[ncl-talk] Bootstrapping method for significant test

[Anahita Amiri Farahani]

Why this one is wrong to calculate the significance level when there is
only one partial derivative? and if this is wrong how can I calculate that
it is significant or not?

And based on this:

   nBoot =   10000
   xBoot = *new*
<http://www.ncl.ucar.edu/Document/Functions/Built-in/new.shtml>
(nBoot, typeof(F))

   do ns=0,nBoot-1                        ; generate multiple estimates
      iw = *generate_sample_indices*
<http://www.ncl.ucar.edu/Document/Functions/Contributed/generate_sample_indices.shtml>(N,*1*))
 ; indices with replacement
      xBoot(ns) = (dF(iw)/dN(iw))*(dN(iw)/dA(iw))
   end do


How can I say if it is significant?


Thanks,

Ana


On Wed, Dec 14, 2016 at 7:58 PM, Dennis Shea <shea at ucar.edu> wrote:

> [1]
> http://www.ncl.ucar.edu/Applications/bootstrap.shtml
> http://www.ncl.ucar.edu/Document/Functions/Bootstrap/
> bootstrap_regcoef.shtml
> Look at examples
> bootstrap_regcoef_1.ncl
> bootstrap_regcoef_2.ncl
> bootstrap_regcoef_3.ncl
>
> [2]
> You don't need the following but it was wrong. FTR:
>
> do k=0,2999
>     ab  = regCoef(AI_fall(:,k),Nd_fall(:,k))
>     df   = ab at nptxy-2
>     tval = ab at tval
>
>     df     = where(df.lt.1,1, df)
>     prob = 1 - betainc(df/(df+tval^2), df/2.0, 0.5)
>     sig_fall(k) = where(prob.lt.0.95, -999, prob)
> end do
>
> On Wed, Dec 14, 2016 at 7:02 PM, Anahita Amiri Farahani <aamir003 at ucr.edu>
> wrote:
>
>> Thanks a lot, your answer was really helpful and I have another question:
>>
>> Before I use regCoef function in NCL to calculate linear regression.
>> Using this function gives other variables such as rcraw_npt, and
>>  rcraw_tval, so I was able to calculate significance at 95%, 90% and 99%
>> confidence level. I've put that part of the code here:
>>
>> do k=0,2999
>>
>>    ab = regCoef(AI_fall(:,k),Nd_fall(:,k))
>>     rcraw_npt=ab at nptxy-2
>>     rcraw_tval=ab at tval
>>     b    = rcraw_tval
>>     b    = 0.5
>>     rcraw_npt=where(rcraw_npt.lt.1,1,rcraw_npt)
>>     rcraw_prob = (1 - betainc(rcraw_npt/(rcraw_npt+rcraw_tval^2),rcraw_npt/2.0,b)
>> )
>>     sig_fall(k)=where(rcraw_prob.lt.0.95,-999,rcraw_prob)
>>
>> end do
>>
>>
>> How can I calculate the significance at different confidence level here
>> by using xBoot?
>>
>> Best,
>> Ana
>>
>>
>>
>>
>> On Wed, Dec 14, 2016 at 2:45 PM, Dennis Shea <shea at ucar.edu> wrote:
>>
>>> I think you will have to decide what is best.
>>>
>>> [a]
>>> Constrain the F,N,A triplets to be 'coupled'
>>>
>>>    nBoot =   10000
>>>    xBoot = *new* <http://www.ncl.ucar.edu/Document/Functions/Built-in/new.shtml> (nBoot, typeof(F))
>>>
>>>    do ns=0,nBoot-1                        ; generate multiple estimates
>>>       iw = *generate_sample_indices* <http://www.ncl.ucar.edu/Document/Functions/Contributed/generate_sample_indices.shtml>(N,*1*))  ; indices with replacement
>>>       xBoot(ns) = (dF(iw)/dN(iw))*(dN(iw)/dA(iw))
>>>    end do
>>>
>>> [b]
>>>
>>> Unconstrained
>>>
>>>
>>>    nBoot =   10000
>>>    xBoot = *new* <http://www.ncl.ucar.edu/Document/Functions/Built-in/new.shtml> (nBoot, typeof(F))
>>>
>>>    do ns=0,nBoot-1                        ; generate multiple estimates
>>>       iwF = *generate_sample_indices* <http://www.ncl.ucar.edu/Document/Functions/Contributed/generate_sample_indices.shtml>(N,*1*)) ; indices with replacement
>>>       iwN = *generate_sample_indices* <http://www.ncl.ucar.edu/Document/Functions/Contributed/generate_sample_indices.shtml>(N,*1*))
>>>       iwA = *generate_sample_indices* <http://www.ncl.ucar.edu/Document/Functions/Contributed/generate_sample_indices.shtml>(N,*1*))
>>>
>>>       xBoot(ns) = (dF(iwF)/dN(iwN))*(dN(iwN)/dA(iwA))
>>>    end do
>>>
>>> [c]
>>> See where your product fits.
>>>
>>>    ia = *dim_pqsort_n* <http://www.ncl.ucar.edu/Document/Functions/Built-in/dim_pqsort_n.shtml>(xBoot, 2, 0)        ; sort bootstrap means into ascending order
>>>
>>>    n025     = *round* <http://www.ncl.ucar.edu/Document/Functions/Built-in/round.shtml>(0.025*(nBoot-1),3)    ; indices for sorted array
>>>    n500     = *round* <http://www.ncl.ucar.edu/Document/Functions/Built-in/round.shtml>(0.500*(nBoot-1),3)
>>>    n975     = *round* <http://www.ncl.ucar.edu/Document/Functions/Built-in/round.shtml>(0.975*(nBoot-1),3)
>>>
>>>    xBoot_025= xBoot(n025)                 ;  2.5% level
>>>    xBoot_500= xBoot(n500)                 ; 50.0% level  (median)
>>>    xBoot_975= xBoot(n975)                 ; 97.5% level
>>>
>>>
>>>
>>> On Wed, Dec 14, 2016 at 3:12 PM, Anahita Amiri Farahani <
>>> aamir003 at ucr.edu> wrote:
>>>
>>>> Dear all,
>>>>
>>>> I have a product of two partial derivatives : dF/dN*dN/dA and for each
>>>> of the variables (F, N, and A) I have data for 720 times. Each partial
>>>> derivatives are calculated  by linear regression. I was wondering how I can
>>>> calculate the significant test for this product. All examples in NCL to
>>>> estimate linear regression by this function: *regline_stats
>>>> <http://www.ncl.ucar.edu/Document/Functions/Contributed/regline_stats.shtml> *
>>>> give the regression coefficient for two variables.
>>>>
>>>> Thanks,
>>>> Ana
>>>>
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>>>
>>
>
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