**[R] fracreg** -- Fractional response regression

__Syntax__

Syntax for fractional probit regression

**fracreg** __pr__**obit** *depvar* [*indepvars*] [*if*] [*in*] [*weight*] [**,** *options*]

Syntax for fractional logistic regression

**fracreg** __log__**it** *depvar* [*indepvars*] [*if*] [*in*] [*weight*] [**,** *options*]

Syntax for fractional heteroskedastic probit regression

**fracreg** __pr__**obit** *depvar* [*indepvars*] [*if*] [*in*] [*weight*]**,** **het(***varlist*[**,**
__off__**set(***varname**_o***)**]**)** [*options*]

*options* Description
-------------------------------------------------------------------------
Model
__nocons__**tant** suppress constant term
__off__**set(***varname***)** include *varname* in model with
coefficient constrained to 1
__const__**raints(***constraints***)** apply specified linear constraints
__col__**linear** keep collinear variables
* **het(***varlist*[**,** __off__**set(***varname**_o*]**)** independent variables to model the
variance and possible offset
variable with **fracreg probit**

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

Reporting
__l__**evel(***#***)** set confidence level; default is
**level(95)**
**or** report odds ratio; only valid with
**fracreg logit**
__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

**nocoef** do not display the coefficient
table; seldom used
__coefl__**egend** display legend instead of statistics
-------------------------------------------------------------------------
* **het()** may be used only with **fracreg probit** to compute fractional
heteroskedastic probit regression.
*indepvars* may contain factor variables; see fvvarlist.
*depvar* and *indepvars* may contain time-series operators; see tsvarlist.
**bayes**, **bootstrap**, **by**, **fp**, **jackknife**, **mi estimate**, **rolling**, **statsby**, and
**svy** are allowed; see prefix. For more details, see **[BAYES] bayes:**
**fracreg**.
**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] fracreg postestimation** for features available after estimation.

__Menu__

**Statistics > Fractional outcomes > Fractional regression**

__Description__

**fracreg** fits a fractional response model for a dependent variable that is
greater than or equal to 0 and less than or equal to 1. It uses a
probit, logit, or heteroskedastic probit model for the conditional mean.
These models are often used for outcomes such as rates, proportions, and
fractional data.

__Options__

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

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

**het(***varlist*[**,** **offset(***varname**_o***)**]**)** specifies the independent variables and
the offset variable, if there is one, in the variance function.
**het()** may only be used with **fracreg probit** to compute fractional
heteroskedastic probit regression.

**offset(***varname_o***)** specifies that selection offset *varname_o* be
included in the model with the coefficient constrained to be 1.

+-----------+
----+ SE/Robust +--------------------------------------------------------

**vce(***vcetype***)** specifies the type of standard error reported, which
includes types 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**.

**or** reports the estimated coefficients transformed to odds ratios, that
is, e^b rather than b. Standard errors and confidence intervals are
similarly transformed. This option affects how results are
displayed, not how they are estimated. **or** may be specified at
estimation or when replaying previously estimated results. This
option may only be used with **fracreg logit**.

**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 **fracreg** 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
**. webuse 401k**

Use fractional probit regression to obtain consistent estimates of the
parameters of the conditional mean
**. fracreg probit prate mrate c.ltotemp##c.ltotemp c.age##c.age i.sole**

Use fractional logistic regression to obtain consistent estimates of the
parameters of the conditional mean
**. fracreg logit prate mrate c.ltotemp##c.ltotemp c.age##c.age i.sole**

Obtain the odds ratios by specifying the option **or**
**. fracreg logit prate mrate c.ltotemp##c.ltotemp c.age##c.age i.sole,**
**or**

__Stored results__

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

Scalars
**e(N)** number of observations
**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)** **fracreg**
**e(cmdline)** command as typed
**e(estimator)** model for conditional mean; **logit**, **probit**, or
**hetprobit**
**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)** offset
**e(chi2type)** **Wald**; 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(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(mns)** vector of means of the independent variables
**e(Cns)** constraints matrix
**e(ilog)** iteration log (up to 20 iterations)
**e(gradient)** gradient vector
**e(V)** variance-covariance matrix of the estimators
**e(V_modelbased)** model-based variance

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