Title stata.

com
oprobit — Ordered probit regression

Description Quick start Menu Syntax

Options Remarks and examples Stored results Methods and formulas
References Also see

Description
oprobit fits ordered probit models of ordinal variable depvar on the independent variables
indepvars. The actual values taken on by the dependent variable are irrelevant, except that larger
values are assumed to correspond to “higher” outcomes.

Quick start
Ordinal probit model of y on x1 and categorical variables a and b
oprobit y x1 i.a i.b
Model of y on x1 and a one-period lagged value of x1 using tsset data
oprobit y x1 L.x1
Same as above, but calculate results for each level of catvar and save statistics to myfile.dta
statsby, by(catvar) saving(myfile): oprobit y x1 L.x1

Menu
Statistics > Ordinal outcomes > Ordered probit regression

1
 2 oprobit — Ordered probit regression

Syntax
         
oprobit depvar indepvars if in weight , options

options Description
Model
offset(varname) include varname in model with coefficient constrained to 1
constraints(constraints) apply specified linear constraints
SE/Robust
vce(vcetype) vcetype may be oim, opg, robust, cluster clustvar, bootstrap,
or jackknife
Reporting
level(#) set confidence level; default is level(95)
nocnsreport do not display constraints
display options control columns and column formats, row spacing, line width,
display of omitted variables and base and empty cells, and
factor-variable labeling
Maximization
maximize options control the maximization process; seldom used
collinear keep collinear variables
coeflegend display legend instead of statistics
indepvars may contain factor variables; see [U] 11.4.3 Factor variables.
depvar and indepvars may contain time-series operators; see [U] 11.4.4 Time-series varlists.
bayes, bootstrap, by, collect, fmm, fp, jackknife, mfp, mi estimate, nestreg, rolling, statsby, stepwise,
and svy are allowed; see [U] 11.1.10 Prefix commands. For more details, see [BAYES] bayes: oprobit and
[FMM] fmm: oprobit.
vce(bootstrap) and vce(jackknife) are not allowed with the mi estimate prefix; see [MI] mi estimate.
Weights are not allowed with the bootstrap prefix; see [R] bootstrap.
vce() and weights are not allowed with the svy prefix; see [SVY] svy.
fweights, iweights, and pweights are allowed; see [U] 11.1.6 weight.
collinear and coeflegend do not appear in the dialog box.
See [U] 20 Estimation and postestimation commands for more capabilities of estimation commands.

Options

 Model
offset(varname), constraints(constraints); see [R] Estimation options.

 SE/Robust
vce(vcetype) specifies the type of standard error reported, which includes types that are derived from
asymptotic theory (oim, opg), that are robust to some kinds of misspecification (robust), that
allow for intragroup correlation (cluster clustvar), and that use bootstrap or jackknife methods
(bootstrap, jackknife); see [R] vce option.
 oprobit — Ordered probit regression 3


 Reporting
level(#); see [R] Estimation options.
nocnsreport; see [R] Estimation options.
display options: noci, nopvalues, noomitted, vsquish, noemptycells, baselevels,
allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style), cformat(% fmt), pformat(% fmt),
sformat(% fmt), and nolstretch; see [R] Estimation options.

 Maximization
 
maximize options: difficult, technique(algorithm spec), iterate(#), no log, trace,
gradient, showstep, hessian, showtolerance, tolerance(#), ltolerance(#),
nrtolerance(#), nonrtolerance, and from(init specs); see [R] Maximize. These options are
seldom used.

The following options are available with oprobit but is not shown in the dialog box:
collinear, coeflegend; see [R] Estimation options.

