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Re: st: Introducing constraints to biprobit model
From
Huybregts <[email protected]>
To
[email protected]
Subject
Re: st: Introducing constraints to biprobit model
Date
Tue, 28 Aug 2012 17:38:25 +0200
Dear Nick, I think there was a misunderstanding. I did post the syntax, but I think you want to see the output. Here is the complete output. First the syntax I have been using, which didn't work, then What Maarten wrote, which is much better. However, I have a remaining question on the r111 error. I don't know if the results obtained by the LR test are correct.
Many thanks for any feedback you can provide on this and my apologies for misunderstanding. I did read the rules well to make this as clear as possible. I use Stata 11.1.
Lieven
First you can see what I have been doing, which didn't work:
/*My original synthax */
. sysuse auto.dta,clear
(1978 Automobile Data)
. egen cat=cut(rep78),grou(2) label
(5 missing values generated)
.
. // model without constraints
. xi: biprobit (cat mpg price) (foreign mpg price)
Fitting comparison equation 1:
Iteration 0: log likelihood = -28.552789
Iteration 1: log likelihood = -27.110671
Iteration 2: log likelihood = -27.076711
Iteration 3: log likelihood = -27.076625
Iteration 4: log likelihood = -27.076625
Fitting comparison equation 2:
Iteration 0: log likelihood = -42.400729
Iteration 1: log likelihood = -33.271394
Iteration 2: log likelihood = -33.188125
Iteration 3: log likelihood = -33.188014
Iteration 4: log likelihood = -33.188014
Comparison: log likelihood = -60.26464
Fitting full model:
Iteration 0: log likelihood = -60.26464
Iteration 1: log likelihood = -57.973106
Iteration 2: log likelihood = -57.880512
Iteration 3: log likelihood = -57.873467
Iteration 4: log likelihood = -57.873061
Iteration 5: log likelihood = -57.873057
Seemingly unrelated bivariate probit Number of obs = 69
Wald chi2(4) = 14.79
Log likelihood = -57.873057 Prob > chi2 = 0.0052
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cat |
mpg | .0710587 .0454513 1.56 0.118 -.0180242 .1601416
price | .0000924 .0000748 1.24 0.216 -.0000541 .0002389
_cons | -.9485728 1.211113 -0.78 0.433 -3.322311 1.425166
-------------+----------------------------------------------------------------
foreign |
mpg | .140959 .0373519 3.77 0.000 .0677506 .2141674
price | .0001253 .0000681 1.84 0.066 -8.08e-06 .0002588
_cons | -4.377398 1.114323 -3.93 0.000 -6.561432 -2.193365
-------------+----------------------------------------------------------------
/athrho | 1.259137 2.237519 0.56 0.574 -3.12632 5.644595
-------------+----------------------------------------------------------------
rho | .8508261 .6177676 -.9961567 .999975
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chi2(1) = 4.78317 Prob > chi2 = 0.0287
. estimates store R1
. matrix define coef=e(b)
. matrix list coef
coef[1,7]
cat: cat: cat: foreign: foreign: foreign: athrho:
mpg price _cons mpg price _cons _cons
y1 .07105866 .00009241 -.94857276 .14095901 .00012534 -4.3773984 1.2591375
. constraint define 1 coef[1,1] = coef[1,4]
. constraint define 2 coef[1,2] = coef[1,5]
.
