95% confidence interval calculation (for the extreme point) using the Fieller method

[Petko Bachvarov]

Dear Statalisters,


I am trying to test for 95% confidence interval calculation (for the extreme point) using the Fieller method. I used a credit risk as a dependent variable and the direct (adjusted lerner) and the squared term (of adjusted lerner)
I managed to read and replicated a paper by (Hirschberg and Lye, 2017) and my results are the following:

 gen _xx_ = 0

. label var _xx_ "Ratio"

. reg llrgl  adjlerner adjlerner2 _xx_ , noconstant
note: _xx_ omitted because of collinearity

      Source |       SS       df       MS              Number of obs =    3124
-------------+------------------------------           F(  2,  3122) =  430.76
       Model |  10.0026565     2  5.00132827           Prob > F      =  0.0000
    Residual |  36.2479737  3122  .011610498           R-squared     =  0.2163
-------------+------------------------------           Adj R-squared =  0.2158
       Total |  46.2506302  3124  .014804939           Root MSE      =  .10775

------------------------------------------------------------------------------
       llrgl |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
   adjlerner |  -.1147687   .0198311    -5.79   0.000     -.153652   -.0758855
  adjlerner2 |   .1708729   .0164604    10.38   0.000     .1385986    .2031473
        _xx_ |          0  (omitted)
------------------------------------------------------------------------------

. nlcom _b[adjlerner] / _b[adjlerner2], level(95)

       _nl_1:  _b[adjlerner] / _b[adjlerner2]

------------------------------------------------------------------------------
       llrgl |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |  -.6716614   .0532586   -12.61   0.000    -.7760464   -.5672763
------------------------------------------------------------------------------

Unfortunately, I am not quite familiar with the test, hence I had to replicate the commands. Therefore, I would appreciate your advice and help of how to determent/interpret the following:
1. How I get the 95% confidence interval
2. How I determine the the interval for extreme point
3. Based on the results what should be me interpretation?

I would appreciate if you can advise whether additional commands are required in order to get 95% confidence interval calculation. In the paper which I am analyzing and trying to replicate the author has displayed the following information?

 This is just an example, just want to understand which figures should be included based on my results
95% confidence interval, Fieller method   [0.485; 0.862]

Thank you in advance for your help.
Kind Regards,
Petko Bachvarov

[Carlo Lazzaro]

Petko:
you might be interested in the community-contributed module; fieller from http://fmwww.bc.edu/RePEc/bocode/f

[Petko Bachvarov]

Dear Carlo,

Thank you very much for the reply.
In the community-contributed module the example test a dummy variable for sex (male and female). In our case we have a real data and I am not quite sure that the results are relevant.
Can you please advise if it is acceptable to contact the author of the module for any further questions clarifications.
Thank you in advance for your help.
Kind Regards,
Petko Bachvarov

[Carlo Lazzaro]

Petko:
in fact, the example reported in the community-contributed module seems to be a ratio of male/female blood pressure.
That said, I think it is a good idea to email Joseph Coveney directly.
In addition of being the author of -fieller- community-contributed module, Joseph is an authoritative, long-standing contributor of this forum.

[Trang Dang]

Dear Statalisters,


I am trying to test for 95% confidence interval calculation (for the extreme point) using the Fieller method. I used a credit risk as a dependent variable and the direct (adjusted lerner) and the squared term (of adjusted lerner)
I managed to read and replicated a paper by (Hirschberg and Lye, 2017) and my results are the following:

 gen _xx_ = 0

. label var _xx_ "Ratio"

. reg llrgl adjlerner adjlerner2 _xx_ , noconstant
note: _xx_ omitted because of collinearity

Source | SS df MS Number of obs = 3124
-------------+------------------------------ F( 2, 3122) = 430.76
Model | 10.0026565 2 5.00132827 Prob > F = 0.0000
Residual | 36.2479737 3122 .011610498 R-squared = 0.2163
-------------+------------------------------ Adj R-squared = 0.2158
Total | 46.2506302 3124 .014804939 Root MSE = .10775

------------------------------------------------------------------------------
llrgl | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
adjlerner | -.1147687 .0198311 -5.79 0.000 -.153652 -.0758855
adjlerner2 | .1708729 .0164604 10.38 0.000 .1385986 .2031473
_xx_ | 0 (omitted)
------------------------------------------------------------------------------

. nlcom _b[adjlerner] / _b[adjlerner2], level(95)

_nl_1: _b[adjlerner] / _b[adjlerner2]

------------------------------------------------------------------------------
llrgl | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_nl_1 | -.6716614 .0532586 -12.61 0.000 -.7760464 -.5672763
------------------------------------------------------------------------------

Unfortunately, I am not quite familiar with the test, hence I had to replicate the commands. Therefore, I would appreciate your advice and help of how to determent/interpret the following:
1. How I get the 95% confidence interval
2. How I determine the the interval for extreme point
3. Based on the results what should be me interpretation?

I would appreciate if you can advise whether additional commands are required in order to get 95% confidence interval calculation. In the paper which I am analyzing and trying to replicate the author has displayed the following information?

 This is just an example, just want to understand which figures should be included based on my results
95% confidence interval, Fieller method [0.485; 0.862]

Thank you in advance for your help.
Kind Regards,
Petko Bachvarov

Dear @Petko Bachvarov, May I ask if you solve this issue? I also have the same question as yours. May you share how to determine the CI for the extreme point? Thank you very much!

[Zubai Khan]

I was facing the same problem. I think I have come up with the command which is:

reg y x xsquarred
utest y x xsquarred , fieller

Reference:
http://http://fmwww.bc.edu/repec/bocode/u/utest.sthlp

that have relevant commands based on

Jo Thori Lind & Halvor Mehlum, 2007. "UTEST: Stata module to test for a U-shaped relationship," Statistical Software Components S456874, Boston College Department of Economics, revised 09 Feb 2019.