March 10 – March 14, 2008
Jeroen
K. Vermunt
(Department
of Methodology and Statistics, Tilburg University)
This
seminar introduces you to the most recent developments in the field of
latent variable modelling. Techniques that were originally developed fully
separate from one another turn out to be special cases of the broad family
of generalized latent variable models (GLVMs). This family includes latent
class analysis, finite mixture models, factor analysis, item response theory
(IRT) models, multilevel models, panel regression models, as well as models
for dealing with missing data and selection bias. Recently, interesting
hybrids combining elements of these special cases have been proposed, such
as mixture factor analysis and IRT and multilevel variants of latent class
analysis and IRT models.
In this
course, I will introduce you into the framework of generalized latent
variable modelling. I will take the most important special cases – mixture,
IRT, factor, growth and multilevel models – as the starting point and from
there elaborate on the connections between these. For example, I will show
that an IRT model can be defined as a multilevel model, that one can perform
multilevel analysis using mixture regression techniques, and that latent
class analysis can be used as a nonparametric or semiparametric IRT or
factor model. I will also pay attention to various recent developments that
are of great interest, such multilevel growth mixture modelling, multilevel
latent class analysis, and hidden Markov modelling. The two main application
types that I will focus on are clustering and scaling on the one hand and
dealing with dependent observations and multilevel modelling on the other
hand. Not only empirical applications, but also technical issues such as
maximum likelihood estimation and numerical integration will be discussed.
The
afternoon sessions of the seminar will be held in a computer lab. This means
that it will not only be theoretical but also practical. You will learn how
to set up the GLVMs of interest with specialized software that I developed
(the new syntax version of Latent GOLD 4.5), as well how to program simple
GLVMs on your own, for example, with the Excel solver or with the maximum
likelihood estimation routines available in packages like R and Stata.
Reading:
Skrondal, A. and Rabe-Hesketh, S. (2004).
Generalized latent variable modeling. Chapman & Hall.
Vermunt, J.K. and Magidson, J. (2005). Technical guide
for Latent GOLD 4.0: Basic and advanced. Statistical Innovations. (www.statisticalinnovations.com/products/LGtechnical.pdf)
Timetable of the 3rd week:
Topics in three-mode analysis