. // Model with constraints
. xi: biprobit (cat mpg price) (foreign mpg price), constraint (1 2)
Fitting comparison equation 1:
(note: constraint number 1 caused error r(131))
(note: constraint number 2 caused error r(131))
Iteration 0: log likelihood = -28.552789
Iteration 1: log likelihood = -27.110671
Iteration 2: log likelihood = -27.076711
Iteration 3: log likelihood = -27.076625
Iteration 4: log likelihood = -27.076625
Fitting comparison equation 2:
(note: constraint number 1 caused error r(131))
(note: constraint number 2 caused error r(131))
Iteration 0: log likelihood = -42.400729
Iteration 1: log likelihood = -33.271394
Iteration 2: log likelihood = -33.188125
Iteration 3: log likelihood = -33.188014
Iteration 4: log likelihood = -33.188014
Comparison: log likelihood = -60.26464
Fitting full model:
(note: constraint number 1 caused error r(131))
(note: constraint number 2 caused error r(131))
Iteration 0: log likelihood = -60.26464
Iteration 1: log likelihood = -57.973106
Iteration 2: log likelihood = -57.880512
Iteration 3: log likelihood = -57.873467
Iteration 4: log likelihood = -57.873061
Iteration 5: log likelihood = -57.873057
Seemingly unrelated bivariate probit Number of obs = 69
Wald chi2(4) = 14.79
Log likelihood = -57.873057 Prob > chi2 = 0.0052
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cat |
mpg | .0710587 .0454513 1.56 0.118 -.0180242 .1601416
price | .0000924 .0000748 1.24 0.216 -.0000541 .0002389
_cons | -.9485728 1.211113 -0.78 0.433 -3.322311 1.425166
-------------+----------------------------------------------------------------
foreign |
mpg | .140959 .0373519 3.77 0.000 .0677506 .2141674
price | .0001253 .0000681 1.84 0.066 -8.08e-06 .0002588
_cons | -4.377398 1.114323 -3.93 0.000 -6.561432 -2.193365
-------------+----------------------------------------------------------------
/athrho | 1.259137 2.237519 0.56 0.574 -3.12632 5.644595
-------------+----------------------------------------------------------------
rho | .8508261 .6177676 -.9961567 .999975
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chi2(1) = 4.78317 Prob > chi2 = 0.0287
. estimates store R2
. lrtest R1 R2
df(unrestricted) = df(restricted) = 7
r(498);
end of do-file
Here you can see what Maarten proposed in his previous posting, my question is how to interpret the (note: constraint number 2 caused error r(111)).
. /* Maarten's proposal */
. sysuse auto.dta,clear
(1978 Automobile Data)
. egen cat=cut(rep78),grou(2) label
(5 missing values generated)
.
. // model without constraints
. biprobit (cat mpg price) ///
> (foreign mpg price)
Fitting comparison equation 1:
Iteration 0: log likelihood = -28.552789
Iteration 1: log likelihood = -27.110671
Iteration 2: log likelihood = -27.076711
Iteration 3: log likelihood = -27.076625
Iteration 4: log likelihood = -27.076625
Fitting comparison equation 2:
Iteration 0: log likelihood = -42.400729
Iteration 1: log likelihood = -33.271394
Iteration 2: log likelihood = -33.188125
Iteration 3: log likelihood = -33.188014
Iteration 4: log likelihood = -33.188014
Comparison: log likelihood = -60.26464
Fitting full model:
Iteration 0: log likelihood = -60.26464
Iteration 1: log likelihood = -57.973106
Iteration 2: log likelihood = -57.880512
Iteration 3: log likelihood = -57.873467
Iteration 4: log likelihood = -57.873061
Iteration 5: log likelihood = -57.873057
Seemingly unrelated bivariate probit Number of obs = 69
Wald chi2(4) = 14.79
Log likelihood = -57.873057 Prob > chi2 = 0.0052
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cat |
mpg | .0710587 .0454513 1.56 0.118 -.0180242 .1601416
price | .0000924 .0000748 1.24 0.216 -.0000541 .0002389
_cons | -.9485728 1.211113 -0.78 0.433 -3.322311 1.425166
-------------+----------------------------------------------------------------
foreign |
mpg | .140959 .0373519 3.77 0.000 .0677506 .2141674
price | .0001253 .0000681 1.84 0.066 -8.08e-06 .0002588
_cons | -4.377398 1.114323 -3.93 0.000 -6.561432 -2.193365
-------------+----------------------------------------------------------------
/athrho | 1.259137 2.237519 0.56 0.574 -3.12632 5.644595
-------------+----------------------------------------------------------------
rho | .8508261 .6177676 -.9961567 .999975
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chi2(1) = 4.78317 Prob > chi2 = 0.0287
. estimates store R1
.
