# st: Bootstrap: Which standard errors to use?

13 messages
Open this post in threaded view
|

## st: Bootstrap: Which standard errors to use?

 Dear all, I am using bootstrap in my study and Stata reports 2 types of standard errors of beta: (1) bootstrap std. err. right to the observed coef. and (2) se shown in the second part of the table. They are quite different. How does Stata calculate both of these SEs? Which one would be better to use? Would anybody please explain or suggest? Thank you Anupit . local vehicle age lnodo peuro pasia pother   . local owner black other . set seed 9999     . bootstrap _b _se, reps(10000) saving("C:\data\logitBOOT2Abse.dta", replace): ///   logit tresimp indlninc `owner' `vehicle', robust Logistic regression                             Number of obs      =       465                                                 Replications       =      4899 ------------------------------------------------------------------------------              |   Observed   Bootstrap                         Normal-based              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- b            |     indlninc |  -.2818828   .4831361    -0.58   0.560    -1.228812    .6650466        black |   1.184949   .6092399     1.94   0.052    -.0091396    2.379037        other |   .5112052     .73946     0.69   0.489    -.9381097     1.96052          age |   .2291411    .091903     2.49   0.013     .0490146    .4092677        lnodo |   .2668319   .5548409     0.48   0.631    -.8206363      1.3543        peuro |   .3441804   .9544531     0.36   0.718    -1.526513    2.214874        pasia |   .1141557   .7772255     0.15   0.883    -1.409178     1.63749       pother |   .1774283   .7139723     0.25   0.804    -1.221932    1.576788 -------------+---------------------------------------------------------------- se           |     indlninc |   .3751495   .1164555     3.22   0.001     .1469009    .6033982        black |   .5377806   .1174539     4.58   0.000     .3075752    .7679861        other |   .6130217   .1737154     3.53   0.000     .2725458    .9534977          age |   .0683818   .0179438     3.81   0.000     .0332126    .1035509        lnodo |   .3736896   .1584534     2.36   0.018     .0631266    .6842526        peuro |   .8376832    .242609     3.45   0.001     .3621782    1.313188        pasia |   .6548303   .1592494     4.11   0.000     .3427073    .9669534       pother |   .7830163   .2246008     3.49   0.000     .3428068    1.223226 * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
Open this post in threaded view
|

## Re: st: Bootstrap: Which standard errors to use?

 --- "Supnithadnaporn, Anupit" <[hidden email]> wrote: > I am using bootstrap in my study and Stata reports 2 types of > standard errors of beta: (1) bootstrap std. err. right to the > observed coef. and (2) se shown in the second part of the table. > They are quite different. > . local vehicle age lnodo peuro pasia pother   > . local owner black other > . set seed 9999     > . bootstrap _b _se, reps(10000) saving("C:\data\logitBOOT2Abse.dta", > replace): /// >   logit tresimp indlninc `owner' `vehicle', robust The standard error in the second part is the standard error of the standard error. Remember that the standard error is also an estimate, so you can have sampling uncertainty around that too. The standard error in the second part of your table tells you about the uncertainty about the estimate of the standard error. So, it can be interesting too look at it, but the standard error you are after is in the first part of the table. Normally you would not ask for the second part of your table (and exclude the -_se- from the -bootstrap- statement). Hope this helps, Maarten ----------------------------------------- Maarten L. Buis Department of Social Research Methodology Vrije Universiteit Amsterdam Boelelaan 1081 1081 HV Amsterdam The Netherlands visiting address: Buitenveldertselaan 3 (Metropolitan), room N515 +31 20 5986715 http://home.fsw.vu.nl/m.buis/-----------------------------------------       * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
Open this post in threaded view
|

