**xtmixed** has been renamed to **mixed**. **xtmixed** continues to work but, as of
Stata 13, is no longer an official part of Stata. This is the original
help file, which we will no longer update, so some links may no longer
work.

-------------------------------------------------------------------------------

__Title__

**[XT] xtmixed** -- Multilevel mixed-effects linear regression

__Syntax__

**xtmixed** *depvar* [*fe_equation*] [**||** *re_equation*] [**||** *re_equation* ...] [**,**
*options*]

where the syntax of *fe_equation* is

[*indepvars*] [*if*] [*in*] [*weight*] [**,** *fe_options*]

and the syntax of *re_equation* is one of the following:

for random coefficients and intercepts

*levelvar***:** [*varlist*] [**,** *re_options*]

for a random effect among the values of a factor variable

*levelvar***:** **R.***varname* [**,** *re_options*]

*levelvar* is a variable identifying the group structure for the random
effects at that level or **_all** representing one group comprising all
observations.

*fe_options* Description
-------------------------------------------------------------------------
Model
__noc__**onstant** suppress constant term from the fixed-effects
equation
-------------------------------------------------------------------------

*re_options* Description
-------------------------------------------------------------------------
Model
__cov__**ariance(***vartype***)** variance-covariance structure of the random
effects
__noc__**onstant** suppress constant term from the random-effects
equation
__col__**linear** keep collinear variables
__fw__**eight(***exp***)** frequency weights at higher levels
__pw__**eight(***exp***)** sampling weights at higher levels
-------------------------------------------------------------------------

*vartype* Description
-------------------------------------------------------------------------
__ind__**ependent** one variance parameter per random effect, all
covariances zero; the default unless a factor
variable is specified
__ex__**changeable** equal variances for random effects, and one
common pairwise covariance
__id__**entity** equal variances for random effects, all
covariances zero; the default for factor
variables
__un__**structured** all variances and covariances distinctly
estimated
-------------------------------------------------------------------------

*options* Description
-------------------------------------------------------------------------
Model
__ml__**e** fit model via maximum likelihood, the default
**reml** fit model via restricted maximum likelihood
**pwscale(***scale_method***)** control scaling of sampling weights in two-level
models
__res__**iduals(***rspec***)** structure of residual errors

SE/Robust
**vce(***vcetype***)** *vcetype* may be **oim**, __r__**obust**, or __cl__**uster** *clustvar*

Reporting
__l__**evel(***#***)** set confidence level; default is **level(95)**
__var__**iance** show random-effects parameter estimates as
variances and covariances
__noret__**able** suppress random-effects table
__nofet__**able** suppress fixed-effects table
__estm__**etric** show parameter estimates in the estimation
metric
__nohead__**er** suppress output header
__nogr__**oup** suppress table summarizing groups
__nostd__**err** do not estimate standard errors of
random-effects parameters
__nolr__**test** do not perform LR test comparing to linear
regression
*display_options* control column formats, row spacing, and display
of omitted variables and base and empty cells

EM options
__emiter__**ate(***#***)** number of EM iterations, default is 20
__emtol__**erance(***#***)** EM convergence tolerance, default is 1e-10
**emonly** fit model exclusively using EM
**emlog** show EM iteration log
__emdot__**s** show EM iterations as dots

Maximization
*maximize_options* control the maximization process; seldom used
**matsqrt** parameterize variance components using matrix
square roots; the default
**matlog** parameterize variance components using matrix
logarithms

__coefl__**egend** display legend instead of statistics
-------------------------------------------------------------------------

*indepvars* may contain factor variables; see fvvarlist.
*depvar*, *indepvars*, and *varlist* may contain time-series operators; see
tsvarlist.
**bootstrap**, **by**, **jackknife**, **mi estimate**, **rolling**, and **statsby** are allowed;
see prefix.
**pweight**s and **fweight**s are allowed; see weight.
**coeflegend** does not appear in the dialog box.
See **[XT] xtmixed postestimation** for features available after estimation.