. // replay the model, but see the coefficient names:
. biprobit, coeflegend
Seemingly unrelated bivariate probit Number of obs = 69
Wald chi2(4) = 14.79
Log likelihood = -57.873057 Prob > chi2 = 0.0052
------------------------------------------------------------------------------
| Coef. Legend
-------------+----------------------------------------------------------------
cat |
mpg | .0710587 _b[cat:mpg]
price | .0000924 _b[cat:price]
_cons | -.9485728 _b[cat:_cons]
-------------+----------------------------------------------------------------
foreign |
mpg | .140959 _b[foreign:mpg]
price | .0001253 _b[foreign:price]
_cons | -4.377398 _b[foreign:_cons]
-------------+----------------------------------------------------------------
/athrho | 1.259137 _b[athrho:_cons]
-------------+----------------------------------------------------------------
rho | .8508261
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chi2(1) = 4.78317 Prob > chi2 = 0.0287
.
. // use those name to define the constraints
. constraint define 1 _b[cat:mpg] = _b[foreign:mpg]
. constraint define 2 _b[cat:price] = _b[foreign:price]
.
. // Model with constraints
. biprobit (cat mpg price) ///
> (foreign mpg price), constraint (1 2)
Fitting comparison equation 1:
(note: constraint number 1 caused error r(111))
(note: constraint number 2 caused error r(111))
Iteration 0: log likelihood = -28.552789
Iteration 1: log likelihood = -27.110671
Iteration 2: log likelihood = -27.076711
Iteration 3: log likelihood = -27.076625
Iteration 4: log likelihood = -27.076625
Fitting comparison equation 2:
(note: constraint number 1 caused error r(111))
(note: constraint number 2 caused error r(111))
Iteration 0: log likelihood = -42.400729
Iteration 1: log likelihood = -33.271394
Iteration 2: log likelihood = -33.188125
Iteration 3: log likelihood = -33.188014
Iteration 4: log likelihood = -33.188014
Comparison: log likelihood = -60.26464
Fitting full model:
Iteration 0: log likelihood = -83.049875
Iteration 1: log likelihood = -65.030586 (not concave)
Iteration 2: log likelihood = -59.728978
Iteration 3: log likelihood = -58.803484
Iteration 4: log likelihood = -58.800879
Iteration 5: log likelihood = -58.800664
Iteration 6: log likelihood = -58.800664
Seemingly unrelated bivariate probit Number of obs = 69
Wald chi2(2) = 14.07
Log likelihood = -58.800664 Prob > chi2 = 0.0009
( 1) [cat]mpg - [foreign]mpg = 0
( 2) [cat]price - [foreign]price = 0
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cat |
mpg | .1214969 .0324577 3.74 0.000 .057881 .1851127
price | .0001177 .0000556 2.12 0.034 8.82e-06 .0002267
_cons | -2.072698 .8765444 -2.36 0.018 -3.790693 -.3547025
-------------+----------------------------------------------------------------
foreign |
mpg | .1214969 .0324577 3.74 0.000 .057881 .1851127
price | .0001177 .0000556 2.12 0.034 8.82e-06 .0002267
_cons | -3.888234 .9489108 -4.10 0.000 -5.748065 -2.028403
-------------+----------------------------------------------------------------
/athrho | 1.776488 175.2688 0.01 0.992 -341.744 345.2969
-------------+----------------------------------------------------------------
rho | .9443162 18.97581 -1 1
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chi2(1) = 2.92795 Prob > chi2 = 0.0871
. estimates store R2
. lrtest R1 R2
Likelihood-ratio test LR chi2(2) = 1.86
(Assumption: R2 nested in R1) Prob > chi2 = 0.3955
.
end of do-file
On Aug 28, 2012, at 3:35 PM, Nick Cox wrote:
> There is plenty of good will to help you, but there is no way round
> this: you have yet to post the entire syntax that you used. So I don't
> think anyone can see what you are doing wrong even in trying to
> reproduce Maarten's example. This logic should seem compelling even to
> first-time posters.
>
> Nick
>
> On Tue, Aug 28, 2012 at 12:50 PM, Huybregts <[email protected]> wrote:
>> Nick, you're quite right, it' s the first time I post here, thought it would add my first message as well.
>> Maarten corrected mistakes in my original coding (so that's solved). My remaining question is regarding the code he proposed.