## Re: st: Bootstrap: Which standard errors to use?

 Thank you Marrten for your explanation. This helps a lot. Anupit ----- "Maarten buis" <[hidden email]> wrote: > --- "Supnithadnaporn, Anupit" <[hidden email]> wrote: > > I am using bootstrap in my study and Stata reports 2 types of > > standard errors of beta: (1) bootstrap std. err. right to the > > observed coef. and (2) se shown in the second part of the table. > > They are quite different. > > > . local vehicle age lnodo peuro pasia pother   > > . local owner black other > > . set seed 9999     > > . bootstrap _b _se, reps(10000) > saving("C:\data\logitBOOT2Abse.dta", > > replace): /// > >   logit tresimp indlninc `owner' `vehicle', robust > > The standard error in the second part is the standard error of the > standard error. Remember that the standard error is also an estimate, > so you can have sampling uncertainty around that too. The standard > error in the second part of your table tells you about the > uncertainty > about the estimate of the standard error. So, it can be interesting > too > look at it, but the standard error you are after is in the first part > of the table. Normally you would not ask for the second part of your > table (and exclude the -_se- from the -bootstrap- statement). > > Hope this helps, > Maarten > > ----------------------------------------- > Maarten L. Buis > Department of Social Research Methodology > Vrije Universiteit Amsterdam > Boelelaan 1081 > 1081 HV Amsterdam > The Netherlands > > visiting address: > Buitenveldertselaan 3 (Metropolitan), room N515 > > +31 20 5986715 > > http://home.fsw.vu.nl/m.buis/> ----------------------------------------- > > >       > * > *   For searches and help try: > *   http://www.stata.com/help.cgi?search> *   http://www.stata.com/support/statalist/faq> *   http://www.ats.ucla.edu/stat/stata/-- Anupit Supnithadnaporn PhD Candidate School of Public Policy Georgia Institute of Technology D.M.Smith Building TPAC Room 018 685 Cherry Street Atlanta GA 30332 * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
Open this post in threaded view
|

## Re: st: Bootstrap: Which standard errors to use?

 In reply to this post by Maarten buis The second part of the table actually shows that the Hessian-based standard errors of logit are biased down by some 10-20%, for whatever reason. The average standard error for indlninc variable is 0.375, while the bootstrap measure of variability is 0.483. The first one is purely model-based, while the second one is more robust to various model misspecifications. I'd be curious as to whether -logit ..., robust- standard errors would be close to the bootstrap ones, in your case. On 12/8/08, Maarten buis <[hidden email]> wrote: > --- "Supnithadnaporn, Anupit" <[hidden email]> wrote: >  > I am using bootstrap in my study and Stata reports 2 types of >  > standard errors of beta: (1) bootstrap std. err. right to the >  > observed coef. and (2) se shown in the second part of the table. >  > They are quite different. > > > > > . local vehicle age lnodo peuro pasia pother >  > . local owner black other >  > . set seed 9999 >  > . bootstrap _b _se, reps(10000) saving("C:\data\logitBOOT2Abse.dta", >  > replace): /// >  >   logit tresimp indlninc `owner' `vehicle', robust > > > The standard error in the second part is the standard error of the >  standard error. Remember that the standard error is also an estimate, >  so you can have sampling uncertainty around that too. The standard >  error in the second part of your table tells you about the uncertainty >  about the estimate of the standard error. So, it can be interesting too >  look at it, but the standard error you are after is in the first part >  of the table. Normally you would not ask for the second part of your >  table (and exclude the -_se- from the -bootstrap- statement). > >  Hope this helps, >  Maarten > >  ----------------------------------------- >  Maarten L. Buis >  Department of Social Research Methodology >  Vrije Universiteit Amsterdam >  Boelelaan 1081 >  1081 HV Amsterdam >  The Netherlands > >  visiting address: >  Buitenveldertselaan 3 (Metropolitan), room N515 > >  +31 20 5986715 > >  http://home.fsw.vu.nl/m.buis/>  ----------------------------------------- > > > > >  * >  *   For searches and help try: >  *   http://www.stata.com/help.cgi?search>  *   http://www.stata.com/support/statalist/faq>  *   http://www.ats.ucla.edu/stat/stata/> -- Stas Kolenikov, also found at http://stas.kolenikov.nameSmall print: I use this email account for mailing lists only. * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
Open this post in threaded view
|

