## Stata 15 help for mixed

```
[ME] mixed -- Multilevel mixed-effects linear regression

Syntax

mixed 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 random effects 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 is _all representing one group comprising all
observations.

fe_options               Description
-------------------------------------------------------------------------
Model
noconstant             suppress constant term from the fixed-effects
equation
-------------------------------------------------------------------------

re_options               Description
-------------------------------------------------------------------------
Model
covariance(vartype)    variance-covariance structure of the random
effects
noconstant             suppress constant term from the random-effects
equation
collinear              keep collinear variables
fweight(exp)           frequency weights at higher levels
pweight(exp)           sampling weights at higher levels
-------------------------------------------------------------------------

options                  Description
-------------------------------------------------------------------------
Model
mle                    fit model via maximum likelihood (ML); the
default
reml                   fit model via restricted maximum likelihood
(REML)
dfmethod(df_method)    specify method for computing degrees of freedom
(DF) of a t distribution
pwscale(scale_method)  control scaling of sampling weights in two-level
models
residuals(rspec)       structure of residual errors

SE/Robust
vce(vcetype)           vcetype may be oim, robust, or cluster clustvar;
types other than oim may not be combined with
dfmethod()

Reporting
level(#)               set confidence level; default is level(95)
variance               show random-effects and residual-error parameter
estimates as variances and covariances; the
default
stddeviations          show random-effects and residual-error parameter
estimates as standard deviations and
correlations
dftable(dftable)       specify contents of fixed-effects table;
requires dfmethod() at estimation
noretable              suppress random-effects table
nofetable              suppress fixed-effects table
estmetric              show parameter estimates as stored in e(b)
nogroup                suppress table summarizing groups
nostderr               do not estimate standard errors of
random-effects parameters
display_options        control columns and column formats, row spacing,
line width, display of omitted variables and
base and empty cells, and factor-variable
labeling

EM options
emiterate(#)           number of EM iterations; default is
emiterate(20)
emtolerance(#)         EM convergence tolerance; default is
emtolerance(1e-10)
emonly                 fit model exclusively using EM
emlog                  show EM iteration log
emdots                 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

small                  replay small-sample inference results
coeflegend             display legend instead of statistics
-------------------------------------------------------------------------

vartype                  Description
-------------------------------------------------------------------------
independent              one unique variance parameter per random effect,
all covariances 0; the default unless the R.
notation is used
exchangeable             equal variances for random effects, and one
common pairwise covariance
identity                 equal variances for random effects, all
covariances 0; the default if the R. notation
is used
unstructured             all variances and covariances to be distinctly
estimated
-------------------------------------------------------------------------

df_method                Description
-------------------------------------------------------------------------
residual                 residual degrees of freedom, n - rank(X)
repeated                 repeated-measures ANOVA
anova                    ANOVA
satterthwaite[, dfopts]  generalized Satterthwaite approximation; REML
estimation only
kroger[, dfopts]         Kenward-Roger; REML estimation only
-------------------------------------------------------------------------

dftable                  Description
-------------------------------------------------------------------------
default                  test statistics, p-values, and confidence
intervals; the default
ci                       DFs and confidence intervals
pvalue                   DFs, test statistics, and p-values
-------------------------------------------------------------------------

indepvars may contain factor variables; see fvvarlist.
depvar, indepvars, and varlist may contain time-series operators; see
tsvarlist.
bayes, bootstrap, by, jackknife, mi estimate, rolling, and statsby are
allowed; see prefix.  For more details, see [BAYES] bayes: mixed.
mi estimate is not allowed if dfmethod() is specified.
Weights are not allowed with the bootstrap prefix.
pweights and fweights are allowed; see weight.  However, no weights are
allowed if either option reml or option dfmethod() is specified.
small and coeflegend do not appear in the dialog box.
See [ME] mixed postestimation for features available after estimation.

Statistics > Multilevel mixed-effects models > Linear regression

Description

mixed fits linear mixed-effects models.  These models are also known as
multilevel models or hierarchical linear models.  The overall error
distribution of the linear mixed-effects 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 of or all the
random-effects equations.