__Menu__

**Statistics > Longitudinal/panel data > Multilevel mixed-effects models >**
**Mixed-effects linear regression**

__Description__

**xtmixed** fits linear mixed models. Mixed models are characterized as
containing both fixed effects and random effects. The fixed effects are
analogous to standard regression coefficients and are estimated directly.
The random effects are not directly estimated but are summarized
according to their estimated variances and covariances. Although random
effects are not directly estimated, you can form best linear unbiased
predictions (BLUPs) of them (and standard errors) by using **predict** after
**xtmixed**; see **[XT] xtmixed postestimation**. Random effects may take the
form of either random intercepts or random coefficients, and the grouping
structure of the data may consist of multiple levels of nested groups.
As such, mixed models are also known in the literature as *multilevel*
*models* and *hierarchical linear models*. The overall error distribution of
the linear mixed model is assumed to be Gaussian, and heteroskedasticity
and correlations within lowest-level groups also may be modeled.

__Options__

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

**noconstant** suppresses the constant (intercept) term and may be specified
for the fixed effects equation and for any or all the random-effects
equations.

**covariance(***vartype***)**, where *vartype* is

**independent**|**exchangeable**|**identity**|**unstructured**

specifies the structure of the covariance matrix for the random
effects and may be specified for each random-effects equation. An
**independent** covariance structure allows a distinct variance for each
random effect within a random-effects equation and assumes that all
covariances are zero. **exchangeable** covariances have common variances
and one common pairwise covariance. **identity** is short for "multiple
of the identity"; that is, all variances are equal and all
covariances are zero. **unstructured** allows for all variances and
covariances to be distinct. If an equation consists of *p*
random-effects terms, the **unstructured** covariance matrix will have
*p*(*p*+1)/2 unique parameters.

**covariance(independent)** is the default, except when the
random-effects equation consists of the factor-variable specification
**R.***varname*, in which case **covariance(identity)** is the default, and
only **covariance(identity)** and **covariance(exchangeable)** are allowed.

**collinear** specifies that **xtmixed** not omit collinear variables from the
random-effects equation. Usually there is no reason to leave
collinear variables in place, and in fact doing so usually causes the
estimation to fail because of the matrix singularity caused by the
collinearity. However, with certain models (for example, a
random-effects model with a full set of contrasts), the variables may
be collinear, yet the model is fully identified because of
restrictions on the random-effects covariance structure. In such
cases, using the **collinear** option allows the estimation to take place
with the random-effects equation intact.

**fweight(***exp***)** specifies frequency weights at higher levels in a multilevel
model, whereas frequency weights at the first level (the observation
level) are specified in the usual manner, for example, **[fw=***fwtvar1***]**.
*exp* can be any valid Stata expression, and you can specify **fweight()**
at levels two and higher of a multilevel model. For example, in the
two-level model

**. xtmixed** *fixed_portion* **[fw = wt1]** **|| school:** ... **,**
**fweight(wt2)** ...

variable **wt1** would hold the first-level (the observation-level)
frequency weights, and **wt2** would hold the second-level (the
school-level) frequency weights.

**pweight(***exp***)** specifies sampling weights at higher levels in a multilevel
model, whereas sampling weights at the first level (the observation
level) are specified in the usual manner, for example, **[pw=***pwtvar1***]**.
*exp* can be any valid Stata expression, and you can specify **pweight()**
at each levels two and higher of a multilevel model. For example, in
the two-level model

**. xtmixed** *fixed_portion* **[pw = wt1]** **|| school:** ... **,**
**pweight(wt2)** ...

variable **wt1** would hold the first-level (the observation-level)
sampling weights, and **wt2** would hold the second-level (the
school-level) sampling weights.

See *Remarks on using sampling weights* below for more information
regarding the use of sampling weights in multilevel models.

Weighted estimation, whether frequency or sampling, is not supported
under restricted maximum-likelihood estimation (REML).

