Stata 15 help for nbreg

[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 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

coeflegend display legend instead of statistics -------------------------------------------------------------------------

gnbreg_options Description ------------------------------------------------------------------------- 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 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

coeflegend display legend instead of statistics -------------------------------------------------------------------------

indepvars and varlist may contain factor variables; see fvvarlist. depvar, indepvars, varname_e, and varname_o may contain time-series operators (nbreg only); see tsvarlist. bayes, bootstrap, by (nbreg only), fmm (nbreg only), fp (nbreg only), jackknife, mfp (nbreg only), mi estimate, nestreg (nbreg only), rolling, statsby, stepwise, and svy are allowed; see prefix. For more details, see [BAYES] bayes: gnbreg, [BAYES] bayes: nbreg, and [FMM] fmm: nbreg. 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. coeflegend does not appear in the dialog box. 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 for a nonnegative count dependent variable. In this model, the count variable is believed to be generated by a Poisson-like process, except that the variation is allowed to be greater than that of a true Poisson. This extra variation is referred to as overdispersion.

gnbreg fits a generalization of the negative binomial mean-dispersion model; the shape parameter alpha may also be parameterized.

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 (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.

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: noci, nopvalues, noomitted, vsquish, noemptycells, baselevels, allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt), pformat(%fmt), sformat(%fmt), and nolstretch; see [R] estimation options.

+--------------+ ----+ Maximization +-----------------------------------------------------

maximize_options: difficult, technique(algorithm_spec), iterate(#), [no]log, trace, gradient, showstep, hessian, showtolerance, tolerance(#), ltolerance(#), nrtolerance(#), nonrtolerance, 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 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 (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.

nocnsreport; see [R] estimation options.

display_options: noci, nopvalues, noomitted, vsquish, noemptycells, baselevels, allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt), pformat(%fmt), sformat(%fmt), and nolstretch; 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, given by the dispersion(mean) option, has dispersion for the ith observation equal to 1 + alpha*exp(x_jb + offset_j); that is, 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; that is, 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)

Stored results

nbreg stores 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 in e(b) e(k_eq_model) number of equations in overall model test e(k_dv) number of dependent variables 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) p-value for model test 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 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) linear offset variable 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(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

gnbreg stores the following in e():

Scalars e(N) number of 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_dv) number of dependent variables 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(N_clust) number of clusters e(chi2) chi-squared e(p) p-value for model test 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) 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(offset1) linear offset variable e(chi2type) Wald or LR; type of model chi-squared test 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


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