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.-
help for ^gllamm^
.-
Generalised linear latent and mixed models
-------------------------------------------
^gllamm^ depvar [varlist] [^if^ exp] [^in^ range] ^,^ ^i(^varlist^)^
[ ^nocons^tant ^o^ffset^(^varname^)^ ^nr^f^(^#^,^...^,^#^)^
^e^qs^(^eqnames^)^ ^frload^(^#^,^...^,^#^)^
^ip(^string^)^ ^ni^p^(^#^,^...^,^#^)^ ^pe^qs^(^eqname^)^
^bmat^rix^(^matrix^)^ ^ge^qs^(^eqnames^)^ ^nocor^rel
^c^onstraints^(^clist^)^ ^we^ight^(^varname^)^ ^pwe^ight^(^varname^)^
^f^amily^(^family^)^ ^fv(^varname^)^ ^de^nom^(^varname^)^
^s(^eqname^)^ ^l^ink^(^link^)^ ^lv(^varname^)^
^expa^nded^(^varname varname string^)^ ^b^asecategory^(^#^)^
^comp^osite^(^varnames^)^ ^th^resh^(^eqnames^)^ ^eth^resh^(^eqnames^)^
^fr^om^(^matrix^)^ ^copy^ ^skip^ ^long^
^lf0(^#^ ^#^)^ ^ga^teaux^(^#^ ^#^ ^#^)^ ^se^arch^(^#^)^
^noe^st ^ev^al ^in^it ^it^erate^(^#^)^ ^adoonly^ ^adapt^
^rob^ust ^clu^ster^(^varname^)^
^l^evel^(^#^)^ ^eform^ ^allc^ ^tr^ace ^nolo^g ^nodis^play ^do^ts
]
where family is and link is
^gau^ssian ^id^entity
^poi^sson ^log^
^gam^ma ^rec^iprocal
^bin^omial ^logi^t
^pro^bit
^cll^ (complementary log-log)
^ll^ (log-log)
^olo^git (o stands for ordinal)
^opr^obit
^ocl^l
^mlo^git
^spr^obit (scaled probit)
^sop^robit
and clist is of the form #[^-^#][^,^ #[^-^#] ...]
^gllamm^ shares the features of all estimation commands; see help @est@.
^gllamm^ typed without arguments redisplays previous results.
Predictions of the latent variables or random effects (and many other
quantities) can be obtained using @gllapred@ and the models can be
simulated using @gllasim@
Description
-----------
^gllamm^ estimates ^G^eneralized ^L^inear ^L^atent ^A^nd ^M^ixed ^M^odels.
These models include multilevel (hierarchical) regression models
with an arbitrary number of levels, generalized linear mixed models,
multilevel factor models and some types of latent class models.
We refer to the random effects (random intercepts, slopes or coefficients),
factors, etc. as latent variables or random effects.
If the latent variables are assumed to be multivariate normal,
^gllamm^ uses Gauss-Hermite quadrature, or adaptive quadrature
if the ^adapt^ option is also specified. Adaptive quadrature
can be considerably more accurate than ordinary quadrature,
see first reference at the bottom of this help file.
With the ^ip(^f^)^ option, the latent variables are specified
as discrete with freely estimated probabilities (masses) and locations.
More information on the models is available from
http://www.gllamm.org
Options
--------
(a) Structure of the model
---------------------------------------------------------------------------
^i(^varlist^)^ gives the variables that define the hierarchical, nested
clusters, from the lowest level (finest clusters) to the highest level,
e.g. i(pupil class school).
^noconstant^ omits the constant term from the fixed effects equation.
^offset(^varname^)^ specifies a variable to be added to the linear predictor
without estimating a corresponding regression coefficient (e.g. log
exposure for Poisson regression).
^nrf(^#^,^...^,^#^)^ specifies the number of random effects for each level,
i.e., for each variable in ^i(^varlist^)^. The default is nrf(1,...,1).
^eqs(^eqnames^)^ specifies equation names (defined before running gllamm)
for the linear predictors multiplying the latent variables; see help @eq_g@.
