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# Re: st: AW: confidence interval of a ratio of coefficients

 From Steve Samuels To statalist@hsphsun2.harvard.edu Subject Re: st: AW: confidence interval of a ratio of coefficients Date Fri, 9 Apr 2010 10:07:01 -0400

```Thanks, Arne!

Steve
:
************************************
sysuse auto, clear
set seed 2940688
logit foreign price weight rep78

nlcom  - _b[price]/_b[weight]  //ratio

logit foreign price weight rep78
wtp   price weight, delta
wtp   price weight, fieller
wtp   price weight, krinsky reps(2000)

bootstrap ratio = (-_b[price]/_b[weight]), rep(500): logit foreign price weight
estat bootstrap, bc
*****************************

On Fri, Apr 9, 2010 at 8:56 AM, Arne Risa Hole <arnehole@gmail.com> wrote:
>
> I've written the -wtp- module (available from SSC) with this
> particular problem in mind. It calculates CIs for the ratio of two
> coefficients using either the delta method, Fieller's method or the
> parametric bootstrap. I've done some simulations to investigate which
> method is more accurate, they are reported in the paper referenced in
> the -wtp- help file.
>
> Arne
>
> On 9 April 2010 13:14, Steve Samuels <sjsamuels@gmail.com> wrote:
>> The following paper
>> (http://mrvar.fdv.uni-lj.si/pub/mz/mz1.1/cedilnik.pdf)  shows that the
>> distribution of the ratio of two jointly-Normal variables is far from
>> simple.  This suggests to me that a bootstrap may be the best approach
>>
>> Steve
>>
>> On Thu, Apr 8, 2010 at 5:29 PM, Steve Samuels <sjsamuels@gmail.com> wrote:
>>> Martin,
>>>
>>> I have to withdraw that code. It gives incorrect results if the ratio
>>> approach.   Note, however that the confidence intervals for the ratio
>>> and  for 1/ratio are not compatible (perhaps "consonant" is the better
>>> word).  One set of limits cannot be derived by inverting the endpoints
>>> of the other set.
>>>
>>> Steve
>>>
>>>
>>> ********************
>>> sysuse auto, clear
>>> logit foreign rep78 price weight
>>>
>>> nlcom _b[price]/_b[weight]  //ratio
>>> nlcom _b[weight]/_b[price] // 1/ratio
>>> ***********************
>>>
>>>
>>>
>>>
>>> On Thu, Apr 8, 2010 at 3:52 PM, Martin Weiss <martin.weiss1@gmx.de> wrote:
>>>>
>>>> <>
>>>>
>>>> Steve,
>>>>
>>>> are you following your own script with this code, or is it necessary for
>>>>
>>>> HTH
>>>> Martin
>>>>
>>>>
>>>> -----Original Message-----
>>>> From: owner-statalist@hsphsun2.harvard.edu
>>>> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Steve Samuels
>>>> Sent: Donnerstag, 8. April 2010 21:40
>>>> To: statalist@hsphsun2.harvard.edu
>>>> Subject: Re: st: AW: confidence interval of a ratio of coefficients
>>>>
>>>> Here are some details.  It's necessary to operate on the log of the
>>>> absolute value of the ratio and attach the sign afterwards:
>>>>
>>>> *************
>>>> sysuse auto, clear
>>>> logit foreign rep78 price weight
>>>> local sgn = sign(_b[price]/_b[weight])
>>>>
>>>> nlcom _b[price]/_b[weight]  //ratio
>>>> nlcom log(abs( _b[price]/_b[weight]))  //log ratio
>>>> return list
>>>> local lratio = el(r(b),1,1)
>>>> local ratio = `sgn'*exp(`lratio')
>>>> local bound = invnormal(1-.05/2)*sqrt(el(r(V),1,1))
>>>> local llim = exp(`lratio' -`bound')
>>>> local ulim = exp(`lratio' + `bound')
>>>> di "ratio =  " `ratio'   " llimit = " `llim'  "  ulimit = " `ulim'
>>>>  *************
>>>>
>>>>
>>>> On Wed, Apr 7, 2010 at 1:21 PM, Steve Samuels <sjsamuels@gmail.com> wrote:
>>>>> Martin is right, but I think that this calculation is better done on
>>>>> the log  of the  ratio and then converted back to the ratio scale.  In
>>>>> that way, the CIs for  x/y and y/x  will be compatible.
>>>>>
>>>>> Steve
>>>>>
>>>>> On Wed, Apr 7, 2010 at 11:53 AM, Martin Weiss <martin.weiss1@gmx.de>
>>>> wrote:
>>>>>>
>>>>>> <>
>>>>>>
>>>>>>
>>>>>>
>>>>>> *************
>>>>>> sysuse auto, clear
>>>>>> logit foreign rep78 price weight
>>>>>> nlcom (ratio: _b[price]/_b[weight])
>>>>>> *************
>>>>>>
>>>>>>
>>>>>>
>>>>>> HTH
>>>>>> Martin
>>>>>>
>>>>>>
>>>>>> -----Ursprüngliche Nachricht-----
>>>>>> Von: owner-statalist@hsphsun2.harvard.edu
>>>> [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Shehzad Ali
>>>>>> Gesendet: Mittwoch, 7. April 2010 17:50
>>>>>> An: Stata List
>>>>>> Betreff: st: confidence interval of a ratio of coefficients
>>>>>>
>>>>>> Dear listers,
>>>>>>
>>>>>> I am modelling choice behaviour using a logit model. I want to calculate
>>>> the marginal rates of subsititution of the attributes of choice alternatives
>>>> by taking the ratio of coefficients (similar to what people do when
>>>> calculating willingness to pay estimates by taking attribute/cost
>>>> coefficients). I need help with calculating the confidence interval around
>>>> the ratio of two coefficients.
>>>>>>
>>>>>> Any help would be appreciated.
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> *
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>>>>>>
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>>>>>>
>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> Steven Samuels
>>>>> sjsamuels@gmail.com
>>>>> 18 Cantine's Island
>>>>> Saugerties NY 12477
>>>>> USA
>>>>> Voice: 845-246-0774
>>>>> Fax:    206-202-4783
>>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> Steven Samuels
>>>> sjsamuels@gmail.com
>>>> 18 Cantine's Island
>>>> Saugerties NY 12477
>>>> USA
>>>> Voice: 845-246-0774
>>>> Fax:    206-202-4783
>>>>
>>>> *
>>>> *   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/
>>>>
>>>>
>>>> *
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>>>>
>>>
>>>
>>>
>>> --
>>> Steven Samuels
>>> sjsamuels@gmail.com
>>> 18 Cantine's Island
>>> Saugerties NY 12477
>>> USA
>>> Voice: 845-246-0774
>>> Fax:    206-202-4783
>>>
>>
>>
>>
>> --
>> Steven Samuels
>> sjsamuels@gmail.com
>> 18 Cantine's Island
>> Saugerties NY 12477
>> USA
>> Voice: 845-246-0774
>> Fax:    206-202-4783
>>
>> *
>> *   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/
>>
>
> *
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>

--
Steven Samuels
sjsamuels@gmail.com
18 Cantine's Island
Saugerties NY 12477
USA
Voice: 845-246-0774
Fax:    206-202-4783

*
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```