covariance(vartype) specifies the structure of the covariance matrix for
the random effects and may be specified for each random-effects
equation.  vartype is one of the following:  independent,
exchangeable, identity, or unstructured.

independent allows for a distinct variance for each random effect
within a random-effects equation and assumes that all covariances
are 0.

exchangeable specifies one common variance for all random effects and
one common pairwise covariance.

identity is short for "multiple of the identity"; that is, all
variances are equal and all covariances are 0.

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 R. notation
is used, in which case covariance(identity) is the default and only
covariance(identity) and covariance(exchangeable) are allowed.

collinear specifies that mixed not omit collinear variables from the
random-effects equation.  Usually, there is no reason to leave
collinear variables in place; 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 variable, and you can specify fweight() at
levels two and higher of a multilevel model.  For example, in the
two-level model

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

the 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 variable, and you can specify pweight() at
each levels two and higher of a multilevel model.  For example, in
the two-level model

. mixed 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.

regarding the use of sampling weights in multilevel models.

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

mle, the default, specifies that the model be fit using ML.  Options
dfmethod(satterthwaite) and dfmethod(kroger) are not supported
under ML estimation.

reml specifies that the model be fit using REML, also known as
residual maximum likelihood.

dfmethod(df_method) requests that reported hypothesis tests for the fixed
effects (coefficients) use a small-sample adjustment.  By default,
inference is based on a large-sample approximation of the sampling
distributions of the test statistics by normal and chi-squared
distributions.  Caution should be exercised when choosing a DF
method; see Small-sample inference for fixed effects in [ME] mixed
for details.

When dfmethod(df_method) is specified, the sampling distributions of
the test statistics are approximated by a t distribution, according
to the requested method for computing the DF.  df_method is one of
the following: residual, repeated, anova, satterthwaite, or kroger.

residual uses the residual degrees of freedom, n - rank(X), as the DF
for all tests of fixed effects.  For a linear model without
random effects with independent and identically distributed
errors, the distributions of the test statistics for fixed
effects are t distributions with the residual DF.  For other
mixed-effects models, this method typically leads to poor
approximations of the actual sampling distributions of the test
statistics.

repeated uses the repeated-measures ANOVA method for computing the
DF.  It is used with balanced repeated-measures designs with
spherical correlation error structures.  It partitions the
residual degrees of freedom into the between-subject degrees of
freedom and the within-subject degrees of freedom.  repeated is
supported only with two-level models.  For more complex
mixed-effects models or with unbalanced data, this method
typically leads to poor approximations of the actual sampling
distributions of the test statistics.

anova uses the traditional ANOVA method for computing the DF.
According to this method, the DF for a test of a fixed effect of
a given variable depends on whether that variable is also
included in any of the random-effects equations.  For traditional
ANOVA models with balanced designs, this method provides exact
sampling distributions of the test statistics.  For more complex
mixed-effects models or with unbalanced data, this method
typically leads to poor approximations of the actual sampling
distributions of the test statistics.

satterthwaite[, dfopts] implements a generalization of the
Satterthwaite (1946) approximation of the unknown sampling
distributions of test statistics for complex linear mixed-effect
models.  This method is supported only with REML estimation.

kroger[, dfopts] implements the Kenward and Roger (1997) method,
which is designed to approximate unknown sampling distributions
of test statistics for complex linear mixed-effects models.  This
method is supported only with REML estimation.

dfopts is either eim or oim.

eim specifies that the expected information matrix be used to
compute Satterthwaite or Kenward-Roger degrees of freedom.
This is the default.

oim specifies that the observed information matrix be used to
compute Satterthwaite or Kenward-Roger degrees of freedom.

Residual, repeated, and ANOVA methods are suitable only when the
sampling distributions of test statistics are known to be t or F.
This is usually only known for certain classes of linear
mixed-effects models with simple covariance structures and when data
are balanced.  These methods are available with both ML and REML
estimation.

