Probit regression - Stata

1 Probit regressionDescriptionQuick startMenuSyntaxOptionsRemarks and examplesStored resultsMethods and formulasReferencesAlso seeDescriptionprobitfits a Probit model for a binary dependent variable, assuming that the probability of apositive outcome is determined by the standard normal cumulative distribution robust and cluster robust standard errors and adjust results for complex survey startProbit model ofyon continuous variablex1probit y x1 Add square ofx1probit y ## above, but report bootstrap standard errorsprobit y ## , vce(bootstrap)Bootstrap estimates of coefficientsbootstrap _b: Probit y ## for complex survey design usingsvysetdata and addx2svy: Probit y ## x2 MenuStatistics>Binary outcomes> Probit regression12 Probit Probit regressionSyntaxprobitdepvar[indepvars] [if] [in] [weight] [,options]optionsDescriptionModelnoconst antsuppress constant termoffset(varname)includevarnamein model with coefficient constrained to 1asisretain perfect predictor variablesconstraints(constraints)apply specified linear constraintsSE/Robustvce(vcetype)vcetypem ay beoim,opg,robust,clusterclustvar,bootstr ap,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; seldom usednocoefdo not display the coefficient table.

2 Seldom usedcollinearkeep collinear variablescoeflegenddisplay legend instead of statisticsindepvarsmay contain factor variables; see[U] Factor contain time-series operators; see[U] Time-series ,bootstrap,by,collect,fmm,fp,jackknife,m fp,mi estimate,nestreg,rolling,statsby,stepwis e, andsvyare allowed; see[U] Prefix commands. For more details, see [BAYES]bayes: probitand [FMM]fmm: (bootstrap)andvce(jackknife)are not allowed with themi estimateprefix; see [MI]mi are not allowed with thebootstrapprefix; see [R] (),nocoef, and weights are not allowed with thesvyprefix; see [SVY] ,iweights, andpweights are allowed; see[U] ,collinear, andcoeflegenddo not appear in the dialog [U] 20 Estimation and postestimation commandsfor more capabilities of estimation Model noconstant,offset(varname),constraints(c onstraints); 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 Normallyprobitomits variables that perfectly predict success or failure in the dependent variable along with theirassociated observations. In those cases, the effective coefficient on the omitted variables is infinity(negative infinity) for variables that completely determine a success (failure). Dropping the variableprobit Probit regression 3and 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 derived fromasymptotic theory (oim,opg), 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 :noci,nopvalues,noomitted,vsquish,noempt ycells,baselevels,allbaselevels,nofvlabe l,fvwrap(#),fvwrapon(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 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 ,coeflegend; see [R]Estimation and are presented under the following headings:Robust standard errorsModel identificationVideo examplesprobitfits maximum likelihood models with dichotomous dependent (left-hand-side) variablescoded as 0/1 (more precisely, coded as 0 and not 0).

5 For grouped data or data in binomial form, a Probit model can be fit usingglmwith thefamily(binomial)andlink( Probit ) 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:4 Probit Probit regression . use (1978 automobile data). keep make mpg weight foreign. describeContains data from : 74 1978 automobile dataVariables: 4 13 Apr 2020 17:45(_dta has notes)Variable Storage Display Valuename type format label Variable labelmake str18 %-18s Make and modelmpg int % Mileage (mpg)weight int % Weight (lbs.)

6 Foreign byte % origin Car originSorted by: foreignNote: Dataset has changed since last inspect foreignforeign: Car origin 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 takes on two unique values, 0 and 1. 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.

7 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 Probit regression 5We 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 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 of6 Probit Probit regressionthese 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 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 = 26,200LR chi2(6) = > chi2 = likelihood = Pseudo R2 = Std.