Remarks and examples stata.com

An ordered probit model is used to estimate relationships between an ordinal dependent variable
and a set of independent variables. An ordinal variable is a variable that is categorical and ordered,
for instance, “poor”, “good”, and “excellent”, which might indicate a person’s current health status or
the repair record of a car. If there are only two outcomes, see [R] logistic, [R] logit, and [R] probit.
This entry is concerned only with more than two outcomes. If the outcomes cannot be ordered (for
example, residency in the north, east, south, or west), see [R] mlogit. This entry is concerned only
with models in which the outcomes can be ordered. See [R] logistic for a list of related estimation
commands.
In ordered probit, an underlying score is estimated as a linear function of the independent variables
and a set of cutpoints. The probability of observing outcome i corresponds to the probability that the
estimated linear function, plus random error, is within the range of the cutpoints estimated for the
outcome:

Pr(outcomej = i) = Pr(κi−1 < β1 x1j + β2 x2j + · · · + βk xkj + uj ≤ κi )

uj is assumed to be normally distributed. In either case, we estimate the coefficients β1 , β2 , . . . ,

βk together with the cutpoints κ1 , κ2 , . . . , κI−1 , where I is the number of possible outcomes.
κ0 is taken as −∞, and κI is taken as +∞. All of this is a direct generalization of the ordinary
two-outcome probit model.

Example 1
In example 2 of [R] ologit, we use a variation of the automobile dataset (see [U] 1.2.2 Example
datasets) to analyze the 1977 repair records of 66 foreign and domestic cars. We use ordered logit
to explore the relationship of rep77 in terms of foreign (origin of manufacture), length (a proxy
for size), and mpg. Here we fit the same model using ordered probit rather than ordered logit:
 4 oprobit — Ordered probit regression

. use https://www.stata-press.com/data/r18/fullauto
(Automobile models)
. oprobit rep77 foreign length mpg
Iteration 0: Log likelihood = -89.895098
Iteration 1: Log likelihood = -78.106316
Iteration 2: Log likelihood = -78.020086
Iteration 3: Log likelihood = -78.020025
Iteration 4: Log likelihood = -78.020025
Ordered probit regression Number of obs = 66
LR chi2(3) = 23.75
Prob > chi2 = 0.0000
Log likelihood = -78.020025 Pseudo R2 = 0.1321

rep77 Coefficient Std. err. z P>|z| [95% conf. interval]

foreign 1.704861 .4246796 4.01 0.000 .8725037 2.537217

length .0468675 .012648 3.71 0.000 .022078 .0716571
mpg .1304559 .0378628 3.45 0.001 .0562463 .2046656

/cut1 10.1589 3.076754 4.128577 16.18923

/cut2 11.21003 3.107527 5.119389 17.30067
/cut3 12.54561 3.155233 6.361467 18.72975
/cut4 13.98059 3.218793 7.671874 20.28931

We find that foreign cars have better repair records, as do larger cars and cars with better mileage
ratings.

Stored results
oprobit stores the following in e():
Scalars
e(N) number of observations
e(N cd) number of completely determined observations
e(k cat) number of categories
e(k) number of parameters
e(k aux) number of auxiliary parameters
e(k eq) number of equations in e(b)
e(k eq model) number of equations in overall model test
e(k dv) number of dependent variables
e(df m) model degrees of freedom
e(r2 p) pseudo-R2
e(ll) log likelihood
e(ll 0) log likelihood, constant-only model
e(N clust) number of clusters
e(chi2) χ2
e(p) p-value for model test
e(rank) rank of e(V)
e(ic) number of iterations
e(rc) return code
e(converged) 1 if converged, 0 otherwise
Macros
e(cmd) oprobit
e(cmdline) command as typed
e(depvar) name of dependent variable
e(wtype) weight type
 oprobit — Ordered probit regression 5

e(wexp) weight expression

e(title) title in estimation output
e(clustvar) name of cluster variable
e(offset) linear offset variable
e(chi2type) Wald or LR; type of model χ2 test
e(vce) vcetype specified in vce()
e(vcetype) title used to label Std. err.
e(opt) type of optimization
e(which) max or min; whether optimizer is to perform maximization or minimization
e(ml method) type of ml method
e(user) name of likelihood-evaluator program
e(technique) maximization technique
e(properties) b V
e(predict) program used to implement predict
e(marginsdefault) default predict() specification for margins
e(asbalanced) factor variables fvset as asbalanced
e(asobserved) factor variables fvset as asobserved
Matrices
e(b) coefficient vector
e(Cns) constraints matrix
e(ilog) iteration log (up to 20 iterations)
e(gradient) gradient vector
e(cat) category values
e(V) variance–covariance matrix of the estimators
e(V modelbased) model-based variance
Functions
e(sample) marks estimation sample