If required, constants should be explicitly included in the equation
definitions using variables equal to 1. If the option is not used, the
latent variables are assumed to be random intercepts and only one random
effect is allowed per level. The first lambda coefficient is set to one
unless the ^frload()^ option is specified. The other coefficients are
estimated together with the (co)variance(s) of the random effect(s).
^frload(^#^,^...^,^#^)^ lists the latent variables for which the first
factor loading should be freely estimated along with the other
factor loadings. It is up to the user to define appropriate constraints
to identify the model. Here the latent variables are referred to
as 1 2 3 etc. in the order in which they are defined by the ^eqs()^
option.
^ip(^sting^)^ if string is g, Gaussian quadrature points are used and if
string is f, the mass-points are freely estimated. The default is
Gaussian quadrature. The ^ip(^f^)^ option causes nip-1 locations to
be estimated, the nipth mass being determined by setting the mean
location to 0 so that an intercept can be included in the fixed
effects equation. The ^ip(^fn^)^ option can be used to set the last mass
to 0 instead of to the mean. If string is m, spherical quadrature rules
are used for multidimensional integrals.
^nip(^#^,^...^,^#^)^ specifies the number of integration points or masses
to be used for each integral or summation. When quadrature is used,
a value may be given for each random effect. When freely estimated masses
are used, a value may be given for each level of the model. If only one
argument is given, the same number of integration points will be used for
each summation. Combined with the ^ip(m)^ option, ^nip()^ specifies
the degree of the approximation instead of the number of points. Only the
following degrees are available: for two random effects, 5, 7, 9, 11, 15
and for more than two random effects 5, 7.
^peqs(^eqname^)^ can be used with the ^ip(^f^)^ or ^ip(^fn^)^ options
to allow the (prior) latent class probabilities to depend on covariates.
The model for the latent class probabilities is a multinomial logit model
with the last latent class as reference category. A constant is
automatically included in addition to the covariates specified in the
equation command; see help @eq_g@.
^geqs(^eqnames^)^ specifies regressions of latent variables on explanatory variables.
The second character of the equation name indicates which latent
variable is regressed on the variables used in the equation definition, e.g.
eq f1: a b means that the first latent variable is regressed on a and b (without
a constant); see help @eq_g@.
^bmatrix(^matrix^)^ specifies a matrix B of regression coefficients for the
dependence of the latent variables on other latent variables. The matrix
must be upper diagonal and have number of rows and columns equal to the
total number of random effects.
^nocorrel^ may be used to constrain all correlations to zero
if there are several random effects at any of the levels and if these are
modeled as multivariate normal.
^constraint(^clist^)^ specifies the constraint numbers of the constraints to
be applied. Constraints are defined using the ^constraint^ command; see
help @constraint@. To find out the equation names needed to specify the
constraints, run gllamm with the noest option.
^weight(^varname^)^ specifies that variables varname1, varname2, etc. contain
frequency weights. The suffixes determine at what level each weight applies.
For example, if the level 1 units are subjects, the level 2 units are
families, and the result is binary, we can collapse dataset A into
dataset B as follows:
A B
family subject result family subject result wt1 wt2
1 1 0 1 1 0 2 1
1 2 0 2 3 1 1 2
2 3 1 2 4 0 1 2
2 4 0
3 5 1
3 6 0
The level 1 weight, wt1, indicates that subject 1 in dataset B
represents two subjects within family 1 in dataset A, whereas subjects
3 and 4 in dataset B represent single subjects within family 2 in
dataset A. The level 2 weight wt2 indicates that family 1 in dataset B
represents one family and family 2 represents two families, i.e. all
the data for family 2 are replicated once. Collapsing the data in this
way can make gllamm run considerably faster.
^pweight(^varname^)^ specifies that variables varname1, varname2, etc. contain
sampling weights for levels 1, 2, etc. As far as the estimates and
log-likelihood are concerned, the effect of specifying these
weights is the same as for frequency weights, but the standard errors
will be different. Robust standard errors will automatically be provided.
