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| From | Nick Cox <njcoxstata@gmail.com> |
| To | statalist@hsphsun2.harvard.edu |
| Subject | Re: st: Introducing constraints to biprobit model |
| Date | Tue, 28 Aug 2012 16:54:10 +0100 |
Someone with experience with these models should now be able to comment. Nick On Tue, Aug 28, 2012 at 4:38 PM, Huybregts <lievenhu@gmail.com> wrote: > 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 >> * 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/ * * 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/