>>
>> If I run Maarten's code, for the "model with constraints" (biprobit (cat mpg price) (foreign mpg price), constraint (1 2),
>> I get the error message:
>> (note: constraint number 1 caused error r(111)) ( no variables defined;)
>> (note: constraint number 2 caused error r(111))
>> It does not seem to accept the constraints, but runs the full model nevertheless. Can I assume for this that since the constraints entail coefficients from both models, when stata runs model 1 and model 2 separately it cannot apply the constraints because they are not known yet (seems logic enough). Just to be sure. The LR test gives results do I assume that stata acknowledged the constraints (as difference in df).
>>
>> Thanks for your help and sorry for the mess,
>> Lieven
>>
>>
>>
>> On Aug 28, 2012, at 11:29 AM, Nick Cox wrote:
>>
>>> Asking this question without showing what you typed wastes everybody's time.
>>>
>>> What is the entire and exact syntax that you typed?
>>>
>>> Can you reproduce Maarten's example? What is different about what you typed.
>>>
>>> Nick
>>>
>>> On Tue, Aug 28, 2012 at 10:29 AM, Huybregts <[email protected]> wrote:
>>>> Many thanks for the reply and the coding Maarten, however if I run the model with constraints, I get the error message:
>>>> (note: constraint number 1 caused error r(111)) ( no variables defined;)
>>>> (note: constraint number 2 caused error r(111))
>>>>
>>>> It does not seem to accept the constraints, but runs the full model nevertheless. Can I assume for this that since the constraints entail coefficients from both models, when stata runs model 1 and model 2 separately it cannot apply the constraints because they are not known yet (seems logic enough). Just to be sure.
>>>> Cheers,
>>>>
>>>> Lieven
>>>>
>>>>
>>>>
>>>>
>>>> On Aug 28, 2012, at 11:05 AM, Maarten Buis wrote:
>>>>
>>>>> sysuse auto.dta,clear
>>>>> egen cat=cut(rep78),grou(2) label
>>>>>
>>>>> // model without constraints
>>>>> biprobit (cat mpg price) ///
>>>>> (foreign mpg price)
>>>>> estimates store R1
>>>>>
>>>>> // replay the model, but see the coefficient names:
>>>>> biprobit, coeflegend
>>>>>
>>>>> // use those name to define the constraints
>>>>> constraint define 1 _b[cat:mpg] = _b[foreign:mpg]
>>>>> constraint define 2 _b[cat:price] = _b[foreign:price]
>>>>>
>>>>> // Model with constraints
>>>>> biprobit (cat mpg price) ///
>>>>> (foreign mpg price), constraint (1 2)
>>>>> estimates store R2
>>>>> lrtest R1 R2
>>
>>
>>
>>>> On Aug 28, 2012, at 10:05 AM, Huybregts wrote:
>> <Dear Stata listers,
>> <
>> <To test if two binary outcomes have the same underlying pattern of predictors, we compared 2 biprobit models (one with constraints, one without) using a LR test. However we encounter a <recurring error for which we can't find a solution. To make this understandable I use the auto.dta dataset to replicate our problem from a different dataset.
>> <
>> <************************************************
>> sysuse auto.dta,clear
>> egen cat=cut(rep78),grou(2) label
>>
>> * model without constraints
>> xi: biprobit (cat mpg price) (foreign mpg price)
>> estimates store R1
>> matrix define coef=e(b)
>> matrix list coef
>> constraint define 1 coef[1,1] = coef[1,4]
>> constraint define 2 coef[1,2] = coef[1,5]
>>
>> * Model with constraints
>> xi: biprobit (cat mpg price) (foreign mpg price), constraint (1 2)
>> estimates store R2
>> lrtest R1 R2
>> <************************************************
>> <The error I get is (just after the model with constraints)
>> <
>> <Fitting comparison equation 1:
>> <(note: constraint number 1 caused error r(131))
>> <(note: constraint number 2 caused error r(131))
>> <
>> <I did not find a similar problem on the statalist, would it be impossible for the biprobit to converge adding constraints of equal coefficients?
>> <I use Stata 11.1.
>> <Many thanks for any help anyone could provide.
>> <
>
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