**[R] probit** -- Probit regression

__Syntax__

__prob__**it** *depvar* [*indepvars*] [*if*] [*in*] [*weight*] [**,** *options*]

*options* Description
-------------------------------------------------------------------------
Model
__nocons__**tant** suppress constant term
__off__**set(***varname***)** include *varname* in model with coefficient
constrained to 1
**asis** retain perfect predictor variables
__const__**raints(***constraints***)** apply specified linear constraints
__col__**linear** keep collinear variables

SE/Robust
**vce(***vcetype***)** *vcetype* may be **oim**, __r__**obust**, __cl__**uster**
*clustvar*, __boot__**strap**, or __jack__**knife**

Reporting
__l__**evel(***#***)** set confidence level; default is **level(95)**
__nocnsr__**eport** 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

__nocoe__**f** do not display the coefficient table;
seldom used
__coefl__**egend** display legend instead of statistics
-------------------------------------------------------------------------
*indepvars* may contain factor variables; see fvvarlist.
*depvar* and *indepvars* may contain time-series operators; see tsvarlist.
**bayes**, **bootstrap**, **by**, **fmm**, **fp**, **jackknife**, **mfp**, **mi estimate**, **nestreg**,
**rolling**, **statsby**, **stepwise**, and **svy** are allowed; see prefix. For more
details, see **[BAYES] bayes: probit** and **[FMM] fmm: probit**.
**vce(bootstrap)** and **vce(jackknife)** are not allowed with the **mi estimate**
prefix.
Weights are not allowed with the **bootstrap** prefix.
**vce()**, **nocoef**, and weights are not allowed with the **svy** prefix.
**fweight**s, **iweight**s, and **pweight**s are allowed; see weight.
**nocoef** and **coeflegend** do not appear in the dialog box.
See **[R] probit postestimation** for features available after estimation.

__Menu__

**Statistics > Binary outcomes > Probit regression**

__Description__

**probit** fits a probit model for a binary dependent variable, assuming that
the probability of a positive outcome is determined by the standard
normal cumulative distribution function. **probit** can compute robust and
cluster-robust standard errors and adjust results for complex survey
designs.

__Options__

+-------+
----+ Model +------------------------------------------------------------

**noconstant**, **offset(***varname***)**, **constraints(***constraints***)**, **collinear**; see **[R]**
**estimation options**.

**asis** specifies that all specified variables and observations be retained
in the maximization process. This option is typically not specified
and may introduce numerical instability. Normally **probit** drops
variables that perfectly predict success or failure in the dependent
variable along with their associated 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 variable and perfectly predicted
observations has no effect on the likelihood or estimates of the
remaining coefficients and increases the numerical stability of the
optimization process. Specifying this option forces 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 from asymptotic theory (**oim**), 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*.

+-----------+
----+ Reporting +--------------------------------------------------------

**level(***#***)**; see **[R] estimation options**.

**nocnsreport**; see **[R] estimation options**.

*display_options*: **noci**, __nopv__**alues**, __noomit__**ted**, **vsquish**, __noempty__**cells**,
__base__**levels**, __allbase__**levels**, __nofvlab__**el**, **fvwrap(***#***)**, **fvwrapon(***style***)**,
**cformat(***%fmt***)**, **pformat(%***fmt***)**, **sformat(%***fmt***)**, and **nolstretch**; see **[R]**
**estimation options**.

+--------------+
----+ Maximization +-----------------------------------------------------

*maximize_options*: __dif__**ficult**, __tech__**nique(***algorithm_spec***)**, __iter__**ate(***#***)**,
[__no__]__lo__**g**, __tr__**ace**, __grad__**ient**, **showstep**, __hess__**ian**, __showtol__**erance**,
__tol__**erance(***#***)**, __ltol__**erance(***#***)**, __nrtol__**erance(***#***)**, __nonrtol__**erance**, and
**from(***init_specs***)**; see **[R] maximize**. These options are seldom used.

The following options are available with **probit** but are not shown in the
dialog box:

**nocoef** specifies that the coefficient table not be displayed. This
option is sometimes used by programmers but is of no use
interactively.

**coeflegend**; see **[R] estimation options**.

__Examples__

---------------------------------------------------------------------------
Setup
**. sysuse auto**

Probit regression
**. probit foreign weight mpg**

Same as above, but with robust standard errors
**. probit foreign weight mpg, vce(robust)**

---------------------------------------------------------------------------
Setup
**. webuse union**

Probit regression
**. probit union age grade not_smsa south##c.year**

Same as above, but adjust standard errors for clusters in **id**
**. probit union age grade not_smsa south##c.year, vce(cluster id)**

---------------------------------------------------------------------------
Setup
**. webuse nhanes2d**
**. svyset**

Probit regression using survey data
**. svy: probit highbp height weight age female**
---------------------------------------------------------------------------

__Stored results__

**probit** stores the following in **e()**:

Scalars
**e(N)** number of observations
**e(N_cds)** number of completely determined successes
**e(N_cdf)** number of completely determined failures
**e(k)** number of 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-R-squared
**e(ll)** log likelihood
**e(ll_0)** log likelihood, constant-only model
**e(N_clust)** number of clusters
**e(chi2)** chi-squared
**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)** **probit**
**e(cmdline)** command as typed
**e(depvar)** name of dependent variable
**e(wtype)** weight type
**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 chi-squared 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(estat_cmd)** program used to implement **estat**
**e(predict)** program used to implement **predict**
**e(marginsok)** predictions allowed by **margins**
**e(marginsnotok)** predictions disallowed by **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(mns)** vector of means of the independent variables
**e(rules)** information about perfect predictors
**e(V)** variance-covariance matrix of the estimators
**e(V_modelbased)** model-based variance

Functions
**e(sample)** marks estimation sample