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Re: st: AW: confidence interval of a ratio of coefficients
From
Steve Samuels <[email protected]>
To
[email protected]
Subject
Re: st: AW: confidence interval of a ratio of coefficients
Date
Fri, 9 Apr 2010 10:07:01 -0400
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
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
*
* 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/