## Re: st: Bootstrap: Which standard errors to use?

 In reply to this post by Supnithadnaporn, Anupit ----- "Stas Kolenikov" <[hidden email]> wrote: > I'd be curious as to whether -logit ..., > robust- standard errors would be close to the bootstrap ones, in your > case. I guess you mean the result from running -logit, robust- one time, right? Would these SE seem to make sense to you at all? Thank you, Anupit Logistic regression                               Number of obs   =        465                                                   Wald chi2(16)   =      44.37                                                   Prob > chi2     =     0.0002 Log pseudolikelihood = -73.949457                 Pseudo R2       =     0.2407 ------------------------------------------------------------------------------              |               Robust      tresimp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+----------------------------------------------------------------     indlninc |  -.2818828   .3751495    -0.75   0.452    -1.017162    .4533968        black |   1.184949   .5377806     2.20   0.028      .130918    2.238979        other |   .5112052   .6130217     0.83   0.404    -.6902953    1.712706          age |   .2291411   .0683818     3.35   0.001     .0951153    .3631669        lnodo |   .2668319   .3736896     0.71   0.475    -.4655863    .9992501        peuro |   .3441804   .8376832     0.41   0.681    -1.297648    1.986009        pasia |   .1141557   .6548303     0.17   0.862    -1.169288      1.3976       pother |   .1774283   .7830163     0.23   0.821    -1.357255    1.712112        displ |  -.0444871   .3161949    -0.14   0.888    -.6642178    .5752435       indefi |   .3926529   .6165853     0.64   0.524     -.815832    1.601138        indfi |  -.5801308   .6734173    -0.86   0.389    -1.900004    .7397428       indmfi |  -1.667607   1.093033    -1.53   0.127    -3.809912    .4746974         egr1 |  -1.307301   .5173223    -2.53   0.012    -2.321235   -.2933684         tac1 |  -.1766159   .7599367    -0.23   0.816    -1.666064    1.312833          car |  -1.189119   .8430763    -1.41   0.158    -2.841518    .4632803          van |  -1.120382   .9862894    -1.14   0.256    -3.053474    .8127092        _cons |  -3.180481   6.637172    -0.48   0.632     -16.1891    9.828137 ------------------------------------------------------------------------------ * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
Open this post in threaded view
|

## Re: st: Bootstrap: Which standard errors to use?

 Those are exactly the reported standard errors in your second panel. That's interesting; I am used to thinking that they are close to the bootstrap standard errors. How about the -oim- standard errors without the -robust- option? On 12/8/08, Supnithadnaporn, Anupit <[hidden email]> wrote: > ----- "Stas Kolenikov" <[hidden email]> wrote: > >  > I'd be curious as to whether -logit ..., >  > robust- standard errors would be close to the bootstrap ones, in your >  > case. > > > I guess you mean the result from running -logit, robust- one time, right? >  Would these SE seem to make sense to you at all? > >  Thank you, >  Anupit > > >  Logistic regression                               Number of obs   =        465 > >                                                   Wald chi2(16)   =      44.37 >                                                   Prob > chi2     =     0.0002 >  Log pseudolikelihood = -73.949457                 Pseudo R2       =     0.2407 > >  ------------------------------------------------------------------------------ >              |               Robust >      tresimp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] >  -------------+---------------------------------------------------------------- >     indlninc |  -.2818828   .3751495    -0.75   0.452    -1.017162    .4533968 >        black |   1.184949   .5377806     2.20   0.028      .130918    2.238979 >        other |   .5112052   .6130217     0.83   0.404    -.6902953    1.712706 >          age |   .2291411   .0683818     3.35   0.001     .0951153    .3631669 >        lnodo |   .2668319   .3736896     0.71   0.475    -.4655863    .9992501 >        peuro |   .3441804   .8376832     0.41   0.681    -1.297648    1.986009 >        pasia |   .1141557   .6548303     0.17   0.862    -1.169288      1.3976 >       pother |   .1774283   .7830163     0.23   0.821    -1.357255    1.712112 >        displ |  -.0444871   .3161949    -0.14   0.888    -.6642178    .5752435 >       indefi |   .3926529   .6165853     0.64   0.524     -.815832    1.601138 >        indfi |  -.5801308   .6734173    -0.86   0.389    -1.900004    .7397428 >       indmfi |  -1.667607   1.093033    -1.53   0.127    -3.809912    .4746974 >         egr1 |  -1.307301   .5173223    -2.53   0.012    -2.321235   -.2933684 >         tac1 |  -.1766159   .7599367    -0.23   0.816    -1.666064    1.312833 >          car |  -1.189119   .8430763    -1.41   0.158    -2.841518    .4632803 >          van |  -1.120382   .9862894    -1.14   0.256    -3.053474    .8127092 >        _cons |  -3.180481   6.637172    -0.48   0.632     -16.1891    9.828137 >  ------------------------------------------------------------------------------ > > > >  * >  *   For searches and help try: >  *   http://www.stata.com/help.cgi?search>  *   http://www.stata.com/support/statalist/faq>  *   http://www.ats.ucla.edu/stat/stata/> -- Stas Kolenikov, also found at http://stas.kolenikov.nameSmall print: I use this email account for mailing lists only. * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
Open this post in threaded view
|

