help xtnbreg dialog: xtnbreg
also see: xtnbreg postestimation
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Title
[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
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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
noskip perform likelihood-ratio test
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.
PA_options description
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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-group 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 spacing and display of omitted
variables and base and empty cells
Optimization
optimize_options control the optimization process; seldom
used
+ coeflegend display coefficients' legend instead of
coefficient table
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+ coeflegend does not appear in the dialog box.
correlation description
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exchangeable exchangeable
independent independent
unstructured unstructured
fixed matname user-specified
ar # autoregressive of order #
stationary # stationary of order #
nonstationary # nonstationary of order #
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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 and statsby are allowed; see prefix.
iweights, fweights, and pweights are allowed for the population-averaged
model, and iweights are allowed in the random-effects and fixed-effects
models; see weight. Weights must be constant within panel.
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 overdispersion models, conditional
fixed-effects overdispersion models, and population-averaged negative
binomial models. Here "random effects" and "fixed effects" apply to the
distribution of the dispersion parameter, not to the xb term in the
model. In the random-effects and fixed-effects overdispersion models,
the dispersion is the same for all elements in the same group (i.e.,
elements with the same value of the panel variable). In the
random-effects model, the dispersion varies randomly from group to group,
such that the inverse of one plus the dispersion follows a b[r,s]
distribution. In the fixed-effects model, the dispersion parameter in a
group can take on any value, because a conditional likelihood is used in
which the dispersion parameter drops out of the estimation.
By default, the population-averaged model is an equal-correlation model;
xtnbreg assumes corr(exchangeable). See [XT] xtgee for details on
fitting other population-averaged models.
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 and that use
bootstrap or jackknife methods; 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.
noskip; see [R] estimation options.
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.
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), force; 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, and that use bootstrap or
jackknife methods; 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 b. For the
negative binomial model, exponentiated coefficients have the
interpretation of incidence-rate ratios.
display_options: noomitted, vsquish, noemptycells, baselevels,
allbaselevels; 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 value of iterate() is 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 should 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)
Saved results
xtnbreg, re saves 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
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(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) 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) xtnbreg
e(cmd2) xtn_re
e(cmdline) command as typed
e(depvar) name of dependent variable
e(ivar) variable denoting groups
e(wtype) weight type
e(wexp) weight expression
e(title) title in estimation output
e(offset) offset
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(vcetype) title used to label Std. Err.
e(method) estimation method
e(distrib) Beta; the distribution of the random effect
e(diparm#) display transformed parameter #
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
e(gradient) gradient vector
e(V) variance-covariance matrix of the estimators
Functions
e(sample) marks estimation sample
xtnbreg, fe saves 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
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(chi2) chi-squared
e(g_min) smallest group size
e(g_avg) average group size
e(g_max) largest group size
e(p) significance
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(cmd2) xtn_fe
e(cmdline) command as typed
e(depvar) name of dependent variable
e(ivar) variable denoting groups
e(wtype) weight type
e(wexp) weight expression
e(title) title in estimation output
e(offset) offset
e(chi2type) LR; type of model chi-squared test
e(vce) vcetype specified in vce()
e(vcetype) title used to label Std. Err.
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(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
e(gradient) gradient vector
e(V) variance-covariance matrix of the estimators
Functions
e(sample) marks estimation sample
xtnbreg, pa saves 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(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(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) offset
e(chi2type) Wald; type of model chi-squared test
e(vce) vcetype specified in vce()
e(vcetype) title used to label Std. Err.
e(robust_prolog) program to prepare estimates for linearized VCE
computations
e(robust_epilog) program to finalize estimates after linearized VCE
computations
e(nbalpha) alpha
e(crittype) optimization criterion
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
Also see
Manual: [XT] xtnbreg
Help: [XT] xtnbreg postestimation;
[XT] xtgee, [XT] xtpoisson, [R] nbreg
