Dear Allstaters,
Please find below information about a forthcoming RSS Leeds/Bradford
Local Group Meeting. Further details can be found on our webpage:
http://www.maths.leeds.ac.uk/statistics/rss/
All welcome!
Regards, Paul
===================================================================
Dr. Paul D. Baxter
Secretary/Treasurer, RSS Leeds/Bradford Local Group,
Department of Statistics, University of Leeds, Leeds, LS2 9JT, UK.
-------------------------------------------------------------------
Leeds/Bradford: Wednesday 22nd March, 4pm, Level 8 (Room Y), Worsley
Building, Leeds University (Tea from 3.30pm)
Jeroen Vermunt (University of Tilburg, Netherlands)
Multilevel Variants of Discrete and Continuous Latent Variable Models
I will present a framework for multilevel latent variable modelling as
(partially) implemented in the Latent GOLD software package. This
framework includes models with discrete and continuous latent variables
(LVs), as well as combinations of these.
One of the special cases, in which both the lower- and higher-level LVs
are discrete, is the hierarchical variant of the latent class (LC) model
proposed by Vermunt (2003). More specifically, lower-level units (cases)
are clustered based on their observed responses as in a standard latent
class model, whereas higher-level units (groups) are clustered based on
the likelihood of their members be in one of the case-level clusters.
Application types include repeated measures and three-way data collected
via panel or experimental designs, as well as multilevel data, such as
from pupils nested in schools, employees nested in firms, citizens
nested in regions, and consumers nested in stores.
Another variant is the multilevel IRT model proposed by Fox and Glas
(2001), in which both the lower-and higher-level LVs are continuous and
the response variables are discrete. Putting together all possible
combinations, we get the following scheme:
Lower-Level LVs
Higer-Level LVs Continuous Discrete
Continuous I. Multilevel random-effects IRT / FA II. Multilevel
random-effects LC
Discrete III. Multilevel mixture IRT / FA IV. Multilevel mixture LC
Whereas variants I, II, and IV have already been explored, variant III -
in which the lower-level LVs are assumed to be continuous and the
higher-level LV is discrete - has not been studied. This specific
combination gives rise to a mixture IRT or FA model in which the mixture
components are formed by groups rather than by cases, as would be the
case in a standard mixture IRT or mixture FA model; in other words,
groups are clustered based on the trait/factor means and variances of
their members, and possibly on (other) model characteristics that may
differ across groups, such as item difficulties and discriminations.
Overall, this seems to be a good way to identify group differences as
well problematic groups in terms of the quality measurement instrument
(item bias) when the number of groups is too large for a standard
multiple-group analysis.
ML estimation of the multilevel LV models by means of the EM algorithm
is straightforward, but requires a special implementation of the E step
of the EM algorithm. The E step of the algorithm is similar to the
well-know forward-backward algorithm for hidden Markov modelling.
Besides discussing the framework and estimation issues, I will present
an empirical application in which I will focus on the unexplored, but
rather interesting, variant III from the above table.
|