**mle** and **reml** specify the statistical method for fitting the model.

**mle**, the default, specifies that the model be fit using maximum
likelihood.

**reml**, specifies that the model be fit using restricted maximum
likelihood (REML), also referred to as residual maximum
likelihood.

**pwscale(***scale_method***)**, where *scale_method* is

**size**|__eff__**ective**|**gk**

controls how sampling weights (if specified) are scaled in two-level
models. See *Survey data* under *Remarks* in **[XT] xtmixed** for more
details on using **pwscale()**.

*scale_method* **size** specifies that first-level (observation-level)
weights be scaled so that they sum to the sample size of
their corresponding second-level cluster. Second-level
sampling weights are left unchanged.

*scale_method* **effective** specifies that first-level weights be
scaled so that they sum to the effective sample size of their
corresponding second-level cluster. Second-level sampling
weights are left unchanged.

*scale_method* **gk** specifies the Graubard and Korn (1996) method.
Under this method, second-level weights are set to the
cluster averages of the products of the weights at both
levels, and first-level weights are then set equal to one.

**pwcale()** is supported only with two-level models.

**residuals(***rspec***)**, where *rspec* is

*restype* [**,** *residual_options*]

specifies the structure of the residual errors within the
lowest-level (the second level of a multilevel model with the
observations comprising the first level) groups of the linear mixed
model. For example, if you are modeling random effects for classes
nested within schools, then **residuals()** refers to the residual
variance-covariance structure of the observations within classes, the
lowest-level groups.

*restype* is

__ind__**ependent**|__ex__**changeable**|**ar** *#*|**ma** *#*|__un__**structured**|__ba__**nded**
*#*|__to__**eplitz** *#*|__exp__**onential**

By default, *restype* is **independent**, which means that all
residuals are i.i.d. Gaussian with one common variance. When
combined with **by(***varname***)**, independence is still assumed, but you
estimate a distinct variance for each level of *varname*. Unlike
with the structures described below, *varname* does not need to be
constant within groups.

*restype* **exchangeable** estimates two parameters, one common
within-group variance and one common pairwise covariance.
When combined with **by(***varname***)**, these two parameters are
distinctly estimated for each level of *varname*. Because you
are modeling a within-group covariance, *varname* must be
constant within lowest-level groups.

*restype* **ar** *#* assumes that within-group errors have an
autoregressive (AR) structure of order *#*;** ar 1** is the
default. The **t(***varname***)** option is required, where *varname* is
an integer-valued time variable used to order the
observations within groups and to determine the lags between
successive observations. Any nonconsecutive time values will
be treated as gaps. For this structure, *#* + 1 parameters are
estimated (*#* AR coefficients and one overall error variance).
*restype* **ar** may be combined with **by(***varname***)**, but *varname* must
be constant within groups.

*restype* **ma** *#* assumes that within-group errors have a moving
average (MA) structure of order *#*;** ma 1** is the default. The
**t(***varname***)** option is required, where *varname* is an
integer-valued time variable used to order the observations
within groups and to determine the lags between successive
observations. Any nonconsecutive time values will be treated
as gaps. For this structure, *#* + 1 parameters are estimated
(*#* MA coefficients and one overall error variance). *restype*
**ma** may be combined with **by(***varname***)**, but *varname* must be
constant within groups.

*restype* **unstructured** is the most general structure; it estimates
distinct variances for each within-group error and distinct
covariances for each within-group error pair. The **t(***varname***)**
option is required, where *varname* is a
nonnegative-integer-valued variable that identifies the
observations within each group. The groups may be unbalanced
in that not all levels of **t()** need to be observed within
every group, but you may not have repeated **t()** values within
any particular group. When you have p levels of **t()**, then
p*(p+1)/2 parameters are estimated. *restype* **unstructured** may
be combined with **by(***varname***)**, but *varname* must be constant
within groups.

