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


From   Steve Samuels <sjsamuels@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: AW: confidence interval of a ratio of coefficients
Date   Thu, 8 Apr 2010 17:29:58 -0400

Martin,

I have to withdraw that code. It gives incorrect results if the ratio
is negative. So, your original -nlcom- statement is  Shehzad's best
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
> Shehzad to obtain a correct answer?
>
> 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.
>>> Shehzad
>>>
>>>
>>>
>>>
>>> *
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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/
>
>
> *
> *   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/
>



-- 
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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