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

[Steve Samuels <sjsamuels@gmail.com>]

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
to the CI that Shehzad originally asked for.

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
> 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:
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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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