Stata 15 help for xtnbreg

[XT] xtnbreg -- Fixed-effects, random-effects, & population-averaged negative binomial models

Syntax

Random-effects (RE) and conditional fixed-effects (FE) overdispersion models

xtnbreg depvar [indepvars] [if] [in] [weight] [, [re|fe] RE/FE_options]

Population-averaged (PA) model

xtnbreg depvar [indepvars] [if] [in] [weight], pa [PA_options]

RE/FE_options Description ------------------------------------------------------------------------- Model noconstant suppress constant term; not available with fe re use random-effects estimator; the default fe use fixed-effects estimator exposure(varname) include ln(varname) in model with coefficient constrained to 1 offset(varname) include varname in model with coefficient constrained to 1 constraints(constraints) apply specified linear constraints collinear keep collinear variables

SE vce(vcetype) vcetype may be oim, bootstrap, or jackknife

Reporting level(#) set confidence level; default is level(95) irr report incidence-rate ratios lrmodel perform the likelihood-ratio model test instead of the default Wald test 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 -------------------------------------------------------------------------

PA_options Description ------------------------------------------------------------------------- Model noconstant suppress constant term pa use population-averaged estimator exposure(varname) include ln(varname) in model with coefficient constrained to 1 offset(varname) include varname in model with coefficient constrained to 1

Correlation corr(correlation) within-panel correlation structure force estimate even if observations unequally spaced in time

SE/Robust vce(vcetype) vcetype may be conventional, robust, bootstrap, or jackknife nmp use divisor N-P instead of the default N scale(parm) override the default scale parameter; parm may be x2, dev, phi, or #

Reporting level(#) set confidence level; default is level(95) irr report incidence-rate ratios display_options control columns and column formats, row spacing, line width, display of omitted variables and base and empty cells, and factor-variable labeling

Optimization optimize_options control the optimization process; seldom used

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

correlation Description ------------------------------------------------------------------------- exchangeable exchangeable independent independent unstructured unstructured fixed matname user-specified ar # autoregressive of order # stationary # stationary of order # nonstationary # nonstationary of order # -------------------------------------------------------------------------

A panel variable must be specified. For xtnbreg, pa, correlation structures other than exchangeable and independent require that a time variable also be specified. Use xtset. indepvars may contain factor variables; see fvvarlist. depvar and indepvars may contain time-series operators; see tsvarlist. by, mi estimate, and statsby are allowed; see prefix. fp is allowed for the random-effects and fixed-effects models. vce(bootstrap) and vce(jackknife) are not allowed with the mi estimate prefix. iweights, fweights, and pweights are allowed for the population-averaged model, and iweights are allowed for the random-effects and fixed-effects models; see weight. Weights must be constant within panel. coeflegend does not appear in the dialog box. See [XT] xtnbreg postestimation for features available after estimation.

Menu

Statistics > Longitudinal/panel data > Count outcomes > Negative binomial regression (FE, RE, PA)

Description

xtnbreg fits random-effects and conditional fixed-effects overdispersion models where the random effects or fixed effects apply to the distribution of the dispersion parameter. The dispersion is the same for all observations in the same panel. In the random-effects model, the dispersion varies randomly from group to group, such that the inverse of one plus the dispersion follows a Beta distribution. In the fixed-effects model, the dispersion parameter in a group can take on any value.

xtnbreg also fits a population-averaged negative binomial model for a nonnegative count dependent variable with overdispersion.

Options for RE/FE models

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

noconstant; see [R] estimation options.

re requests the random-effects estimator, which is the default.

fe requests the conditional fixed-effects estimator.

exposure(varname), offset(varname), constraints(constraints), collinear; see [R] estimation options.

+----+ ----+ SE +---------------------------------------------------------------

vce(vcetype) specifies the type of standard error reported, which includes types that are derived from asymptotic theory (oim) and that use bootstrap or jackknife methods (bootstrap, jackknife); see [XT] vce_options.

+-----------+ ----+ Reporting +--------------------------------------------------------

level(#); see [R] estimation options.

irr reports exponentiated coefficients e^b rather than b. For the negative binomial model, exponentiated coefficients have the interpretation of incidence-rate ratios.

lrmodel, 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.

The following option is available with xtnbreg but is not shown in the dialog box:

coeflegend; see [R] estimation options.

Options for PA model

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

noconstant; see [R] estimation options.

pa requests the population-averaged estimator.

exposure(varname), offset(varname); see [R] estimation options.

+-------------+ ----+ Correlation +------------------------------------------------------

corr(correlation) specifies the within-panel correlation structure; the default corresponds to the equal-correlation model, corr(exchangeable).

When you specify a correlation structure that requires a lag, you indicate the lag after the structure's name with or without a blank; for example, corr(ar 1) or corr(ar1).

If you specify the fixed correlation structure, you specify the name of the matrix containing the assumed correlations following the word fixed, for example, corr(fixed myr).

force specifies that estimation be forced even though the time variable is not equally spaced. This is relevant only for correlation structures that require knowledge of the time variable. These correlation structures require that observations be equally spaced so that calculations based on lags correspond to a constant time change. If you specify a time variable indicating that observations are not equally spaced, the (time dependent) model will not be fit. If you also specify force, the model will be fit, and it will be assumed that the lags based on the data ordered by the time variable are appropriate.

