oprobit — Ordered probit regression - Data Analysis and ...

1 Ordered probit regressionDescriptionQuick startMenuSyntaxOptionsRemarks and examplesStored resultsMethods and formulasReferencesAlso seeDescriptionoprobitfits Ordered probit models of ordinal variabledepvaron the independent variablesindepvars. The actual values taken on by the dependent variable are irrelevant, except that largervalues are assumed to correspond to higher startOrdinal probit model ofyonx1and categorical variablesaandboprobit y x1 ofyonx1and a one-period lagged value ofx1usingtssetdataoprobit y x1 above, but calculate results for each level ofcatvarand save statistics , by(catvar) saving(myfile): oprobit y x1 >Ordinal outcomes> Ordered probit regression12 oprobit Ordered probit regressionSyntaxoprobitdepvar[indepvars] [if][in][weight][,options]optionsDescrip tionModeloffset(varname)includevarnamein model with coefficient constrained to 1constraints(constraints)apply specified linear constraintscollinearkeep collinear variablesSE/Robustvce(vcetype)vcetypemay beoim,robust,clusterclustvar,bootstrap, orjackknifeReportinglevel(#)set confidence level; default islevel(95)nocnsreportdo not display constraintsdisplayoptionscontrol columns and column formats, row spacing, line width,display of omitted variables and base and empty cells, andfactor-variable labelingMaximizationmaximizeoptionscontr ol the maximization process.

2 Seldom usedcoeflegenddisplay legend instead of statisticsindepvarsmay contain factor variables; see[U] Factor contain time-series operators; see[U] Time-series ,by,fp,jackknife,mfp,mi estimate,nestreg,rolling,statsby,stepwis e, andsvyare allowed;see[U] Prefix (bootstrap)andvce(jackknife)are not allowed with themi estimateprefix; see [MI]mi are not allowed with thebootstrapprefix; see [R] ()and weights are not allowed with thesvyprefix; see [SVY] ,iweights, andpweights are allowed; see[U] not appear in the dialog [U] 20 Estimation and postestimation commandsfor more capabilities of estimation Model offset(varname),constraints(constraints) ,collinear; see [R]estimation options. SE/Robust vce(vcetype)specifies the type of standard error reported, which includes types that are derivedfrom asymptotic theory (oim), that are robust to some kinds of misspecification (robust), thatallow for intragroup correlation (clusterclustvar), and that use bootstrap or jackknife methods(bootstrap,jackknife); see [R] Ordered probit regression 3 Reporting level(#); see [R]estimation ; see [R]estimation :noci,nopvalues,noomitted,vsquish,noempt ycells,baselevels,allbaselevels,nofvlabe l,fvwrap(#),fvwrapon(style),cformat(%fmt ),pformat(%fmt),sformat(%fmt), andnolstretch; see [R]estimation options.

3 Maximization maximizeoptions:difficult,technique(algo rithmspec),iterate(#),[no]log,trace,grad ient,showstep,hessian,showtolerance,tole rance(#),ltolerance(#),nrtolerance(#),no nrtolerance, andfrom(initspecs); see [R]maximize. These options areseldom following option is available withoprobitbut is not shown in the dialog box:coeflegend; see [R]estimation and Ordered probit model is used to estimate relationships between an ordinal dependent variableand a set of independent variables. Anordinalvariable is a variable that is categorical and Ordered ,for instance, poor , good , and excellent , which might indicate a person s current health status orthe repair record of a car. If there are only two outcomes, see [R]logistic, [R]logit, and [R] entry is concerned only with more than two outcomes.

4 If the outcomes cannot be Ordered (forexample, residency in the north, east, south, or west), see [R]mlogit. This entry is concerned onlywith models in which the outcomes can be Ordered . See [R]logisticfor a list of related Ordered probit , an underlying score is estimated as a linear function of the independent variablesand a set of cutpoints. The probability of observing outcomeicorresponds to the probability that theestimated linear function, plus random error, is within the range of the cutpoints estimated for theoutcome:Pr(outcomej=i) = Pr( i 1< 1x1j+ 2x2j+ + kxkj+uj i)ujis assumed to be normally distributed. In either case, we estimate the coefficients 1, 2,.., ktogether with the cutpoints 1, 2.

5 , I 1, whereIis the number of possible outcomes. 0is taken as , and Iis taken as+ . All of this is a direct generalization of the ordinarytwo-outcome probit 1In example 2 of [R]ologit, we use a variation of the automobile dataset (see[U] Exampledatasets) to analyze the 1977 repair records of 66 foreign and domestic cars. We use Ordered logitto explore the relationship ofrep77in terms offoreign(origin of manufacture),length(a proxyfor size), andmpg. Here we fit the same model using Ordered probit rather than Ordered logit:4 oprobit Ordered probit regression . use (Automobile Models). oprobit rep77 foreign length mpgIteration 0: log likelihood = 1: log likelihood = 2: log likelihood = 3: log likelihood = 4: log likelihood = probit regression Number of obs = 66LR chi2(3) = > chi2 = likelihood = Pseudo R2 = Std.