*restype* **banded** *#* is a special case of **unstructured** that restricts
estimation to the covariances within the first *#*
off-diagonals and sets the covariances outside this band to
zero. The **t(***varname***)** option is required, where *varname* is a
nonnegative-integer-valued variable that identifies the
observations within each group. *#* is an integer between zero
and p-1, where p is the number of levels of **t()**. By default,
*#* is p-1; that is, all elements of the covariance matrix are
estimated. When *#* is zero, only the diagonal elements of the
covariance matrix are estimated. *restype* **banded** may be
combined with **by(***varname***)**, but *varname* must be constant
within groups.

*restype* **toeplitz** *#* assumes that within-group errors have Toeplitz
structure of order *#*, for which correlations are constant
with respect to time lags less than or equal to *#* and are
zero for lags greater than *#*. The **t(***varname***)** option is
required, where *varname* is an integer-valued time variable
used to order the observations within groups and to determine
the lags between successive observations. *#* is an integer
between one and the maximum observed lag (the default). Any
nonconsecutive time values will be treated as gaps. For this
structure, *#* + 1 parameters are estimated (*#* correlations and
one overall error variance). *restype* **toeplitz** may be
combined with **by(***varname***)**, but *varname* must be constant
within groups.

*restype* **exponential** is a generalization of the autoregressive
(AR) covariance model that allows for unequally spaced and
noninteger time values. The **t(***varname***)** option is required,
where *varname* is real-valued. For the exponential covariance
model, the correlation between two errors is the parameter
rho, raised to a power equal to the absolute value of the
difference between the **t()** values for those errors. For this
structure, two parameters are estimated (the correlation
parameter rho and one overall error variance). *restype*
**exponential** may be combined with **by(***varname***)**, but *varname*
must be constant within groups.

*residual_options* are **by(***varname***)** and **t(***varname***)**.

**by(***varname***)** is for use within the **residuals()** option and
specifies that a set of distinct residual-error parameters be
estimated for each level of *varname*. In other words, you use
**by()** to model heteroskedasticity.

**t(***varname***)** is for use within the **residuals()** option to specify a
time variable for the **ar**, **ma**, **toeplitz**, and **exponential**
structures, or to ID the observations when *restype* is
**unstructured** or **banded**.

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

**vce(***vcetype***)** specifies the type of standard error reported, which
includes types that are robust to some kinds of misspecification and
that allow for intragroup correlation; see **[R] ***vce_option*. **vce(oim)**
is the default. If **vce(robust)** is specified, robust variances are
clustered at the highest level in the multilevel model.

**vce(robust)** and **vce(cluster** *clustvar***)** are not supported with REML
estimation.

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

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

**variance** displays the random-effects and residual-error parameter
estimates as variances and covariances. The default is to display
them as standard deviations and correlations.

**noretable** suppresses the random-effects table from the output.

**nofetable** suppresses the fixed-effects table from the output.

**estmetric** displays all parameter estimates in the estimation metric.
Fixed-effects estimates are unchanged from those normally displayed,
but random-effects parameter estimates are displayed as log-standard
deviations and hyperbolic arctangents of correlations, with equation
names that organize them by model level. Residual-variance parameter
estimates are also displayed in their original estimation metric.

**noheader** suppresses the output header, either at estimation or upon
replay.

**nogroup** suppresses the display of group summary information (number of
groups, average group size, minimum, and maximum) from the output
header.

**nostderr** prevents **xtmixed** from calculating standard errors for the
estimated random-effects parameters, although standard errors are
still given for the fixed-effects parameters. Specifying this option
will speed up computation times. **nostderr** is available only when
residuals are modeled as independent with constant variance.

**nolrtest** prevents **xtmixed** from fitting a reference linear regression
model and using this model to calculate a likelihood-ratio test
comparing the mixed model to ordinary regression. This option may
also be specified upon replay to suppress this test from the output.

