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help for hcnbreg                                                 (Joseph Hilbe)
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Heterogeneous canonical negative binomial regression

        hcnbreg  depvar [varlist] [if exp] [in range] [, lnalpha(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.

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

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


Description

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

    hcnbreg 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 lnalpha() option parameterizes the natural log of alpha, the negative
    binomial heterogeniety or ancillary parameter. When parameterized, the
    displayed value of alpha 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 +------------------------------------------------------------

    lnalpha(varlist) in which ancillary parameter alpha 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, cnbreg does
        support the bootstrap and jacknife commands, so these modeling
        capabilities are allowed.


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

    nolog suppresses the iteration log.


        +-------------+
    ----+ 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

    hcnbreg is a user authored program. Support is by author.  NOTE: The
    canonical parameterization of the negative binomial derives directly from
    the exponential family form negative binomial probability function; not a
    Poisson-gamma mixture model.  Unlike NB-1 and NB-2, the heterogeniety or
    ancillary parameter is a term of the mean and variance functions.


    hcnbreg requires a nonnegative response.


Examples

    . hcnbreg los hmo white type2 type3, nolog irr

    . hcnbreg los hmo white type2 type3, nolog lnalpha(hmo white)

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

    . bootstrap: hcnbreg los hmo white type2 type3, nolog lnalpha(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