-------------------------------------------------------------------------------
help for hnbreg1                                                 (Joseph Hilbe)
-------------------------------------------------------------------------------

Heterogeneous linear negative binomial regression (NB-1)

        hnbreg1  depvar [varlist] [if exp] [in range] [, lndelta(varlist)
             offset(varname) exposure(varname) cluster(varname) level(#)
             from(asis) irr eform robust nolog maximize_options
             survey_options]


    aweights, fweights, iweights, and pweights are allowed; see help weights.

    hnbreg1 provides access to all maximize options; see help maximize.

    hnbreg1 provides access to all survey options; see help svy.


Description

    hnbreg1 fits a maximum-likelihood linear negative binomial regression
    model (NB-1), with a heterogeneous (Stata: -generalized-)
    parameterization of depvar on indepvars, where depvar is a non-negative
    count variable.

    hnbreg1 acccepts all of the help maximize options, the constraint()
    option, and all survey options and capabilities documented in [SVY];
    including multi-level surveys; poststratification; and BRR, jackknife,
    and linearization VCE estimators.

    The lndelta() option parameterizes the natural log of delta, the linear
    negative binomial heterogeneity or ancillary parameter. When
    parameterized, the displayed value of delta is the exponential of the
    parameterized constant, and has little value for understanding predictor
    contributions to the parameter.

    This program uses ml lf method.


Options

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

    lndelta(varlist) in which ancillary parameter delta is parameterized by
        listed variables.

    offset(varname) specifies a varname in model with coefficient constrained
        to 1.

    exposure(varname) specifies a ln(varname) in model with coefficient
        constrained to 1.

    constraints(constraints) apply specified linear constraints.



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

    cluster(varname)

    robust specifies that the Huber/White/sandwich estimator of variance is
        to be used in place of the traditional calculation.  robust combined
        with cluster() allows observations which are not independent within
        cluster (although they must be independent between clusters).  If you
        specify pweights, robust is implied.

    vce(options) allowed. vce() supports robust, opg, and native.  vce does
        not support options bootstrap or jacknife, However, hnbreg1 supports
        the bootstrap and jacknife commands.


        +-----------+
    ----+ Reporting +--------------------------------------------------------
   
    level(#) specifies the confidence level, in percent, for confidence
        intervals of the coefficients; see help level.

    nolog suppresses the iteration log.

    A likelihood ratio test is provided between hnbreg1 with delta=0 and the
        estimated model.  hnbreg1 with delta=0 is a poisson model.


        +-------------+
    ----+ max options +------------------------------------------------------


    maximize_options: technique(algorithm_spec), [no]log, trace, hessian,
        gradient, showstep, shownrtolerance, difficult, iterate(#),
        tolerance(#), ltolerance(#), gtolerance(#), nrtolerance(#),
        nonrtolerance, from(init_specs); see maximize.


        +-------------+
    ----+ svy options +------------------------------------------------------

    survey_options are all available. See help svy




Author and support

    Joseph Hilbe, Arizona State University:  Hilbe@asu.edu


Remarks

    hnbreg1 is a user authored program. Support is by author.  NOTE: The
    heterogeneous linear negative binomial is similar to Stata's gnbreg
    command, except that it provides for the parameterization of the negative
    binomial heterogeneity parameter when the dispersion is specified as
    constant.

    hnbreg1 requires a nonnegative response.


Examples

    . hnbreg1 los hmo white type2 type3, nolog irr

    . hnbreg1 los hmo white type2 type3, nolog lndelta(hmo white)

    . hnbreg1 los hmo white type2 type3, nolog exposure(pop) cluster(state)

    . bootstrap: hnbreg1 los hmo white type2 type3, nolog lndelta(hmo white)
        eform


Reference

    Hilbe, J. (2007), Negative Binomial Regression, Cambridge, UK: Cambridge
        University Press.

    Hardin, J. & J. Hilbe (2007), Generalized Linear Models and Extensions,
        2nd ed., Stata Press.


Also see

    Online:  help gnbreg nbreg