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# Re: st: Introducing constraints to biprobit model

 From Huybregts To statalist@hsphsun2.harvard.edu 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 <lievenhu@gmail.com> 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 <lievenhu@gmail.com> 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.
>> <
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
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> *   http://www.ats.ucla.edu/stat/stata/

*
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```