*display_options*: __noomit__**ted**, **vsquish**, __noempty__**cells**, __base__**levels**,
__allbase__**levels**, **cformat(***%fmt***)**, **pformat(%***fmt***)**, **sformat(%***fmt***)**, and
**nolstretch**; see **[R] estimation options**.

+------------+
----+ EM options +-------------------------------------------------------

These options control the EM (expectation-maximization) iterations that
take place before estimation switches to a gradient-based method. When
residuals are modeled as independent with constant variance, EM will
either converge to the solution or bring parameter estimates close to the
solution. For other residual structures or for weighted estimation, EM
is used to obtain starting values.

**emiterate(***#***)** specifies the number of EM (expectation-maximization)
iterations to perform. The default is **emiterate(20)**.

**emtolerance(***#***)** specifies the convergence tolerance for the EM
algorithm. The default is **emtolerance(1e-10)**. EM iterations
will be halted once the log (restricted) likelihood changes by a
relative amount less than *#*. At that point, optimization
switches to a gradient-based method, unless **emonly** is specified.

**emonly** specifies that the likelihood be maximized exclusively using
EM. The advantage of specifying **emonly** is that EM iterations are
typically much faster than those for gradient-based methods. The
disadvantages are that EM iterations can be slow to converge (if
at all) and that EM provides no facility for estimating standard
errors for the random-effects parameters. **emonly** is available
only with unweighted estimation and when residuals are modeled as
independent with constant variance.

**emlog** specifies that the EM iteration log be shown. The EM iteration
log is, by default, not displayed unless the **emonly** option is
specified.

**emdots** specifies that the EM iterations be shown as dots. This
option can be convenient because the EM algorithm may require
many iterations to converge.

+--------------+
----+ 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(***#***)**, and __nonrtol__**erance**; see
**[R] maximize**. Those that require special mention for** xtmixed** are
listed below.

For the **technique()** option, the default is **technique(nr)**. The **bhhh**
algorithm may not be specified.

**matsqrt** (the default), during optimization, parameterizes variance
components by using the matrix square roots of the
variance-covariance matrices formed by these components at each model
level.

**matlog**, during optimization, parameterizes variance components by using
the matrix logarithms of the variance-covariance matrices formed by
these components at each model level.

The **matsqrt** parameterization ensures that variance-covariance
matrices are positive semidefinite, while **matlog** ensures matrices
that are positive definite. For most problems, the matrix square
root is more stable near the boundary of the parameter space.
However, if convergence is problematic, one option may be to try the
alternate **matlog** parameterization. When convergence is not an issue,
both parameterizations yield equivalent results.

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

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

__Remarks__

Remarks are presented under the following headings:

Remarks on specifying random-effects equations
Remarks on using sampling weights

__Remarks on specifying random-effects equations__

Mixed models consist of fixed effects and random effects. The fixed
effects are specified as regression parameters in a manner similar to
most other Stata estimation commands, that is, as a dependent variable
followed by a set of regressors. The random-effects portion of the model
is specified by first considering the grouping structure of the data.
For example, if random effects are to vary according to variable **school**,
then the call to **xtmixed** would be of the form

**. xtmixed** *fixed_portion* **|| school:** ... **,** *options*

The variable lists that make up each equation describe how the random
effects enter into the model, either as random intercepts (constant term)
or as random coefficients on regressors in the data. One may also
specify the variance-covariance structure of the within-equation random
effects, according to the four available structures described above. For
example,

**. xtmixed** *f_p* **|| school: z1, covariance(unstructured)** *options*

will fit a model with a random intercept and random slope for variable **z1**
and treat the variance-covariance structure of these two random effects
as unstructured.

