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RE: st: Computing the proportion of significant variables after running numerous regressions


From   Nick Cox <n.j.cox@durham.ac.uk>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Computing the proportion of significant variables after running numerous regressions
Date   Mon, 14 May 2012 11:43:25 +0100

I think it depends what George wants by way of standard errors. If you run -bootstrap: regress- the effect is not just to add the confidence intervals.

Nick 
n.j.cox@durham.ac.uk 

Phil Clayton

I don't see the problem Nick - I think your code reports the correct values. -bootstrap- reports the same beta coefficients as -regress- since these are the best (least biased) point estimates, and otherwise the estimates that your code extracts seem to come from the bootstrapping as desired.

I completely agree that 10 repetitions is not enough - my example was only designed to demonstrate the use of -post- - but thanks for pointing it out.

Phil

On 14/05/2012, at 7:15 PM, Nick Cox wrote:

> No, you (and I) need to be more circumspect. After -bootstrap:
> regress- the results in memory are a mix of results for -bootstrap-
> and for the last replication of -regress-. So, you need to separate
> that out in your code.
> 
> On Mon, May 14, 2012 at 9:52 AM, Nick Cox <njcoxstata@gmail.com> wrote:
>> You seem to be guessing that after -bootstrap: regress- there is a
>> quantity left in memory called -_ci_bc_cons-. Not so. Also, each
>> confidence interval is a pair of numbers, so you need to create two
>> variables to hold it, not one. The trick to these calculations is to
>> see what is left in memory after a command. By the way, 10
>> replications would not be enough for most serious work.
>> 
>> * load dataset
>>  sysuse auto, clear
>> 
>>  * set up temporary file for results
>>  tempfile results
>>  tempname postfile
>>  postfile `postfile' foreign _b_cons _se_cons _b_mpg _se_mpg _cons_ll
>> _cons_ul _b_ll _b_ul using "`results'"
>> 
>>  * run bootstrapped regression for each level of foreign
>>  set seed 1 // so that you can repeat your analysis
>>  levelsof foreign, local(levels)
>>  foreach level of local levels {
>>        bootstrap, rep(10): regress price mpg if foreign==`level'
>>                mat ci = e(ci_bc)
>>        post `postfile' (`level') (_b[_cons]) (_se[_cons]) (_b[mpg])
>> (_se[mpg]) (ci[1,2]) (ci[2,2]) (ci[1,1]) (ci[2,1])
>>  }
>>  postclose `postfile'
>> 
>>  * display results
>>  use "`results'", clear
>>  list
>> 
>> 
>> On Mon, May 14, 2012 at 9:30 AM, George Murray
>> <george.murray16@gmail.com> wrote:
>>> Phil,
>>> 
>>> Thank you so much for your help, this worked perfectly.
>>> 
>>> I have one more query, however.
>>> 
>>> I also need a vector of the bias-corrected confidence intervals (which
>>> can be obtained with the -estat bootstrap- command). I replace two of
>>> the commands you suggested with these two commands as follows:
>>> 
>>> -postfile `postfile' foreign _b_cons _se_cons _ci_bc_cons _b_mpg
>>> _se_mpg using "`results'"- .............(all I did was add
>>> "_ci_bc_cons")
>>> 
>>> -post `postfile' (`level') (_b[_cons]) (_se[_cons]) (_ci_bc[_cons])
>>> (_b[mpg]) (_se[mpg])- .............(all I did was add
>>> "(_ci_bc[_cons])")
>>> 
>>> and I also wrote -estat boostrap- after the bootstrap, rep(10)... command
>>> 
>>> However, I get the following error:
>>> 
>>> _ci_bc not found
>>> post:  above message corresponds to expression 3, variable _ci_bc_cons
>>> r(111);
>>> 
>>> Does anyone know how to solve this problem?
>> 
>> 
>> On Mon, May 14, 2012 at 12:05 AM, Phil Clayton
>>> <philclayton@internode.on.net> wrote:
>>>> George,
>>>> 
