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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 Thu, 8 Apr 2010 15:39:45 -0400

```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/
```