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

 From Arne Risa Hole To statalist@hsphsun2.harvard.edu Subject Re: st: AW: confidence interval of a ratio of coefficients Date Fri, 9 Apr 2010 13:56:07 +0100

```Steve, Martin and Shehzad,

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
>>>
>>> *
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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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```