For unbalanced data or balanced data with complicated covariance
structures, the sampling distributions of the test statistics are
unknown and can only be approximated.  The Satterthwaite and
Kenward-Roger methods provide approximations to the distributions in
these cases.  According to Schaalje, McBride, and Fellingham (2002),
the Kenward-Roger method should, in general, be preferred to the
Satterthwaite method.  However, there are situations in which the two
methods are expected to perform similarly, such as with compound
symmetry covariance structures.  The Kenward-Roger method is more
computationally demanding than the Satterthwaite method.  Both
methods are available only with REML estimation.  See Small-sample
inference for fixed effects under Remarks and examples in [ME] mixed
for examples and more detailed descriptions of the DF methods.

dfmethod() may not be combined with weighted estimation, the mi
estimate prefix, or vce() unless it is the default vce(oim).

pwscale(scale_method) controls how sampling weights (if specified) are
scaled in two-level models.  scale_method is one of the following:
size, effective, or gk.

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.

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.

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 1.

pwscale() is supported only with two-level models.  See Survey data
under Remarks and examples in [ME] mixed for more details on using
pwscale().  pwscale() may not be combined with the dfmethod() option.

residuals(rspec) specifies the structure of the residual errors within
the lowest-level groups (the second level of a multilevel model with
the observations comprising the first level) 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. rspec has the following syntax:

restype [, residual_options]

restype is one of the following:  independent, exchangeable, ar #, ma
#, unstructured, banded #, toeplitz #, or exponential.

independent, the default, specifies that all residuals be independent
and identically distributed 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.

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.

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.

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.

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.

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 0.  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 0 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 0, 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.

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 0 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 1 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.

exponential is a generalization of the 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 identify the observations when restype is unstructured or
banded.

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

vce(vcetype) specifies the type of standard error reported, which
includes types that are derived from asymptotic theory (oim), that
are robust to some kinds of misspecification (robust), and that allow
for intragroup correlation (cluster clustvar); see [R] vce_option.
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.  Only vce(oim) is allowed in combination with
dfmethod().

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

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

variance, the default, displays the random-effects and residual-error
parameter estimates as variances and covariances.

stddeviations displays the random-effects and residual-error parameter
estimates as standard deviations and correlations.

dftable(dftable) specifies the contents of the fixed-effects table for
small-sample inference when dfmethod() is used during estimation.
dftable is one of the following:  default, ci, or pvalue.

default displays the default standard fixed-effects table that
contains test statistics, p-values, and confidence intervals.

ci displays the fixed-effects table in which the columns containing
statistics and p-values are replaced with a column containing
coefficient-specific DFs.  Confidence intervals are also
displayed.

pvalue displays the fixed-effects table that includes a column
containing DFs with the standard columns containing test
statistics and p-values.  Confidence intervals are not displayed.

noretable suppresses the random-effects table from the output.

nofetable suppresses the fixed-effects table from the output.

estmetric displays all parameter estimates in one table using the metric
in which they are stored in e(b).  The results are stored in the same
metric regardless of the parameterization of the variance components,
matsqrt or matlog, used at estimation time.  Random-effects parameter
estimates are stored as log-standard deviations and hyperbolic
arctangents of correlations, with equation names that organize them
by model level.  Residual-variance parameter estimates are stored as
log-standard deviations and, when applicable, as hyperbolic
arctangents of correlations.  Note that fixed-effects estimates are
always stored and displayed in the same metric.

replay.

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

nostderr prevents mixed from calculating standard errors for the
estimated random-effects parameters, although standard errors are
still provided 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.

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.

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

These options control the expectation-maximization (EM) 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 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,
in which case maximization stops.

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:  difficult, technique(algorithm_spec), iterate(#),
[no]log, trace, gradient, showstep, hessian, showtolerance,
tolerance(#), ltolerance(#), nrtolerance(#), and nonrtolerance; see
[R] maximize.  Those that require special mention for mixed 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 options are available with mixed but are not shown in the
dialog box:

small replays previously obtained small-sample results.  This option is
available only upon replay and requires that the dfmethod() option be
used during estimation. small is equivalent to dftable(default) upon
replay.