>>>> There are various ways to do this. One is to use -post- after each bootstrapped regression to store the results of that regression in a "results" dataset, similar to a Monte Carlo simulation. You can then access the results dataset and manipulate it however you like.
>>>> 
>>>> Here's a basic example that uses the auto dataset and loops over the levels of "foreign" (ie 0 and 1), runs a bootstrapped regression of price on mpg for each level, and displays the resulting coefficients and standard errors.
>>>> 
>>>> --------- begin example ---------
>>>> * load dataset
>>>> sysuse auto, clear
>>>> 
>>>> * set up temporary file for results
>>>> tempfile results
>>>> tempname postfile
>>>> postfile `postfile' foreign _b_cons _se_cons _b_mpg _se_mpg using "`results'"
>>>> 
>>>> * run bootstrapped regression for each level of foreign
>>>> set seed 1 // so that you can repeat your analysis
>>>> levelsof foreign, local(levels)
>>>> foreach level of local levels {
>>>>        bootstrap, rep(10): regress price mpg if foreign==`level'
>>>>        post `postfile' (`level') (_b[_cons]) (_se[_cons]) (_b[mpg]) (_se[mpg])
>>>> }
>>>> postclose `postfile'
>>>> 
>>>> * display results
>>>> use "`results'", clear
>>>> list
>>>> --------- end example ---------
>>>> 
>>>> Since you're running ~1000 models you may wish to change "foreach" to "qui foreach", and monitor the iterations using the _dots command (see Harrison DA. Stata tip 41: Monitoring loop iterations. Stata Journal 2007;7(1):140, available at http://www.stata-journal.com/article.html?article=pr0030)
>>>> 
>>>> Phil
>>>> 
>>>> 
>>>> On 13/05/2012, at 10:06 PM, George Murray wrote:
>>>> 
>>>>> Dear Statalist,
>>>>> 
>>>>> I am using the -foreach- command to run approximately 1000
>>>>> (bootstrapped) regression models, however I require an efficient way
>>>>> of calculating the proportion of the regression models which have a
>>>>> statistically significant constant at the 5% level; and of the
>>>>> constants which are statistically significant, the proportion which
>>>>> are positive.  Below each of the 1000 regressions I run, a table is
>>>>> displayed with the following format:
>>>>> 
>>>>> ---------------------------------------------------------------------------------------------------
>>>>>             |    Observed                         Bootstrap
>>>>>        V0 |       Coef.             Bias         Std. Err.
>>>>> [95% Conf. Interval]
>>>>> -------------+------------------------------------------------------------------------------------
>>>>>         V1 |   .00968169  -.0000537   .00057051     .008721   .0111218  (BC)
>>>>>         V2 |  -.00110469   .0000782     .000691   -.0023101    .000459  (BC)
>>>>>         V3 |   .00468313  -.0001562   .00084971    .0031954   .0064538  (BC)
>>>>>         _cons |  -.00076976   .0001811   .00176677   -.0044496   .0025584  (BC)
>>>>> --------------------------------------------------------------------------------------------------
>>>>> 
>>>>> I would be *very* grateful if someone knew the commands which would
>>>>> allow me calculate this. In the past, I have used (a highly tedious
>>>>> and embarrassing approach on) Excel where I filtered every Nth row,
>>>>> and wrote a command to display 1 if the coefficient lies within the
>>>>> confidence interval, and 0 if not. This time, however, I am running
>>>>> numerous models and require a quicker approach.
>>>>> 
>>>>> One more question -- is there a way to create a new variable where the
>>>>> coefficients of V1 (for example) are saved, so I can calculate the
>>>>> mean, standard deviation etc.of V1?
>>>>> 
>>>>> If someone could answer at least one of these two questions, it would
>>>>> be very much appreciated.

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