1.958316
(P)
|                                      -4.468464  -1.938175
(BC)
b_x4 |  1000 -1.279128  .0311197  .3723199  -2.009746  -.5485089
(N)
|                                      -1.958411  -.4930105
(P)
|                                      -1.960265  -.4994082
(BC)
b_x5 |  1000  -.365843  .0290434  .3521309  -1.056844   .3251582
(N)
|                                      -.9971553   .4314241
(P)
|                                      -1.042248   .3425232
(BC)
b_Z4 |  1000 -.1012986 -.0010356  .0334018  -.1668444  -.0357529
(N)
|                                      -.1695864  -.0428685
(P)
|                                      -.1746111  -.0461127
(BC)
b_cons |  1000    5.9239  .0343191  3.088323  -.1364438   11.98424
(N)
|                                       .5156874   12.15566
(P)
|                                        .706053   12.60186
(BC)
----------------------------------------------------------------------------
--

Note:  N   = normal
P   = percentile
BC  = bias-corrected

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```