help nbreg, help gnbreg dialogs: nbreg gnbreg
svy: nbreg svy: gnbreg
also see: nbreg postestimation
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Title
[R] nbreg -- Negative binomial regression
Syntax
Negative binomial regression model
nbreg depvar [indepvars] [if] [in] [weight] [, nbreg_options]
Generalized negative binomial model
gnbreg depvar [indepvars] [if] [in] [weight] [, gnbreg_options]
nbreg_options description
-------------------------------------------------------------------------
Model
noconstant suppress constant term
dispersion(mean) parameterization of dispersion; the default
dispersion(constant) constant dispersion for all observations
exposure(varname_e) include ln(varname_e) in model with
coefficient constrained to 1
offset(varname_o) include varname_o in model with coefficient
constrained to 1
constraints(constraints) apply specified linear constraints
collinear keep collinear variables
SE/Robust
vce(vcetype) vcetype may be oim, robust, cluster
clustvar, opg, bootstrap, or jackknife
Reporting
level(#) set confidence level; default is level(95)
nolrtest suppress likelihood-ratio test
irr report incidence-rate ratios
nocnsreport do not display constraints
display_options control spacing and display of omitted
variables and base and empty cells
Maximization
maximize_options control the maximization process; seldom
used
+ coeflegend display coefficients' legend instead of
coefficient table
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gnbreg_options description
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Model
noconstant suppress constant term
lnalpha(varlist) dispersion model variables
exposure(varname_e) include ln(varname_e) in model with
coefficient constrained to 1
offset(varname_o) include varname_o in model with coefficient
constrained to 1
constraints(constraints) apply specified linear constraints
collinear keep collinear variables
SE/Robust
vce(vcetype) vcetype may be oim, robust, cluster
clustvar, opg, bootstrap, or jackknife
Reporting
level(#) set confidence level; default is level(95)
irr report incidence-rate ratios
nocnsreport do not display constraints
display_options control spacing and display of omitted
variables and base and empty cells
Maximization
maximize_options control the maximization process; seldom
used
+ coeflegend display coefficients' legend instead of
coefficient table
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+ coeflegend does not appear in the dialog box.
indepvars may contain factor variables; see fvvarlist.
depvar, indepvars, varname_e, and varname_o may contain time-series
operators (nbreg only); see tsvarlist.
bootstrap, by (nbreg only), fracpoly (nbreg only), jackknife, mfp (nbreg
only), mi estimate, nestreg (nbreg only), rolling, statsby, stepwise,
and svy are allowed; see prefix.
vce(bootstrap) and vce(jackknife) are not allowed with the mi estimate
prefix.
Weights are not allowed with the bootstrap prefix.
vce() and weights are not allowed with the svy prefix.
fweights, iweights, and pweights are allowed; see weight.
See [R] nbreg postestimation for features available after estimation.
Menu
nbreg
Statistics > Count outcomes > Negative binomial regression
gnbreg
Statistics > Count outcomes > Generalized negative binomial
regression
Description
nbreg fits a negative binomial regression model of depvar on indepvars,
where depvar is a nonnegative count variable. In this model, the count
variable is believed to be generated by a Poisson-like process, except
that the variation is greater than that of a true Poisson. This extra
variation is referred to as overdispersion. See [R] poisson.
gnbreg fits a generalization of the negative binomial mean-dispersion
model; the shape parameter alpha may also be parameterized.
If you have panel data, see [XT] xtnbreg.
Options for nbreg
+-------+
----+ Model +------------------------------------------------------------
noconstant; see [R] estimation options.
dispersion(mean|constant) specifies the parameterization of the model.
dispersion(mean), the default, yields a model with dispersion equal
to 1 + alpha*exp(xb + offset); that is, the dispersion is a function
of the expected mean: exp(xb + offset). dispersion(constant) has
dispersion equal to 1 + delta; that is, it is a constant for all
observations.
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, that are
robust to some kinds of misspecification, that allow for intragroup
correlation, and that use bootstrap or jackknife methods; see [R]
vce_option.
+-----------+
----+ Reporting +--------------------------------------------------------
level(#); see [R] estimation options.
nolrtest suppresses fitting the Poisson model. Without this option, a
comparison Poisson model is fit, and the likelihood is used in a
likelihood-ratio test of the null hypothesis that the dispersion
parameter is zero.
irr reports estimated coefficients transformed to incidence-rate ratios,
that is, exp(b) rather than b. 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: noomitted, vsquish, noemptycells, baselevels
allbaselevels; see [R] estimation options.
+--------------+
----+ Maximization +-----------------------------------------------------
maximize_options: difficult, technique(algorithm_spec), iterate(#),
[no]log, trace, gradient, showstep, hessian, showtolerance,
tolerance(#), ltolerance(#), nrtolerance(#), nonrtolerance,
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 nbreg but is not shown in the
dialog box:
coeflegend; see [R] estimation options.
