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RE: st: AW: confidence interval of a ratio of coefficients
From
Rodolphe Desbordes <[email protected]>
To
"'[email protected]'" <[email protected]>
Subject
RE: st: AW: confidence interval of a ratio of coefficients
Date
Fri, 9 Apr 2010 16:01:21 +0100
Would this approach make sense?
sysuse auto, clear
set seed 2940688
logit foreign price weight rep78
preserve
drawnorm b1-b4, n(20000) means(e(b)) cov(e(V)) clear
gen ratio=-(b2)/(b1)
egen mean=mean(ratio)
_pctile ratio, p(2.5,97.5)
gen ll=r(r1)
gen ul= r(r2)
sum ratio ll ul
restore
Rodolphe
-----Original Message-----
From: [email protected] [mailto:[email protected]] On Behalf Of Steve Samuels
Sent: vendredi 9 avril 2010 15:30
To: [email protected]
Subject: Re: st: AW: confidence interval of a ratio of coefficients
The bootstrap command should have been:
bootstrap ratio = (-_b[price]/_b[weight]), rep(500): logit foreign
price weight rep78
Steve
On Fri, Apr 9, 2010 at 10:07 AM, Steve Samuels <[email protected]> wrote:
> 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 rep78
> estat bootstrap, bc
> *****************************
>
>
>
> On Fri, Apr 9, 2010 at 8:56 AM, Arne Risa Hole <[email protected]> wrote:
>> 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 <[email protected]> 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
>>> to the CI that Shehzad originally asked for.
>>>
>>> Steve
>>>
>>> On Thu, Apr 8, 2010 at 5:29 PM, Steve Samuels <[email protected]> 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 <[email protected]> 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: [email protected]
>>>>> [mailto:[email protected]] On Behalf Of Steve Samuels
>>>>> Sent: Donnerstag, 8. April 2010 21:40
>>>>> To: [email protected]
>>>>> 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 <[email protected]> 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 <[email protected]>
>>>>> wrote:
>>>>>>>
>>>>>>> <>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> *************
>>>>>>> sysuse auto, clear
>>>>>>> logit foreign rep78 price weight
>>>>>>> nlcom (ratio: _b[price]/_b[weight])
>>>>>>> *************
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> HTH
>>>>>>> Martin
>>>>>>>
>>>>>>>
>>>>>>> -----Ursprüngliche Nachricht-----
>>>>>>> Von: [email protected]
>>>>> [mailto:[email protected]] 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
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> *
>>>>>>> * 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
>>>>>> [email protected]
>>>>>> 18 Cantine's Island
>>>>>> Saugerties NY 12477
>>>>>> USA
>>>>>> Voice: 845-246-0774
>>>>>> Fax: 206-202-4783
>>>>>>
>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> Steven Samuels
>>>>> [email protected]
>>>>> 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
>>>> [email protected]
>>>> 18 Cantine's Island
>>>> Saugerties NY 12477
>>>> USA
>>>> Voice: 845-246-0774
>>>> Fax: 206-202-4783
>>>>
>>>
>>>
>>>
>>> --
>>> Steven Samuels
>>> [email protected]
>>> 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
> [email protected]
> 18 Cantine's Island
> Saugerties NY 12477
> USA
> Voice: 845-246-0774
> Fax: 206-202-4783
>
--
Steven Samuels
[email protected]
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:
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* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/