Title stata.com probit — Probit regression

1 Probit regressionSyntaxMenuDescriptionOptionsRe marks and examplesStored resultsMethods and formulasReferencesAlso seeSyntaxprobitdepvar[indepvars] [if] [in] [weight] [,options]optionsDescriptionModelnoconst antsuppress constant termoffset(varname)includevarnamein model with coefficient constrained to 1asisretain perfect predictor variablesconstraints(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 column formats, row spacing, line width, display of omittedvariables and base and empty cells, and factor-variable labelingMaximizationmaximizeoptionscontr ol the maximization process; seldom usednocoefdo not display the coefficient table; 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.

2 See [R] (),nocoef, 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 Probit Probit regressionMenuStatistics>Binary outcomes> Probit regressionDescriptionprobitfits a maximum-likelihood Probit estimating on grouped data, see thebprobitcommand described in [R] auxiliary commands may be run afterprobit,logit, orlogistic; see [R]logisticpostestimationfor a description of these [R]logisticfor a list of related estimation Model noconstant,offset(varname),constraints(c onstraints),collinear; see [R]estimation that all specified variables and observations be retained in the maximization option is typically not specified and may introduce numerical instability.

3 Normallyprobitdrops variables that perfectly predict success or failure in the dependent variable along with theirassociated observations. In those cases, the effective coefficient on the dropped variables is infinity(negative infinity) for variables that completely determine a success (failure). Dropping the variableand perfectly predicted observations has no effect on the likelihood or estimates of the remainingcoefficients and increases the numerical stability of the optimization process. Specifying this optionforces retention of perfect predictor variables and their associated observations. 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]vceoption.

4 Reporting level(#); see [R]estimation ; see [R]estimation :noomitted,vsquish,noemptycells,baseleve ls,allbaselevels,nofvla-bel,fvwrap(#),fv wrapon(style),cformat(%fmt),pformat(%fmt ),sformat(%fmt), andnolstretch; see [R]estimation options. 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 Probit regression 3 The following options are available withprobitbut are not shown in the dialog box:nocoefspecifies that the coefficient table not be displayed. This option is sometimes used byprogrammers but is of no use ; see [R]estimation and are presented under the following headings:Robust standard errorsModel identificationprobitfits maximum likelihood models with dichotomous dependent (left-hand-side) variablescoded as 0/1 (more precisely, coded as 0 and not 0).

5 Example 1We have data on the make, weight, and mileage rating of 22 foreign and 52 domestic wish to fit a Probit model explaining whether a car is foreign based on its weight and is an overview of our data:. use (1978 Automobile Data). keep make mpg weight foreign. describeContains data from : 74 1978 Automobile Datavars: 4 13 Apr 2013 17:45size: 1,702 (_dta has notes)storage display valuevariable name type format label variable labelmake str18 %-18s Make and Modelmpg int % Mileage (mpg)weight int % Weight (lbs.)

6 Foreign byte % origin Car typeSorted by: foreignNote: dataset has changed since last saved. inspect foreignforeign: Car type Number of ObservationsTotal Integers Nonintegers# Negative - - -# Zero 52 52 -# Positive 22 22 -## # Total 74 74 -# # Missing -0 1 74(2 unique values)foreign is labeled and all values are documented in the Probit Probit regressionTheforeignvariable takes on two unique values, 0 and 1.

7 The value 0 denotes a domestic car,and 1 denotes a foreign model that we wish to fit isPr(foreign= 1) = ( 0+ 1weight+ 2mpg)where is the cumulative normal fit this model, we type. Probit foreign weight mpgIteration 0: log likelihood = 1: log likelihood = (output omitted)Iteration 5: log likelihood = regression Number of obs = 74LR chi2(2) = > chi2 = likelihood = Pseudo R2 = Std. Err. z P>|z| [95% Conf. Interval] .0005661 .0515689 find that heavier cars are less likely to be foreign and that cars yielding better gas mileage arealso less likely to be foreign, at least holding the weight of the car [R]maximizefor an explanation of the noteStata interprets a value of 0 as a negative outcome (failure) and treats all other values (exceptmissing) as positive outcomes (successes).

8 Thus if your dependent variable takes on the values 0 and1, then 0 is interpreted as failure and 1 as success. If your dependent variable takes on the values 0,1, and 2, then 0 is still interpreted as failure, but both 1 and 2 are treated as you prefer a more formal mathematical statement, when you typeprobity x, Stata fits themodelPr(yj6= 0|xj) = (xj )where is the standard cumulative standard errorsIf you specify thevce(robust)option,probitreports robust standard errors; see[U] Ob-taining robust variance 2 For the model from example 1, the robust calculation increases the standard error of the coefficientonmpgby almost 15%: Probit Probit regression 5. Probit foreign weight mpg, vce(robust) nologProbit regression Number of obs = 74 Wald chi2(2) = > chi2 = pseudolikelihood = Pseudo R2 = Std.

9 Err. z P>|z| [95% Conf. Interval] .0004934 .0593548 . (robust), the standard error for the coefficient onmpgwas reported to be witha resulting confidence interval of[ , ].Example 3 Thevce(clusterclustvar)option can relax the independence assumption required by the probitestimator to independence between clusters. To demonstrate, we will switch to a different are studying unionization of women in the United States and have a dataset with 26,200observations on 4,434 women between 1970 and 1988. We will use the variablesage(the womenwere 14 26 in 1968, and our data span the age range of 16 46),grade(years of schooling completed,ranging from 0 to 18),notsmsa(28% of the person-time was spent living outside anSMSA standardmetropolitan statistical area),south(41% of the person-time was in the South), andyear.

10 Each ofthese variables is included in the regression as a covariate along with the interaction betweensouthandyear. This interaction, along with thesouthandyearvariables, is specified in theprobitcommand using factor-variables notation,south## We also have variableunion, indicatingunion membership. Overall, 22% of the person-time is marked as time under union membership, and44% of these women have belonged to a Probit Probit regressionWe fit the following model, ignoring that the women are observed an average of times eachin these data:. use , clear(NLS Women 14-24 in 1968). Probit union age grade not_smsa south## 0: log likelihood = 1: log likelihood = 2: log likelihood = 3: log likelihood = regression Number of obs = 26200LR chi2(6) = > chi2 = likelihood = Pseudo R2 = Std.