**[R] heckpoisson** -- Poisson regression with sample selection

__Syntax__

**heckpoisson** *depvar* *indepvars* [*if*] [*in*] [*weight*]**,** __sel__**ect(**[*depvar_s* **=**]
*indepvars_s* [**,** __nocons__**tant** __off__**set(***varname_os***)**]**)** [*options*]

*options* Description
-------------------------------------------------------------------------
Model
* __sel__**ect()** specify selection equation: dependent and
independent variables; whether to have
constant term and offset variable
__nocons__**tant** suppress constant term
__exp__**osure(***varname_e***)** include ln(*varname_e*) in model with
coefficient constrained to 1
__off__**set(***varname_o***)** include *varname_o* in model with coefficient
constrained to 1
__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*, **opg**, __boot__**strap**, or __jack__**knife**

Reporting
__l__**evel(***#***)** set confidence level; default is **level(95)**
__ir__**r** report incidence-rate ratios
__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

Integration
__intp__**oints(***#***)** set the number of integration (quadrature)
points; default is **intpoints(25)**

Maximization
*maximize_options* control the maximization process; seldom
used

__coefl__**egend** display legend instead of statistics
-------------------------------------------------------------------------
* **select()** is required. The full specification is
__sel__**ect(**[*depvar_s* **=**] *indepvars_s* [**,** __nocons__**tant** __off__**set(***varname_os***)**]**)**.
*indepvars* and *indepvars_s* may contain factor variables; see fvvarlist.
*indepvars* and *indepvars_s* may contain time-series operators; see
tsvarlist.
**bootstrap**, **by**, **jackknife**, **rolling**, **statsby**, and **svy** are allowed; see
prefix.
Weights are not allowed with the **bootstrap** prefix.
**vce()** and weights are not allowed with the **svy** prefix.
**fweight**s, **iweight**s, and **pweight**s are allowed; see weight.
**coeflegend** does not appear in the dialog box.
See **[R] heckpoisson postestimation** for features available after
estimation.

__Menu__

**Statistics > Sample-selection models > Poisson model with sample**
**selection**

__Description__

**heckpoisson** fits a Poisson regression model with endogenous sample
selection. This is sometimes called nonignorability of selection,
missing not at random, or selection bias. Unlike the standard Poisson
model, there is no assumption of equidispersion.

__Options__

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

**select(**[*depvar_s* **=**] *indepvars_s* [**,** **noconstant** **offset(***varname_os***)**]**)**
specifies the variables and options for the selection equation. It
is an integral part of specifying a sample-selection model and is
required.

If *depvar_s* is specified, it should be coded as 0 or 1, with 0
indicating an observation not selected and 1 indicating a selected
observation. If *depvar_s* is not specified, then observations for
which *depvar* is not missing are assumed selected and those for which
*depvar* is missing are assumed not selected.

**noconstant** suppresses the selection constant term (intercept).

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

**noconstant**, **exposure(***varname_e***)**, **offset(***varname_o***)**,
**constraints(***constraints***)**, **collinear**; 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*.

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

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

**irr** reports estimated coefficients transformed to incidence-rate ratios,
that is, e^{beta_i} rather than beta_i. Standard errors and
confidence intervals are similarly transformed. This option affects
how results are displayed, not how they are estimated or stored. **irr**
may be specified at estimation or when replaying previously estimated
results.

**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**.

+-------------+
----+ Integration +------------------------------------------------------

**intpoints(***#***)** specifies the number of integration points to use for
quadrature. The default is **intpoints(25)**, which means that 25
quadrature points are used. The maximum number of allowed integration
points is 128.

The more integration points, the more accurate the approximation to
the log likelihood. However, computation time increases with the
number of quadrature points and is roughly proportional to the number
of points used.

+--------------+
----+ 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 option is available with **heckpoisson** but is not shown in
the dialog box:

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

__Examples__

Setup
**. webuse patent**

Fit a poisson model with endogenous sample selection
**. heckpoisson npatents expenditure i.tech, select(applied =**
**expenditure size i.tech)**

Replay results, but display legend of coefficients rather than the
statistics for the coefficients
**. heckpoisson, coeflegend**

__Stored results__

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

Scalars
**e(N)** number of observations
**e(N_selected)** number of selected observations
**e(N_nonselected)** number of nonselected 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_aux)** number of auxiliary parameters
**e(k_dv)** number of dependent variables
**e(df_m)** model degrees of freedom
**e(ll)** log likelihood
**e(N_clust)** number of clusters
**e(chi2)** chi-squared
**e(chi2_c)** chi-squared for comparison, rho=0 test
**e(n_quad)** number of quadrature points
**e(p)** p-value for model test
**e(p_c)** p-value for comparison 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)** **heckpoisson**
**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(title2)** secondary title in estimation output
**e(clustvar)** name of cluster variable
**e(offset1)** offset for regression equation
**e(offset2)** offset for selection equation
**e(chi2type)** **Wald**; type of model chi-squared test
**e(chi2_ct)** **Wald**; type of comparison 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(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(V)** variance-covariance matrix of the estimators
**e(V_modelbased)** model-based variance

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