In addition to the above, the following is stored in r():

Matrices
r(table) matrix containing the coefficients with their standard errors, test statistics, p-values,
and confidence intervals

Note that results stored in r() are updated when the command is replayed and will be replaced when
any r-class command is run after the estimation command.

Methods and formulas

See Methods and formulas of [R] ologit.

References
Aitchison, J., and S. D. Silvey. 1957. The generalization of probit analysis to the case of multiple responses. Biometrika
44: 131–140. https://doi.org/10.2307/2333245.
Bauldry, S., J. Xu, and A. S. Fullerton. 2018. gencrm: A new command for generalized continuation-ratio models.
Stata Journal 18: 924–936.
Cameron, A. C., and P. K. Trivedi. 2005. Microeconometrics: Methods and Applications. New York: Cambridge
University Press.
Canette, I. 2013. Fitting ordered probit models with endogenous covariates with Stata’s gsem command. The Stata Blog:
Not Elsewhere Classified. http://blog.stata.com/2013/11/07/fitting-ordered-probit-models-with-endogenous-covariates-
with-statas-gsem-command/.
Chiburis, R., and M. Lokshin. 2007. Maximum likelihood and two-step estimation of an ordered-probit selection
model. Stata Journal 7: 167–182.
De Luca, G., and V. Perotti. 2011. Estimation of ordered response models with sample selection. Stata Journal 11:
213–239.
 6 oprobit — Ordered probit regression

Drukker, D. M. 2016. An ordered-probit inverse probability weighted (IPW) estimator. The Stata Blog: Not Elsewhere
Classified. http://blog.stata.com/2016/09/13/an-ordered-probit-inverse-probability-weighted-ipw-estimator/.
Huismans, J., J. W. Nijenhuis, and A. Sirchenko. 2022. A mixture of ordered probit models with endogenous switching
between two latent classes. Stata Journal 22: 557–596.
Long, J. S. 1997. Regression Models for Categorical and Limited Dependent Variables. Thousand Oaks, CA: Sage.
Long, J. S., and J. Freese. 2014. Regression Models for Categorical Dependent Variables Using Stata. 3rd ed. College
Station, TX: Stata Press.
Miranda, A., and S. Rabe-Hesketh. 2006. Maximum likelihood estimation of endogenous switching and sample
selection models for binary, ordinal, and count variables. Stata Journal 6: 285–308.
Smith, E. K., M. G. Lacy, and A. Mayer. 2019. Performance simulations for categorical mediation: Analyzing khb
estimates of mediation in ordinal regression models. Stata Journal 19: 913–930.
Stewart, M. B. 2004. Semi-nonparametric estimation of extended ordered probit models. Stata Journal 4: 27–39.
Williams, R. 2010. Fitting heterogeneous choice models with oglm. Stata Journal 10: 540–567.
Xu, J., and J. S. Long. 2005. Confidence intervals for predicted outcomes in regression models for categorical
outcomes. Stata Journal 5: 537–559.

Also see
[R] oprobit postestimation — Postestimation tools for oprobit
[R] heckoprobit — Ordered probit model with sample selection
[R] hetoprobit — Heteroskedastic ordered probit regression
[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
[R] zioprobit — Zero-inflated ordered probit regression
[BAYES] bayes: oprobit — Bayesian ordered probit regression
[CM] cmroprobit — Rank-ordered probit choice model
[ERM] eoprobit — Extended ordered probit regression
[FMM] fmm: oprobit — Finite mixtures of ordered probit regression models
[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

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