**[XT] xttobit** -- Random-effects tobit models

__Syntax__

**xttobit** *depvar* [*indepvars*] [*if*] [*in*] [*weight*] [**,** *options*]

*options* Description
-------------------------------------------------------------------------
Model
__nocons__**tant** suppress constant term
**ll(***varname*|*#***)** left-censoring variable or limit
**ul(***varname*|*#***)** right-censoring variable or limit
__off__**set(***varname***)** include *varname* in model with coefficient
constrained to 1
__const__**raints(***constraints***)** apply specified linear constraints
__col__**linear** keep collinear variables

SE
**vce(***vcetype***)** *vcetype* may be **oim**, __boot__**strap**, or __jack__**knife**

Reporting
__l__**evel(***#***)** set confidence level; default is **level(95)**
**tobit** perform likelihood-ratio test comparing
against pooled tobit model
**lrmodel** perform the likelihood-ratio model test
instead of the default Wald test
__nocnsr__**eport** 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

Integration
__intm__**ethod(***intmethod***)** integration method; *intmethod* may be
__mv__**aghermite** (the default) or __gh__**ermite**
__intp__**oints(***#***)** use # quadrature points; default is
**intpoints(12)**

Maximization
*maximize_options* control the maximization process; seldom
used

__coefl__**egend** display legend instead of statistics
-------------------------------------------------------------------------
A panel variable must be specified; use **xtset**.
*indepvars* may contain factor variables; see fvvarlist.
*depvar* and *indepvars* may contain time-series operators; see tsvarlist.
**by**, **fp**, and **statsby** are allowed; see prefix.
**iweight**s are allowed; see weight. Weights must be constant within panel.
**coeflegend** does not appear in the dialog box.
See **[XT] xttobit postestimation** for features available after estimation.

__Menu__

**Statistics > Longitudinal/panel data > Censored outcomes >** **Tobit**
**regression (RE)**

__Description__

**xttobit** fits random-effects tobit models for panel data where the outcome
variable is censored. Censoring limits may be fixed for all observations
or vary across observations. The user can request that a
likelihood-ratio test comparing the panel tobit model with the pooled
tobit model be conducted at estimation time.

__Options__

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

**noconstant**; see **[R] estimation options**.

**ll(***varname*|*#***)** and **ul(***varname*|*#***)** indicate the lower and upper limits for
censoring, respectively. Observations with *depvar* __<__ **ll()** are
left-censored; observations with *depvar* __>__ **ul()** are right-censored;
and remaining observations are not censored.

**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**.

**tobit** specifies that a likelihood-ratio test comparing the random-effects
model with the pooled (tobit) model be included in the output.

**lrmodel**, **nocnsreport**; see **[R] estimation options**.

*display_options*: **noci**, __nopv__**alues**, __noomit__**ted**, **vsquish**, __noempty__**cells**,
__base__**levels**, __allbase__**levels**, __nofvlab__**el**, **fvwrap(***#***)**, **fvwrapon(***style***)**,
**cformat(***%fmt***)**, **pformat(%***fmt***)**, **sformat(%***fmt***)**, and **nolstretch**; see **[R]**
**estimation options**.

+-------------+
----+ Integration +------------------------------------------------------

**intmethod(***intmethod***)**, **intpoints(***#***)**; see **[R] estimation options**.

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

*maximize_options*: __dif__**ficult**, __tech__**nique(***algorithm_spec***)**, __iter__**ate(***#***)**,
[__no__]__lo__**g**, __tr__**ace**, __grad__**ient**, **showstep**, __hess__**ian**, __showtol__**erance**,
__tol__**erance(***#***)**, __ltol__**erance(***#***)**, __nrtol__**erance(***#***)**, __nonrtol__**erance**, and
**from(***init_specs***)**; see **[R] maximize**. These options are seldom used.

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

**coeflegend**; see **[R] estimation options**.

__Technical note__

The random-effects model is calculated using quadrature, which is an
approximation whose accuracy depends partially on the number of
integration points used. We can use the **quadchk** command to see if
changing the number of integration points affects the results. If the
results change, the quadrature approximation is not accurate given the
number of integration points. Try increasing the number of integration
points using the **intpoints()** option and again run **quadchk**. Do not
attempt to interpret the results of estimates when the coefficients
reported by **quadchk** differ substantially. See **[XT] quadchk** for details
and **[XT] xtprobit** for an example.

Because the **xttobit** likelihood function is calculated by Gauss-Hermite
quadrature, on large problems, the computations can be slow. Computation
time is roughly proportional to the number of points used for the
quadrature.

__Examples__

Setup
**. webuse nlswork3**
**. xtset idcode**

Fit random-effects (RE) tobit model
**. xttobit ln_wage union age grade not_smsa south##c.year, ul(1.9)**

Same as above, but increase the number of integration points from 12 to
25
**. xttobit ln_wage union age grade not_smsa south##c.year, ul(1.9)**
**intpoints(25)**

Same as above, but report likelihood-ratio test comparing RE model with
the pooled model
**. xttobit ln_wage union age grade not_smsa south##c.year, ul(1.9)**
**intpoints(25) tobit**

__Stored results__

**xttobit** stores the following in **e()**:

Scalars
**e(N)** number of observations
**e(N_g)** number of groups
**e(N_unc)** number of uncensored observations
**e(N_lc)** number of left-censored observations
**e(N_rc)** number of right-censored observations
**e(N_cd)** number of completely determined 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(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(rho)** rho
**e(sigma_u)** panel-level standard deviation
**e(sigma_e)** standard deviation of epsilon_it
**e(n_quad)** number of quadrature points
**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(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)** **xttobit**
**e(cmdline)** command as typed
**e(depvar)** names of dependent variables
**e(ivar)** variable denoting groups
**e(llopt)** contents of **ll()**
**e(ulopt)** contents of **ul()**
**e(k_aux)** number of auxiliary parameters
**e(wtype)** weight type
**e(wexp)** weight expression
**e(title)** title in estimation output
**e(offset1)** 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(intmethod)** integration method
**e(distrib)** **Gaussian**; 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(marginsok)** predictions allowed by **margins**
**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