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

vce(vcetype) specifies the type of standard error reported, which includes types that are derived from asymptotic theory (conventional), that are robust to some kinds of misspecification (robust), and that use bootstrap or jackknife methods (bootstrap, jackknife); see [XT] vce_options.

vce(conventional), the default, uses the conventionally derived variance estimator for generalized least-squares regression.

nmp, scale(x2|dev|phi|#); see [XT] vce_options.

+-----------+ ----+ Reporting +--------------------------------------------------------

level(#); see [R] estimation options.

irr reports exponentiated coefficients e^b rather than coefficients b. For the negative binomial model, exponentiated coefficients have the interpretation of incidence-rate ratios.

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.

+--------------+ ----+ Optimization +-----------------------------------------------------

optimize_options control the iterative optimization process. These options are seldom used.

iterate(#) specifies the maximum number of iterations. When the number of iterations equals #, the optimization stops and presents the current results, even if the convergence tolerance has not been reached. The default is iterate(100).

tolerance(#) specifies the tolerance for the coefficient vector. When the relative change in the coefficient vector from one iteration to the next is less than or equal to #, the optimization process is stopped. tolerance(1e-6) is the default.

nolog suppress the display of the iteration log.

trace specifies that the current estimates be printed at each iteration.

The following option is available with xtnbreg but is not shown in the dialog box:

coeflegend; see [R] estimation options.

Examples

Setup . webuse airacc

Random-effects model . xtnbreg i_cnt inprog, exposure(pmiles) irr

Fixed-effects model . xtnbreg i_cnt inprog, exposure(pmiles) irr fe

Equal-correlation population-averaged model with robust variance . xtnbreg i_cnt inprog, exposure(pmiles) eform pa vce(robust)

Stored results

xtnbreg, re stores the following in e():

Scalars e(N) number of observations e(N_g) number of groups 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(ll) log likelihood e(ll_0) log likelihood, constant-only model e(ll_c) log likelihood, comparison model e(chi2) chi-squared e(chi2_c) chi-squared for comparison test e(g_min) smallest group size e(g_avg) average group size e(g_max) largest group size e(r) value of r in Beta(r,s) e(s) value of s in Beta(r,s) 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) xtnbreg e(cmdline) command as typed e(depvar) name of dependent variable e(ivar) variable denoting groups e(model) re e(wtype) weight type e(wexp) weight expression e(title) title in estimation output 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(vce) vcetype specified in vce() e(method) estimation method e(distrib) Beta; the distribution of the random effect 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 e(gradient) gradient vector e(V) variance-covariance matrix of the estimators

Functions e(sample) marks estimation sample

xtnbreg, fe stores the following in e():

Scalars e(N) number of observations e(N_g) number of groups 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(ll) log likelihood e(ll_0) log likelihood, constant-only model e(chi2) chi-squared e(g_min) smallest group size e(g_avg) average group size e(g_max) largest group size e(p) p-value for model test e(rank) rank of e(V) e(ic) number of iterations e(rc) return code e(converged) 1 if converged, 0 otherwise

Macros e(cmd) xtnbreg e(cmdline) command as typed e(depvar) name of dependent variable e(ivar) variable denoting groups e(model) fe e(wtype) weight type e(wexp) weight expression e(title) title in estimation output e(offset) linear offset variable e(chi2type) LR; type of model chi-squared test e(vce) vcetype specified in vce() e(method) requested estimation method 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 e(gradient) gradient vector e(V) variance-covariance matrix of the estimators

Functions e(sample) marks estimation sample

xtnbreg, pa stores the following in e():

Scalars e(N) number of observations e(N_g) number of groups e(df_m) model degrees of freedom e(chi2) chi-squared e(p) p-value for model test e(df_pear) degrees of freedom for Pearson chi-squared e(chi2_dev) chi-squared test of deviance e(chi2_dis) chi-squared test of deviance dispersion e(deviance) deviance e(dispers) deviance dispersion e(phi) scale parameter e(g_min) smallest group size e(g_avg) average group size e(g_max) largest group size e(rank) rank of e(V) e(tol) target tolerance e(dif) achieved tolerance e(rc) return code

Macros e(cmd) xtgee e(cmd2) xtnbreg e(cmdline) command as typed e(depvar) name of dependent variable e(ivar) variable denoting groups e(tvar) variable denoting time within groups e(model) pa e(family) negative binomial(k=1) e(link) log; link function e(corr) correlation structure e(scale) x2, dev, phi, or #; scale parameter e(wtype) weight type e(wexp) weight expression e(offset) linear offset variable e(chi2type) Wald; type of model chi-squared test e(vce) vcetype specified in vce() e(vcetype) title used to label Std. Err. e(nmp) nmp, if specified e(nbalpha) alpha e(properties) b V e(predict) program used to implement predict e(marginsnotok) predictions disallowed by margins e(asbalanced) factor variables fvset as asbalanced e(asobserved) factor variables fvset as asobserved

Matrices e(b) coefficient vector e(R) estimated working correlation matrix e(V) variance-covariance matrix of the estimators e(V_modelbased) model-based variance

Functions e(sample) marks estimation sample


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