This should be used with caution if the sampling weights apply
to units at a lower level than the highest level in the multilevel model.
The weights are not rescaled; scaling is the responsibility of the user.
(b) Densities, links, etc. for the response model
------------------------------------------------------------------------------
^family(^families^)^ specifies the families to be used for the conditional
densities. The default is ^family(^gauss^)^. Several families may be given
in which case the variable allocating families to observations must be
given using ^fv(^varname^)^.
^fv(^varname^)^ is required if mixed responses requiring more than a single
family of conditional distributions are analyzed. The variable indicates
which family applies to which observation. A value of one refers to the
first family etc.
^denom(^varname^)^ gives the variable containing the binomial denominator for
the responses whose family is specified as binomial. The default
denominator is 1.
^s(^eqname^)^ specifies that the log of the standard deviation (or coefficient
of variation) at level 1 for normally (or gamma) distributed responses
should be given by the linear predictor defined by eqname. This is
necessary if the level-1 variance is heteroscedastic. For example, if
dummy variables for groups are used, different variances are estimated
for different groups.
^link(^link^)^ specifies the links to be used for the conditional densities. If
a single family is specified, the default link is the canonical link.
Several links may be given in which case the variable allocating links to
observations must be given using ^lv(^varname^)^. This option is currently
not available if the ordinal or mlogit links are used. Numerically
feasible choices of link depend upon the distributions of the covariates
and choice of conditional error and random effects distributions. The
sprobit link is only identified in special cases; it may be used for
Heckman-type selection models or to model floor or ceiling effects.
^lv(^varname^)^ is the variable whose values indicate which link applies to
which observation.
^expanded(^varname varname string^)^ is used together with the mlogit
link and specifies that the data have been expanded as illustrated
below:
A B
choice response altern selected
1 1 1 1
2 1 2 0
1 3 0
2 1 0
2 2 1
2 3 0
where the variable "choice" is the multinomial response
(possible values 1,2,3), the "response" labels the original lines
of data, "altern" gives the possible responses or alternatives
and "selected" is an indicator for the option that was selected.
The syntax would be expanded(response selected m) and the variable
"altern" would be used as the dependent variable. This expanded
form allows the user to use different random effects etc. for
different categories of the multinomial response. The third
argument is o if one set of coefficients should be estimated
for the explanatory variables and m if one set of coefficients
is to be estimated for each category of the response except the
reference category.
^basecategory^(^#^)^ When the mlogit link is used, this specifies the
value of the response to be used as the reference category. This option is
ignored if the expanded() option is used with the third argument equal
to m.
^composite^(varname varname varname [more varnames]) specifies that a
composite link is used. The first variable is a cluster identifier
("cluster" below) so that linear predictors within the cluster can
be combined into a single composite link. The second variable
("ind" below) indicates to which response the composite links defined
by the susequent weight variables belong. Observations with ind=0
have a missing link. The remaining variables ("c1" and "c2" below)
specify weights for the composite links. The composite link based on
the first weight variable will go to where ind=1, etc.
Example:
Data setup with form of inverse link Interpretation of
h_i determined by link() and lv(): composite(cluster ind c1 c2)
cluster ind c1 c2 inverse link cluster composite link
1 1 1 0 h_1 1 h_1 - h_2
1 2 -1 1 h_2 1 n_2 + h_3
1 0 0 1 h_3 ==> 1 missing
2 1 1 0 h_4 2 h_4 + h_5
2 2 1 1 h_5 2 h_5 + 2*h_6
2 0 0 2 h_6 2 missing
^thresh(^eqnames^)^ specifies equation(s) for the thresholds for ordinal
response(s); see help @eq_g@. One equation is specified for each
ordinal response. The purpose of this option is to allow the effects of some
covariates to be different for different categories of the ordinal variable
rather than assumming a constant effect - the proportional odds assumption
if the ologit link is used. Variables used in the model for the
thresholds cannot appear in the fixed part of the linear predictor.
