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help for gnbstrat                                                (Joseph Hilbe)
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Generalized Negative Binomial with Endogenous Stratification

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


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

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

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


Description

    gnbstrat fits a maximum-likelihood generalized negative binomial with
    endogenous stratification regression model of depvar on indepvars, where
    depvar is a nonnegative count variable > 0.  lnalpha is parameterized by
    the predictors entered within its parentheses.

    gnbstrat 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.

    This program uses ml lf method.


Options

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

    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, gnbstrat 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:  jhilbe@aol.com


Remarks

    gnbstrat is a user authored program. Support is by author. gnbstrat was
    developed by Joseph Hilbe. Roberto Martinez-Espineira, Dept. of
    Economics, St. Francis Xavier Univ, Antigonish, Nova Scotia, Canada,
    provided the likelihood for the non-generalized model as well as the
    remarks found below. Both are working together on research involving this
    model.

    gnbstrat simultaneously accommodates three features of on-site samples
    dealing with count data: overdispersion relative to the Poisson;
    truncation at zero, and endogenous stratification due to oversampling of
    frequent users of the site. Endogenous stratification occurs when the
    likelihood of sampling observations is dependent on a choice made by the
    subject of study which is in itself the dependent variable. For example,
    in recreational demand analysis, if an on-site survey is conducted, one
    is more likely to interview subjects who visit the site more times per
    week and ask how many times they visit, hence the endogeneity. Also
    patients who visit the doctor more frequently are also more likely to be
    sampled if the survey is conducted at the clinic, etc.  Note: if the data
    are equidispersed but still truncated and endogenously stratified this
    model is equivalent to running poisson depvar-1 [varlist].

    The lnalpha option provides an opportunity to parameterize the ancillary
    parameter by user specified predictors. If the parameterization option is
    not used, one should model with the nbstrat command instead.

    gnbstrat requires a nonnegative count response, or any positive real
    number > 0. If the response has a value of zero, the algorithm will
    display an error message.

    gnbstrat has not been available prior to this implementation and no
    literature exits related to research based on the parameterization of
    lnalpha for this model.

Examples

    . gnbstrat los hmo white type2 type3, nolog irr

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

    . bootstrap: gnbstrat los hmo white type2 type3, nolog irr lnalpha(hmo
        white type2 type3)


Also see

    Reference:  Shaw, D. (1988), On-Site Samples' Regression, J Econometrics
             37, 211-223.

    Reference:  Englin, J. and J. Shonkwiler (1995a). Estimating social
             welfare using count data models: An application under conditions
             of endogenous stratification and truncation. Review of Economics
             and Statistics 77, 104-112.


    Online:  help gnbreg