## Re: st: Bootstrap: Which standard errors to use?

 ----- "Stas Kolenikov" <[hidden email]> wrote: > How about the -oim- standard errors > without > the -robust- option? > As you requested. What would -oim- stand for? Thank you, Anupit Logistic regression                               Number of obs   =        465                                                   LR chi2(16)     =      46.89                                                   Prob > chi2     =     0.0001 Log likelihood = -73.949457                       Pseudo R2       =     0.2407 ------------------------------------------------------------------------------      tresimp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+----------------------------------------------------------------     indlninc |  -.2818828   .3439042    -0.82   0.412    -.9559228    .3921571        black |   1.184949   .5615598     2.11   0.035     .0843117    2.285586        other |   .5112052   .6401804     0.80   0.425    -.7435253    1.765936          age |   .2291411   .0710728     3.22   0.001      .089841    .3684412        lnodo |   .2668319   .3439181     0.78   0.438    -.4072352     .940899        peuro |   .3441804    .896089     0.38   0.701    -1.412122    2.100483        pasia |   .1141557   .6634897     0.17   0.863     -1.18626    1.414572       pother |   .1774283   .8487587     0.21   0.834    -1.486108    1.840965        displ |  -.0444871   .2766297    -0.16   0.872    -.5866715    .4976972       indefi |   .3926529   .6296414     0.62   0.533    -.8414216    1.626727        indfi |  -.5801308   .6346339    -0.91   0.361     -1.82399    .6637289       indmfi |  -1.667607   1.121463    -1.49   0.137    -3.865634    .5304192         egr1 |  -1.307301   .5190509    -2.52   0.012    -2.324623   -.2899803         tac1 |  -.1766159   .7663102    -0.23   0.818    -1.678556    1.325324          car |  -1.189119   .8525678    -1.39   0.163    -2.860121    .4818834          van |  -1.120382   .9176824    -1.22   0.222    -2.919007    .6782421        _cons |  -3.180481   5.519478    -0.58   0.564    -13.99846    7.637497 ------------------------------------------------------------------------------ * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
Open this post in threaded view
|

## Re: st: Bootstrap: Which standard errors to use?

 "Observed Information Matrix" HTH Martin _______________________ ----- Original Message ----- From: "Supnithadnaporn, Anupit" <[hidden email]> To: <[hidden email]> Sent: Monday, December 08, 2008 9:01 PM Subject: Re: st: Bootstrap: Which standard errors to use? > ----- "Stas Kolenikov" <[hidden email]> wrote: >> How about the -oim- standard errors >> without >> the -robust- option? >> > > As you requested. What would -oim- stand for? > > Thank you, > > Anupit > > > > Logistic regression                               Number of obs   = > 465 >                                                  LR chi2(16)     = > 46.89 >                                                  Prob > chi2     = > 0.0001 > Log likelihood = -73.949457                       Pseudo R2       = > 0.2407 > > ------------------------------------------------------------------------------ >     tresimp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. > Interval] > -------------+---------------------------------------------------------------- >    indlninc |  -.2818828   .3439042    -0.82   0.412    -.9559228 > .3921571 >       black |   1.184949   .5615598     2.11   0.035     .0843117 > 2.285586 >       other |   .5112052   .6401804     0.80   0.425    -.7435253 > 1.765936 >         age |   .2291411   .0710728     3.22   0.001      .089841 > .3684412 >       lnodo |   .2668319   .3439181     0.78   0.438    -.4072352 > .940899 >       peuro |   .3441804    .896089     0.38   0.701    -1.412122 > 2.100483 >       pasia |   .1141557   .6634897     0.17   0.863     -1.18626 > 1.414572 >      pother |   .1774283   .8487587     0.21   0.834    -1.486108 > 1.840965 >       displ |  -.0444871   .2766297    -0.16   0.872    -.5866715 > .4976972 >      indefi |   .3926529   .6296414     0.62   0.533    -.8414216 > 1.626727 >       indfi |  -.5801308   .6346339    -0.91   0.361     -1.82399 > .6637289 >      indmfi |  -1.667607   1.121463    -1.49   0.137    -3.865634 > .5304192 >        egr1 |  -1.307301   .5190509    -2.52 > 0.012    -2.324623   -.2899803 >        tac1 |  -.1766159   .7663102    -0.23   0.818    -1.678556 > 1.325324 >         car |  -1.189119   .8525678    -1.39   0.163    -2.860121 > .4818834 >         van |  -1.120382   .9176824    -1.22   0.222    -2.919007 > .6782421 >       _cons |  -3.180481   5.519478    -0.58   0.564    -13.99846 > 7.637497 > ------------------------------------------------------------------------------ > > > * > *   For searches and help try: > *   http://www.stata.com/help.cgi?search> *   http://www.stata.com/support/statalist/faq> *   http://www.ats.ucla.edu/stat/stata/> * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
Open this post in threaded view
|