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 small-sample inference for fixed effects

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 mixed would be of the form

. mixed 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,

. mixed 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

. mixed 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

. mixed 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,
mixed allows the special group designation _all.  mixed also allows the
R.varname notation, which is shorthand for describing the levels of
varname as a series of indicator variables.  See Crossed-effects models
in [ME] mixed 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, mixed 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, mixed has the pwscale() option for rescaling weights
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 mixed; see

Remarks on small-sample inference for fixed effects

By default, mixed performs large-sample inference for fixed effects using
asymptotic normal and chi-squared distributions.  These large-sample
approximations may not be appropriate in small samples, and t and F
distributions may provide better approximations.  You can specify the
dfmethod() option to request small-sample inference for fixed effects.
mixed, dfmethod() uses a t distribution for one-hypothesis tests and an F
distribution for multiple-hypotheses tests for inference about fixed
effects.  It also provides five different methods for calculating the DF:
residual, repeated, anova, satterthwaite, and kroger.  See Small-sample

Examples

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

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

Random-intercept and random-slope (coefficient) model
. mixed 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
. mixed 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
. mixed weight week || id:

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

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

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

Three-level nested random interactions model with ANOVA DF
. mixed gsp private emp hwy water other unemp || region:water ||
state:other, dfmethod(anova)

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

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

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Setup
. webuse ovary

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

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Setup
. webuse childweight

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

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Setup
. webuse pig

Random-intercept and random-slope model with Kenward-Roger DF
. mixed weight week || id:week, reml dfmethod(kroger)

Display degrees-of-freedom table containing p-values
. mixed, dftable(pvalue)

Display degrees-of-freedom table containing confidence intervals
. mixed, dftable(ci)

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Setup
. webuse t43

Repeated-measures model with the repeated DF
. mixed score i.drug || person:, reml dfmethod(repeated)

Replay large-sample results
. mixed

Replay small-sample results using the repeated DF
. mixed, small

Stored results

mixed stores the following in e():

Scalars
e(N)                   number of observations
e(k)                   number of parameters
e(k_f)                 number of fixed-effects parameters
e(k_r)                 number of random-effects parameters
e(k_rs)                number of variances
e(k_rc)                number of covariances
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(small)               1 if dfmethod() option specified, 0 otherwise
e(F)                   overall F test statistic when dfmethod() is
specified
e(ddf_m)               model DDF
e(df_max)              maximum DF
e(df_avg)              average DF
e(df_min)              minimum DF
e(ll)                  log (restricted) likelihood
e(chi2)                chi-squared
e(p)                   p-value for model test
e(ll_c)                log likelihood, comparison model
e(chi2_c)              chi-squared, comparison test
e(df_c)                degrees of freedom, comparison test
e(p_c)                 p-value for comparison 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)                 mixed
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(fweightk)            fweight variable for kth highest level, if
specified
e(pweightk)            pweight variable for kth 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(dfmethod)            DF method specified in dfmethod()
e(dftitle)             title for DF method
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(datasignature)       the checksum
e(datasignaturevars)   variables used in calculation of checksum
e(properties)          b V
e(estat_cmd)           program used to implement estat
e(predict)             program used to implement predict
e(marginswtype)        weight type for margins
e(marginswexp)         weight expression for margins
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
e(df)                  parameter-specific DF for fixed effects
e(V_df)                variance-covariance matrix of the estimators
when dfmethod(kroger) is specified

Functions
e(sample)              marks estimation sample

References

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.

Kenward, M. G., and J. H. Roger. 1997.  Small sample inference for fixed
effects from restricted maximum likelihood.  Biometrics 53: 983-997.

Satterthwaite, F. E. 1946. An approximate distribution of estimates of
variance components. Biometrics Bulletin 2: 110-114.

Schaalje, G. B., J. B. McBride, and G. W. Fellingham. 2002. Adequacy of
approximations to distributions of test statistics in complex mixed
linear models. Journal of Agricultural, Biological, and Environmental
Statistics 7: 512-524.

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