If the data are organized by a series of nested groups, for example,
classes within schools, then the random-effects structure is specified by
a series of equations, each separated by **||**. The order of nesting
proceeds from left to right. For our example, this would mean that an
equation for schools would be specified first, followed by an equation
for classes. As an example, consider

**. xtmixed** *f_p* **|| school: z1, cov(un) || class: z1 z2 z3, nocons**
**cov(ex)** *options*

where variables **school** and **class** identify the schools and classes within
schools, respectively. This model contains a random intercept and random
coefficient on **z1** at the school level and has random coefficients on
variables **z1**, **z2**, and **z3** at the class level. The covariance structure
for the random effects at the class level is exchangeable, meaning that
the random effects share a common variance and common pairwise
covariance.

Group variables may be repeated, allowing for more general covariance
structures to be constructed as block-diagonal matrices based on the four
original structures. Consider

**. xtmixed** *f_p* **|| school: z1 z2, nocons cov(id) || school: z3 z4,**
**nocons cov(un)** *options*

which specifies four random coefficients at the school level. The
variance-covariance matrix of the random effects is the 4 x 4 matrix
where the upper 2 x 2 diagonal block is a multiple of the identity matrix
and the lower 2 x 2 diagonal block is unstructured. In effect, the
coefficients on **z1** and **z2** are constrained to be independent and share a
common variance. The coefficients on **z3** and **z4** each have a distinct
variance and a variance distinct from that of the coefficients on **z1** and
**z2**. They are also allowed to be correlated, yet they are independent
from the coefficients on **z1** and **z2**.

For mixed models with no nested grouping structure, thinking of the
entire estimation data as one group is convenient. Toward this end,
**xtmixed** allows the special group designation **_all**. **xtmixed** also allows
the factor variable notation **R.***varname*, which is shorthand for describing
the levels of *varname* as a series of indicator variables. See
*Random-effects factor notation and crossed-effects models* in **[XT] xtmixed**
for more details.

__Remarks on using sampling weights__

Sampling weights are treated differently in multilevel models than they
are in standard models such as OLS regression. In a multilevel model,
observation-level weights are not indicative of overall inclusion.
Instead, they indicate inclusion conditional on the corresponding cluster
being included at the next highest-level of sampling.

For example, if you include only observation-level weights in a two-level
model, **xtmixed** will assume sampling with equal probabilities at level
two, and this may or may not be what you intended. If the sampling at
level two is weighted, then including only level-one weights can lead to
biased results even if weighting at level two has been incorporated into
the level-one weight variable. For example, it is a common practice to
multiply conditional weights from multiple levels into one overall
weight. By contrast, weighted multilevel analysis requires the component
weights from each level of sampling.

Even if you specify sampling weights at all model levels, the scale of
sampling weights at lower levels can affect your estimated parameters in
a multilevel model. That is, not only do the relative sizes of the
weights at lower levels matter, the scale of these weights matters also.
To deal with this, **xtmixed** has the **pwscale()** option for rescaling weights
in two-level models; see above for more information on **pwscale()**. Three
scaling methods are offered, with each method known to perform well under
certain data situations and posited models.

In general, exercise caution when using sampling weights with **xtmixed**;
see *Survey data* in **[XT] xtmixed** for more information.

__Examples__

---------------------------------------------------------------------------
Setup
**. webuse nlswork**

Random-intercept model, analogous to **xtreg**
**. xtmixed ln_w grade age c.age#c.age ttl_exp** **tenure c.tenure#c.tenure**
**|| id:**

Random-intercept and random-slope (coefficient) model
**. xtmixed ln_w grade age c.age#c.age ttl_exp** **tenure c.tenure#c.tenure**
**|| id: tenure**

Random-intercept and random-slope (coefficient) model, correlated random
effects
**. xtmixed ln_w grade age c.age#c.age ttl_exp** **tenure c.tenure#c.tenure**
**|| id: tenure,** **cov(unstruct)**

---------------------------------------------------------------------------
Setup
**. webuse pig**

Two-level model
**. xtmixed weight week || id:**

Two-level model with robust standard errors
**. xtmixed weight week || id:, vce(robust)**

---------------------------------------------------------------------------
Setup
**. webuse productivity**