Options for gnbreg
+--------+
----+ Model +-----------------------------------------------------------
noconstant; see [R] estimation options.
lnalpha(varlist) allows you to specify a linear equation for ln(alpha).
Specifying lnalpha(male old) means that ln(alpha)=a_0 + a_1male +
a_2old, where a_0, a_1, and a_2 are parameters to be estimated along
with the other model coefficients. If this option is not specified,
gnbreg and nbreg will produce the same results because the shape
parameter will be parameterized as a constant.
exposure(varname_e), offset(varname_o), constraints(constraints), and
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, that are
robust to some kinds of misspecification, that allow for intragroup
correlation, and that use bootstrap or jackknife methods; 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.
nocnsreport; see [R] estimation options.
display_options: noomitted, vsquish, noemptycells, baselevels,
allbaselevels; see [R] estimation options.
+--------------+
----+ Maximization +-----------------------------------------------------
maximize_options: difficult, technique(algorithm_spec), iterate(#),
[no]log, trace, gradient, showstep, hessian, showtolerance,
tolerance(#), ltolerance(#), nrtolerance(#), nonrtolerance,
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 gnbreg but is not shown in the
dialog box:
coeflegend; see [R] estimation options.
Remarks
nbreg will fit two different parameterizations of the negative binomial
model. The default, also given by the dispersion(mean) option, has
dispersion for the ith observation equal to 1 + alpha*exp(x_jb +
offset_j); i.e., the dispersion is a function of the expected mean of the
counts for the jth observation. The alternative parameterization, given
by the dispersion(constant) option, has dispersion equal to 1 + delta;
i.e., it is a constant for all observations.
For the default model, alpha = 0 (or ln(alpha) = -infinity) corresponds
to dispersion = 1, and, thus, it is simply a Poisson model. Likewise,
for the alternative parameterization, delta = 0 (or ln(delta) =
-infinity) corresponds to dispersion = 1, and it is simply a Poisson
model.
Users may want to fit both parameterizations and choose the one with the
larger (least negative) log likelihood. Both parameterizations will
yield similar results, and the parameterizations will usually not
significantly differ from each other. Hence, the choice of
parameterization is usually not important.
See [XT] xtpoisson and [XT] xtnbreg for closely related panel estimators.
Examples
Setup
. webuse rod93
. generate logexp=ln(exposure)
Fit a negative binomial regression model
. nbreg deaths i.cohort, exposure(exp)
Same as above command
. nbreg deaths i.cohort, offset(logexp)
Same as above command, but change dispersion from mean to constant
. nbreg deaths i.cohort, offset(logexp) dispersion(constant)
Fit a generalized negative binomial model
. gnbreg deaths age_mos, lnalpha(i.cohort) offset(logexp)
Saved results
nbreg and gnbreg save the following in e():
Scalars
e(N) number of observations
e(k) number of parameters
e(k_aux) number of auxiliary parameters
e(k_eq) number of equations
e(k_eq_model) number of equations in model Wald test
e(k_dv) number of dependent variables
e(k_autoCns) number of base, empty, and omitted constraints
e(df_m) model degrees of freedom
e(r2_p) pseudo-R-squared
e(ll) log likelihood
e(ll_0) log likelihood, constant-only model
e(ll_c) log likelihood, comparison model
e(alpha) value of alpha
e(delta) value of delta
e(N_clust) number of clusters
e(chi2) chi-squared
e(chi2_c) chi-squared for comparison test
e(p) significance
e(rank) rank of e(V)
e(rank0) rank of e(V) for constant-only model
e(ic) number of iterations
e(rc) return code
e(converged) 1 if converged, 0 otherwise
Macros
e(cmd) nbreg or gnbreg
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(clustvar) name of cluster variable
e(offset) offset (nbreg)
e(offset1) offset (gnbreg)
e(chi2type) Wald or LR; type of model chi-squared test
e(chi2_ct) Wald or LR; type of model chi-squared test
corresponding to e(chi2_c)
e(dispers) mean or constant
e(vce) vcetype specified in vce()
e(vcetype) title used to label Std. Err.
e(diparm#) display transformed parameter #
e(diparm_opt2) options for displaying transformed parameters
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(singularHmethod) m-marquardt or hybrid; method used when Hessian is
singular
e(crittype) optimization criterion
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
e(ml_h) derivative tolerance, (abs(b)+1e-3)*1e-3 (gnbreg
only)
e(ml_scale) derivative scale factor (gnbreg only)
Functions
e(sample) marks estimation sample
Also see
Manual: [R] nbreg
Help: [R] nbreg postestimation;
[R] glm, [R] poisson, [SVY] svy estimation, [XT] xtnbreg, [R]
zinb, [R] ztnb
