**[R] zinb** -- Zero-inflated negative binomial regression

__Syntax__

**zinb** *depvar* [*indepvars*] [*if*] [*in*] [*weight*]**,** __inf__**late(***varlist*[**,** __off__**set(**
*varname***)**]|**_cons)** [*options*]

*options* Description
-------------------------------------------------------------------------
Model
* __inf__**late()** equation that determines whether the count
is zero
__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
**probit** use probit model to characterize excess
zeros; default is logit

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)**.
**irr** report incidence-rate ratios
**zip** perform ZIP likelihood-ratio test
__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

__coefl__**egend** display legend instead of statistics
-------------------------------------------------------------------------
* __inf__**late(***varlist*[**,** __off__**set(***varname***)**]|**_cons)** is required.
*indepvars* and *varlist* may contain factor variables; see fvvarlist.
**bayes**, **bootstrap**, **by**, **fp**, **jackknife**, **rolling**, **statsby**, and **svy** are
allowed; see prefix. For more details, see **[BAYES] bayes: zinb**.
Weights are not allowed with the **bootstrap** prefix.
**vce()**, **zip**, 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] zinb postestimation** for features available after estimation.

__Menu__

**Statistics > Count outcomes > Zero-inflated negative binomial regression**

__Description__

**zinb** fits a zero-inflated negative binomial (ZINB) model to overdispersed
count data with excess zero counts. The ZINB model assumes that the
excess zero counts come from a logit or probit model and the remaining
counts come from a negative binomial model.

__Options__

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

**inflate(***varlist*[**,** **offset(***varname***)**]|**_cons)** specifies the equation that
determines whether the observed count is zero. Conceptually,
omitting **inflate()** would be equivalent to fitting the model with
**nbreg**.

**inflate(***varlist*[**, offset(***varname***)**]**)** specifies the variables in the
equation. You may optionally include an offset for this *varlist*.

**inflate(_cons)** specifies that the equation determining whether the
count is zero contains only an intercept. To run a zero-inflated
model of *depvar* with only an intercept in both equations, type
**zinb** *depvar***,** **inflate(_cons)**.

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

**probit** requests that a probit, instead of logit, model be used to
characterize the excess zeros in the data.

+-----------+
----+ 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.
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.

**zip** requests that a likelihood-ratio test comparing the ZINB model with
the zero-inflated Poisson model be included in the output.

**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.

Setting the optimization type to **technique(bhhh)** resets the default
*vcetype* to **vce(opg)**.

The following option is available with **zinb** but is not shown in the
dialog box:

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

__Examples__

Setup
**. webuse fish**

Fit zero-inflated negative binomial regression model
**. zinb count persons livebait, inflate(child camper)**

Replay results, displaying coefficients, standard errors, and CIs to 4
decimal places
**. zinb, cformat(%8.4f)**

__Stored results__

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

Scalars
**e(N)** number of observations
**e(N_zero)** number of zero 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(ll_0)** log likelihood, constant-only model
**e(df_c)** degrees of freedom for comparison test
**e(N_clust)** number of clusters
**e(chi2)** chi-squared
**e(p)** p-value for model test
**e(chi2_cp)** chi-squared for test of alpha = 0
**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)** **zinb**
**e(cmdline)** command as typed
**e(depvar)** name of dependent variable
**e(inflate)** **logit** or **probit**
**e(wtype)** weight type
**e(wexp)** weight expression
**e(title)** title in estimation output
**e(clustvar)** name of cluster variable
**e(offset1)** offset
**e(offset2)** offset for **inflate()**
**e(chi2type)** **Wald** or **LR**; type of model chi-squared test
**e(chi2_cpt)** **Wald** or **LR**; type of model chi-squared test
corresponding to **e(chi2_cp)**
**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(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