^ethresh(^eqnames^)^ is the same as ^thresh(^eqnames^)^ except that
a different parameterization is used for the threshold model. To
ensure that k_{s-1} <= k_{s}, the model is k_{s} = k_{s-1} + exp(xb),
for response categories s=2,...,S.
(c) Starting values
-----------------------------------------------------------------------------
^from(^matrix^)^ specifies the matrix to be used for the initial values.
Note that the column-names and equation-names have to be correct
(see help @matrname@, @matrix@), unless the ^copy^ option is specified.
The matrix may be obtained from a previous estimation command using e(b).
This is useful if the number of quadrature points needs to be increased
or of a new explanatory variable is added. Use the ^skip^ option if
the matrix of has extra parameters.
^copy^ and ^skip^ see above.
^long^ may be used with the from(matrix) option when constraints are used
to indicate that the matrix of initial values has as many elements
as would be needed for the unconstrained model, i.e. more elements
than will be estimated.
^lf0(^# #^)^ gives the number of parameters and the log-likelihood for a
likelihood ratio test to compare the model to be estimated with a simpler
model. A likelihood ratio chi-squared test is only performed if the
^lf0(^# #^)^ option is used.
^gateaux(^min^,^max^,^n^)^ may be used with method ip(f) to increase the
number of mass-points by one from a previous solution with parameter
estimates specified using from(matrix) and number of parameters and
log-likelihood specified by lf0(# #). The program searches for the
location of the new mass-point by placing a very small mass at the
location given by the first argument and moving it to the second argument
in the number of steps specified by the third argument. (If there are
several random effects, this search is done in each dimension resulting
in a regular grid of search points.) If the maximum increase in likelihood
is greater than 0, the location corresponding to this maximum is used as
the initial value of the new location, otherwise the program stops. When
this happens, it can be shown that for certain models the current solution
represents the non-parametric maximum likelihood estimate.
^search(^#^)^ causes the program to search for initial values for the random
effects at level 2 (in range 0 to 3). The argument specifies the number
of random searches. This option may only be used with ^ip(^g^)^ and when
^fr^om^(^matrix^)^ is not used.
(d) Estimation and output options
------------------------------------------------------------------------------
^noest^ is used to prevent the program from carrying out the estimation. This
may be used with the trace option to check that the model is correct and
get the information needed to set up a matrix of initial values. Global
macros are available that are normally deleted. Particularly useful may
be M_initf and M_initr, matrices for the parameters (fixed part and
random part respectively).
^eval^ causes the program to simply evaluate the loglikelihood for values passed
to it using the from(matrix) option.
^init^ causes the program to compute initial estimates of fixed effects
only, setting all latent variables to zero. gllamm will be used for
estimating initial values even if a Stata command is available for the
model (without the init option, gllamm uses Stata commands for initial values
whenever they are available).
^iterate(^#^)^ specifies the (maximum) number of iterations. With the ^adapt^
option, use of the ^iterate(^#^)^ option will cause ^gllamm^ to skip the
"Newton Raphson" iterations usually performed at the end without updating
the quadrature locations. ^iterate(^0^)^ is like ^eval^ except that standard
errors are computed.
^adoonly^ causes all gllamm to use only ado-code. Gllamm will be faster if
if it uses internalised versions of some of the functions available in
Stata 7 if updated on or after 26oct2001
^nip(^#^,^...^,^#^)^ when quadrature is used, this specifies the number
of quadrature points (integration points) to be used. A value may be
given for each random effect. If only one argument is given, the
same number of quadrature points will be used for each summation.
^adapt^ causes adaptive quadrature to be used instead of ordinary quadrature.
This option cannot be used with the ^ip(^f^)^ or ^ip(^f0^)^ options.
^robust^ specifies that the Huber/White/sandwich estimator of the covariance
matrix of the parameter estimates is to be used. If a model has been
estimated without the ^robust^ option, the robust standard errors can be
obtained by simply typing ^gllamm, robust^.