Three-level nested model, observations nested within **state** nested within
**region**, fit by maximum likelihood
**. xtmixed gsp private emp hwy water other unemp || region: ||** **state:,**
**mle**

---------------------------------------------------------------------------
Setup
**. webuse pig**

Two-way crossed random effects
**. xtmixed weight week || _all: R.id || _all: R.week**

---------------------------------------------------------------------------
Setup
**. webuse ovary**

Linear mixed model with MA 2 errors
**. xtmixed follicles sin1 cos1 || mare: sin1, residuals(ma 2, t(time))**

---------------------------------------------------------------------------
Setup
**. webuse childweight**

Linear mixed model with heteroskedastic error variances
**. xtmixed weight age || id:age, residuals(independent, by(girl))**

---------------------------------------------------------------------------

__Saved results__

**xtmixed** saves the following in **e()**:

Scalars
**e(N)** number of observations
**e(k)** number of parameters
**e(k_f)** number of FE parameters
**e(k_r)** number of RE parameters
**e(k_rs)** number of standard deviations
**e(k_rc)** number of correlations
**e(k_res)** number of residual-error parameters
**e(N_clust)** number of clusters
**e(nrgroups)** number of residual-error **by()** groups
**e(ar_p)** AR order of residual errors, if specified
**e(ma_q)** MA order of residual errors, if specified
**e(res_order)** order of residual-error structure, if appropriate
**e(df_m)** model degrees of freedom
**e(ll)** log (restricted) likelihood
**e(chi2)** chi-squared
**e(p)** p-value for chi-squared
**e(ll_c)** log likelihood, comparison model
**e(chi2_c)** chi-squared, comparison model
**e(df_c)** degrees of freedom, comparison model
**e(p_c)** p-value, comparison model
**e(rank)** rank of **e(V)**
**e(rc)** return code
**e(converged)** **1** if converged, **0** otherwise

Macros
**e(cmd)** **xtmixed**
**e(cmdline)** command as typed
**e(depvar)** name of dependent variable
**e(wtype)** weight type (first-level weights)
**e(wexp)** weight expression (first-level weights)
**e(fweight***k***)** fweight expression for *k*th-highest level, if specified
**e(pweight***k***)** pweight expression for *k*th-highest level, if specified
**e(ivars)** grouping variables
**e(title)** title in estimation output
**e(redim)** random-effects dimensions
**e(vartypes)** variance-structure types
**e(revars)** random-effects covariates
**e(resopt)** **residuals()** specification, as typed
**e(rstructure)** residual-error structure
**e(rstructlab)** residual-error structure output label
**e(rbyvar)** residual-error **by()** variable, if specified
**e(rglabels)** residual-error **by()** group labels
**e(pwscale)** sampling-weight scaling method
**e(timevar)** residual-error **t()** variable, if specified
**e(chi2type)** **Wald**; type of model chi-squared test
**e(clustvar)** name of cluster variable
**e(vce)** *vcetype* specified in **vce()**
**e(vcetype)** title used to label Std. Err.
**e(method)** **ML** or **REML**
**e(opt)** type of optimization
**e(optmetric)** **matsqrt** or **matlog**; random-effects matrix
parameterization
**e(emonly)** **emonly**, if specified
**e(ml_method)** type of **ml** method
**e(technique)** maximization technique
**e(properties)** **b V**
**e(estat_cmd)** program used to implement **estat**
**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(N_g)** group counts
**e(g_min)** group-size minimums
**e(g_avg)** group-size averages
**e(g_max)** group-size maximums
**e(tmap)** ID mapping for unstructured residual errors
**e(V)** variance-covariance matrix of the estimators
**e(V_modelbased)** model-based variance

Functions
**e(sample)** marks estimation sample

__Reference__

Graubard, B. I., and E. L. Korn. 1996. Modelling the sampling design in
the analysis of health surveys. *Statistical Methods in Medical*
*Research* 5: 263-281.