Steve Raudenbush, University
of Michigan & Tony Bryk,
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applications of HLM analysis of hierarchical data structures
continue to expand as new models are incorporated in the computing
procedures. The models make possible a highly efficient and
informative analysis of complex survey data, including those
from two- and three-stage unbalanced sampling designs, possibly
with explanatory variables and random effects at all three
stages. For example, in studies of factors that influence
year-to-year gains in the achievement of school students,
the level-1 model may describe the course-of-growth in the
achievement of individual students over a number of years,
the level-2 model represents differences between classrooms,
and the level-3 model incorporates effects between schools.
variables specified at each level, the program generates the
linear model with the respective explanatory variables that
account for response variability at each level. The hierarchical
linear analysis not only estimates the model coefficients
at each level, but it also predicts the random effects associated
with each sampling unit at each level.
analyses can now be carried out by full-information maximum
likelihood methods using a combination of EM and Fisher scoring
algorithms for fast and stable convergence to the solution
optimum. These procedures provide standard errors for both
the fixed effects and the variance-covariance components that
describe the random effects.
these analyses were available only for data in which the errors
of prediction at each level could be assumed approximately
normally distributed. New statistical developments now allow
Bernoulli and binomial models for binary data to be analyzed
with a logit link function, and a Poisson model allows count
data to be analyzed with a log link function.
session will cover the principles and assumptions of hierarchical
linear analysis, applications to a wide variety of practical
problems, and the interpretation and reporting of results.
The presentation will include many worked examples and computer
demonstrations. A prerequisite for the workshop is a working
knowledge of simple regression analysis.
you are completely new to multilevel analysis, it is recommended
as a preparation for the workshop to download the free student
edition of HLM and work through some of the examples as described
in HLM's online Help system. The free HLM student edition
may be downloaded from the HLM