## Re: st: Bootstrap: Which standard errors to use?

 In reply to this post by Stas Kolenikov Stas Kolenikov wrote: > Those are exactly the reported standard errors in your second panel. Which, if I followed the thread correctly, should not come as a surprise since Anupit's original -bootstrap- command called -logit, robust- Antoine * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
Open this post in threaded view
|

## Re: st: Bootstrap: Which standard errors to use?

 On 12/8/08, Antoine Terracol <[hidden email]> wrote: > > Those are exactly the reported standard errors in your second panel. >  Which, if I followed the thread correctly, should not come as a surprise > since Anupit's original -bootstrap- command called -logit, robust- Right, I did not really pay much attention up there :)). Well the -robust- standard errors are in fact closer to -oim- standard errors than to the bootstrap standard errors. It is difficult to come up with a meaningful suggestion in this situation as to which standard errors are better. A (former) econometrician inside me would like to remind that modeling the 0/1 decision to buy something (which this application seem to be related to based on the variable names at least) treated as the imperfect observation of the underlying continuous propensity to buy is subject to the scale indeterminacy, so that the identified combinations of parameters are "slope"/"standard deviation of the error term" rather than "slope" as it is the case with linear regression. Biostatisticians would rightfully raise a brow here -- "What is he talking about? This is a GLM with a canonical link... and the scale parameter here is 1". Well this is a matter of interpretation! If you want an economics interpretation, then you would need to make sure you control that sigma in the denominator to really talk about betas being on the same scale (and only then the bootstrap will make sense) -- which unfortunately cannot be guaranteed. Another aspect is the numeric stability of the logistic regression estimates. For some bootstrap samples, the logit estimates are not defined -- say if you sampled all zeroes, or as many ones as you have regressors in the model so that the outcome of 1 can be perfectly predicted with coefficient values at infinity. In some likelihood, the samples that are "close", in some sense, to those extreme outcomes may also produce "large" estimates of coefficients. Are those sensible outcomes for the bootstrap? Probably not; hence the bootstrap procedure might need to be modified to control the relative proportions of 0s and 1s. In the simplest way, you do some sort of stratified bootstrap: resample separately as many zero outcomes as there were in the original sample, and as many ones as there were originally. Is that a better bootstrap scheme? At least it takes care of that infinite estimates issue. In Stata, you can do this by simply adding -strata(response_variable)- to your bootstrap options. Stratification usually brings down variances, and I would expect in this case that the standard errors will now be much closer to the -oim- and -robust- ones. -- Stas Kolenikov, also found at http://stas.kolenikov.nameSmall print: I use this email account for mailing lists only. * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
Open this post in threaded view
|