6 Err. z P>|z| [95% Conf. Interval] .4246796 .8725037 .012648 .022078 ..0378628 .0562463 .2046656 find that foreign cars have better repair records, as do larger cars and cars with better Ordered probit regression 5 Stored resultsoprobitstores the following ine():Scalarse(N)number of observationse(Ncd)number of completely determined observationse(kcat)number of categoriese(k)number of parameterse(kaux)number of auxiliary parameterse(keq)number of equations ine(b)e(keqmodel)number of equations in overall model teste(kdv)number of dependent variablese(dfm)model degrees of freedome(r2p)pseudo-R-squarede(ll)log likelihoode(ll0)log likelihood, constant-only modele(Nclust)number of clusterse(chi2) 2e(p)significance of model teste(rank)rank ofe(V)e(ic)number of iterationse(rc)return codee(converged) 1if converged,0otherwiseMacrose(cmd) oprobite(cmdline)command as typede(depvar)name of dependent variablee(wtype)weight typee(wexp)

7 Weight expressione(title)title in estimation outpute(clustvar)name of cluster variablee(offset)linear offset variablee(chi2type) WaldorLR; type of model 2teste(vce)vcetypespecified invce()e(vcetype)title used to label Std. (opt)type of optimizatione(which) maxormin; whether optimizer is to perform maximization or minimizatione(mlmethod)type ofmlmethode(user)name of likelihood-evaluator programe(technique)maximization techniquee(properties) b Ve(predict)program used to implementpredicte(marginsdefault)default predict()specification formarginse(asbalanced)factor variablesfvsetasasbalancede(asobserved)f actor variablesfvsetasasobservedMatricese(b)co efficient vectore(Cns)constraints matrixe(ilog)iteration log (up to 20 iterations)e(gradient)gradient vectore(cat)category valuese(V)variance covariance matrix of the estimatorse(Vmodelbased)model-based varianceFunctionse(sample)

8 Marks estimation sample6 oprobit Ordered probit regressionMethods and formulasSeeMethods and formulasof [R] , J., and S. D. Silvey. 1957. The generalization of probit Analysis to the case of multiple : 131 , A. C., and P. K. Trivedi. : Methods and Applications. New York: CambridgeUniversity , R., and M. Lokshin. 2007. Maximum likelihood and two-step estimation of an Ordered - probit Journal7: 167 Luca, G., and V. Perotti. 2011. Estimation of Ordered response models with sample Journal11:213 , R. 1997. sg59: Index of ordinal variation and Neyman Barton Technical Bulletin33: 10 inStata Technical Bulletin Reprints, vol. 6, pp. 145 147. College Station, TX: Stata , J. S. Models for Categorical and Limited Dependent Variables.

9 Thousand Oaks, CA: , J. S., and J. Freese. Models for Categorical Dependent Variables Using Stata. 3rd ed. CollegeStation, TX: Stata , A., and S. Rabe-Hesketh. 2006. Maximum likelihood estimation of endogenous switching and sampleselection models for binary, ordinal, and count Journal6: 285 , M. B. 2004. Semi-nonparametric estimation of extended Ordered probit Journal4: 27 , R. 2010. Fitting heterogeneous choice models with Journal10: 540 , R. 1998. sg86: Continuation-ratio models for ordinal response Technical Bulletin44: 18 inStata Technical Bulletin Reprints, vol. 8, pp. 149 153. College Station, TX: Stata , R., and W. W. Gould. 1998. sg76: An approximate likelihood-ratio test for ordinal response Bulletin42: 24 27.

10 Reprinted inStata Technical Bulletin Reprints, vol. 7, pp. 199 204. College Station,TX: Stata , J., and J. S. Long. 2005. Confidence intervals for predicted outcomes in regression models for Journal5: 537 see[R] oprobit postestimation Postestimation tools for oprobit [R]heckoprobit Ordered probit model with sample selection[R]logistic Logistic regression , reporting odds ratios[R]mlogit Multinomial (polytomous) logistic regression [R]mprobit Multinomial probit regression [R]ologit Ordered logistic regression [R] probit probit regression [ME]meoprobit Multilevel mixed-effects Ordered probit regression [MI]estimation Estimation commands for use with mi estimate[SVY]svy estimation Estimation commands for survey data[XT]xtoprobit Random-effects Ordered probit models[U] 20 Estimation and postestimation commands