^cluster(^varname^)^ specifies that the highest level units of the GLLAMM
model are nested in even higher level clusters where ^varname^ contains
the cluster identifier. Robust standard errors will be provided that
take this clustering into account. If a model has been estimated without
this option, the robust standard errors for clustered data can be obtained
using the command ^gllamm, cluster(varname)^.
^level(^#^)^ specifies the confidence level in percent for confidence
intervals of the coefficients.
^eform^ causes the expnentiated coefficients and confidence intervals to be
displayed.
^allc^ causes all estimated parameters to be displayed in a regression table
(including the raw parameters for the random effects) in addition to the
usual output.
^trace^ causes more output to be displayed. Before estimation begins,
details of the specified model are displayed. In addition, a
detailed iteration log is shown including parameter estimates
and log-likelihood values for each iteration.
^nolog^ suppresses output for maximum likelihood iterations.
^nodisplay^ suppresses output of the estimates but still shows iteration log
unless ^nolog^ is used.
^dots^ causes a dot to be printed (if used together with trace) every time the
likelihood evaluation program is called by ml. This helps to assess how long
gllamm is likely to take to run and reassures the user that it is making
some progress when it is very slow.
Examples
--------
(a) 3-level random intercept model
----------------------------------
Some response "resp" and covariate "x" are available for pupils
in different schools. "id" is the identifier or label for the pupils
and "school" is the identifier for the schools. A linear model
with random intercepts at the pupil and school levels can be specified
as follows:
. ^gllamm resp x, i(id school) adapt trace^
(b) 2-level random coefficient model - growth curve model
---------------------------------------------------------
subjects identified by "id" have been measured repeatedly over
time giving responses in "resp". "cons" is a variable equal to 1
and "time" contains the time-points. A model with a random
intercept and slope for time is specified as follows:
. ^eq int: cons^
. ^eq slope: time^
. ^gllamm resp time, i(id) nrf(2) eqs(int slope) adapt trace ^
(c) two-parameter logistic item-response model
----------------------------------------------
variable "resp" contains responses to 5 items (e.g. 5 test questions)
for each subject. The subject identifier is "id". There are five
dummy variables "i1" to "i5" for the items, e.g. "i1" is equal
to 1 if the item is item 1 and 0 otherwise.
. ^eq discrim: i1 i2 i3 i4 i5^
. ^gllamm resp i1 i2 i3 i4 i5, link(logit) fam(binom) nocons /*^
^*/ i(id) eqs(discrim) adapt trace^
Author
------
Sophia Rabe-Hesketh (sophiarh@@berkeley.edu)
as part of joint work with Andrew Pickles and Anders Skrondal.
We would like to acknowledge Colin Taylor for helping in the
early stages of gllamm development. We are also very grateful
to Stata Corporation for helping us to speed up gllamm.
Web-page
--------
http://www.gllamm.org
References (available from sophiarh@@berkeley.edu)
----------
Rabe-Hesketh, S. and Skrondal, A. (2005). Multilevel and Longitudinal
Modeling using Stata. College Station, TX: Stata Press.
Rabe-Hesketh, S., Pickles, A. and Skrondal, S. (2004).
GLLAMM Manual. U.C. Berkeley Division of Biostatistics Working
Paper Series. Working Paper 160.
see http://www.bepress.com/ucbbiostat/paper160/
Rabe-Hesketh, S., Skrondal, A. and Pickles, A. (2005). Maximum
likelihood estimation of limited and discrete dependent variable
models with nested random effects. Journal of Econometrics 128, 301-323.
Rabe-Hesketh, S., Skrondal, A. and Pickles, A. (2002).
Reliable estimation of generalized linear mixed models
using adaptive quadrature. The Stata Journal 2, 1-21.
Rabe-Hesketh, S., Skrondal, A. and Pickles, A. (2004).
Generalised multilevel structural equation modelling.
Psychometrika 69 , 167-190.
Also see
--------
Manual: ^[U] 23 Estimation and post-estimation commands^
^[U] 29 Overview of model estimation in Stata^
On-line: help for @gllapred@, @gllasim@, @ml@, @glm@, @xtreg@,
@xtlogit@, @xtpois@, @quadchk@, @test@