## Re: st: Bootstrap: Which standard errors to use?

 I really appreciate Stas for your elaborative explanation. My data and model are simpler than your speculation. Pr(FailEmissionTest) = f(OwnerCharacteristics,VehicleCharacteristics) Owner characteristics = {Income, Race} Vehicle characteristics = {Age,Mileage,Type(car,van,truck),ProductionCountry,                           OtherEmissionControlTechnologies} tresimp = First test result (1=Fail, 0=Pass) indlninc = Ln of Individual household income Vehicle emission test is legally required in some places in order to control for pollution. However, this might cause more burden to the poor because they tend to own old vehicles (I control for vehicle age as well). In my data, only around 5.37% fail the first emission test. As you suggested, ... Thank you Anupit . bootstrap _b _se, reps(10000) strata(tresimp) saving("C:\ANUPIT\e1outACIlogitBOOT2Abse > S.dta", replace): /// > logit tresimp indlninc `owner' `vehicle', robust (running logit on estimation sample) Logistic regression Number of strata   =         2                  Number of obs      =       465                                                 Replications       =      5070 ------------------------------------------------------------------------------              |   Observed   Bootstrap                         Normal-based              |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval] -------------+---------------------------------------------------------------- b            |     indlninc |  -.2818828    .491087    -0.57   0.566    -1.244396      .68063        black |   1.184949   .6017671     1.97   0.049     .0055069     2.36439        other |   .5112052   .7492401     0.68   0.495    -.9572784    1.979689          age |   .2291411    .088497     2.59   0.010     .0556902    .4025921        lnodo |   .2668319   .5443578     0.49   0.624    -.8000898    1.333754        peuro |   .3441804   .9920844     0.35   0.729    -1.600269     2.28863        pasia |   .1141557   .7469322     0.15   0.879    -1.349805    1.578116       pother |   .1774283   .7320229     0.24   0.808     -1.25731    1.612167        displ |  -.0444871   .3925379    -0.11   0.910    -.8138473     .724873       indefi |   .3926529    .808736     0.49   0.627    -1.192441    1.977746        indfi |  -.5801308   .8902797    -0.65   0.515    -2.325047    1.164785       indmfi |  -1.667607   .7216526    -2.31   0.021     -3.08202   -.2531942         egr1 |  -1.307301    .609217    -2.15   0.032    -2.501345   -.1132581         tac1 |  -.1766159   .9885491    -0.18   0.858    -2.114137    1.760905          car |  -1.189119   1.641974    -0.72   0.469    -4.407329    2.029092          van |  -1.120382   1.712288    -0.65   0.513    -4.476406    2.235641        _cons |  -3.180481   9.098116    -0.35   0.727    -21.01246     14.6515 -------------+---------------------------------------------------------------- se           |     indlninc |   .3751495   .1107681     3.39   0.001      .158048    .5922511        black |   .5377806   .1017104     5.29   0.000     .3384319    .7371293        other |   .6130217   .1557758     3.94   0.000     .3077068    .9183367          age |   .0683818   .0153066     4.47   0.000     .0383814    .0983822        lnodo |   .3736896   .1499676     2.49   0.013     .0797586    .6676207        peuro |   .8376832   .2292782     3.65   0.000     .3883061     1.28706        pasia |   .6548303   .1297987     5.04   0.000     .4004296    .9092311       pother |   .7830163   .2208942     3.54   0.000     .3500715    1.215961        displ |   .3161949    .082542     3.83   0.000     .1544155    .4779743       indefi |   .6165853   .1236292     4.99   0.000     .3742765     .858894        indfi |   .6734173   .1310668     5.14   0.000     .4165312    .9303034       indmfi |   1.093033   .2006469     5.45   0.000      .699772    1.486293         egr1 |   .5173223   .0856415     6.04   0.000     .3494679    .6851766         tac1 |   .7599367   .1663593     4.57   0.000     .4338784    1.085995          car |   .8430763   .3607768     2.34   0.019     .1359668    1.550186          van |   .9862894   .3964712     2.49   0.013     .2092202    1.763359        _cons |   6.637172   1.948067     3.41   0.001     2.819031    10.45531 ------------------------------------------------------------------------------ Note: One or more parameters could not be estimated in 4930 bootstrap replicates;       standard error estimates include only complete replications.     Variable |       Obs        Mean    Std. Dev.       Min        Max -------------+--------------------------------------------------------          age |       465    6.926882    3.313216          3         20        lnodo |       465    11.41426    .5641127   8.209309    12.9082        black |       465     .255914    .4368437          0          1        other |       465     .144086    .3515552          0          1       indefi |       465    .2129032    .4098007          0          1 -------------+--------------------------------------------------------        indfi |       465    .2236559    .4171428          0          1       indmfi |       465    .2903226    .4544001          0          1          car |       465    .7225806    .4482074          0          1          van |       465    .1849462    .3886721          0          1        peuro |       465    .0666667    .2497125          0          1 -------------+--------------------------------------------------------        pasia |       465    .2430108    .4293635          0          1       pother |       465    .1204301    .3258143          0          1     indlninc |       465    10.82838    .5955187   8.517183   11.51293      tresimp |       465    .0537634    .2257932          0          1         egr1 |       465    .7591398    .4280662          0          1 -------------+--------------------------------------------------------         tac1 |       465    .0688172    .2534157          0          1        displ |       465    2.936825     1.05423          1        5.9 * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/