gllamm runs in the statistical package
Stata and estimates
GLLAMMs (Generalized Linear Latent And Mixed Models)
by maximum likelihood (see
help gllamm after installation).
gllamm maximises the marginal log-likelihood
using Stata's version of the Newton Raphson Algorithm
ml with method
In the case of discrete random effects or factors, the marginal
log-likelihood is evaluated exactly whereas numerical integration
is used for continuous (multivariate) normal random effects or factors.
Two methods are available for numerical integration: Quadrature or adaptive
In both cases it is essential to make sure that a sufficient number of quadrature
points has been used by comparing solutions with different numbers quadrature points.
In most cases adaptive quadrature will perform better than ordinary quadrature.
This is particularly the case if the cluster sizes are large and the responses
include (large) counts and/or continuous variables.
Even where ordinary quadrature performs well, adaptive
quadrature often requires fewer quadrature points making it faster.
Since heavy computation is involved,
gllamm can be slow when there
are many latent variables (random effects or factors), many parameters to be estimated and many
observations. There are two ways of speeding up the program:
- Collapse the data as much as possible and use the
The time required to estimate a model is approximately proportional to the
number of observations in the collapsed dataset. In the case of categorical
responses and covariates, datasets can often be collapsed considerably
(see the manual for examples).
- Start with the simplest model of interest (or fewer integration points) and
introduce additional features (more integration points), passing the parameter
estimates from the simpler model to
gllamm as starting values for the
more complicated model using the
gllapred is a 'post-estimation command'
gllamm. It can be used to obtain empirical Bayes predictions of
the random effects or factors (also known as posterior means, factor scores or shrinkage estimators)
for all GLLAMMs. Posterior standard deviations are also provided as well as various
other options (see
help gllapred after installation).
gllasim is a 'post-estimation command'
gllamm. It can be used to simulate the responses
or latent variables for a model just estimated using
help gllasim after installation).
The main citations are Rabe-Hesketh, Skrondal, and Pickles (2005) on estimation,
showing that adaptive quadrature is accurate, and Rabe-Hesketh, Skrondal,
and Pickles (2004) on the GLLAMM framework, showing the range of models
that can be estimated in
for specific special cases of models are given below.
For generalized linear mixed models or multilevel regression
models and adaptive quadrature:
For factor, IRT or structural equation models:
For nominal data, discrete choice data and rankings:
For nonparametric maximum likelihood estimation (NPMLE) and
covariate measurement error models:
For complex survey data:
For twin and family data:
For empirical Bayes prediction: