Multiple-Level Data
Recently, increasing attention has been paid to models for describing
data that are collected at several levels. These models are called
multilevel, hierarchical, or mixed models. For example, data may
be
collected on characteristics of children (1st level), classrooms (2nd
level), and schools (3rd level). The researcher may be interested
in
how the outcome variable measured for each child depends on
characteristics of the child, the classroom, and the school. Factors
at
the child level may include sex, race, and socioeconomic status.
Factors at the classroom level may include teaching method and teacher's
level of experience. Factors at the school level may include location
and type of school.
An interesting example of multilevel data collected by Sue Rhee in Tom
Brenna's lab comes from a study in which subjects are randomly assigned
to one of three diets. Fatty acids are measured at the beginning
of the study and at four subsequent weeks. In order to deal with
potential measurement error, two measurements of fatty acids are taken
for each subject at each time period. The study evaluates how two
measurements of fatty acids taken on the same day for the same subject
vary (1st level), how the fatty acids for each subject vary over time (2nd
level), and how the fatty acids vary across subjects depending on the diet
(3rd level).
In multilevel data, a different source of variability is present at each
level. In this second example there are three sources of random
variation in the outcome: 1) the variation between two
measurements
taken on the same subject at the same time, 2) the variation across time
for each subject, and 3) the variation among subjects, after accounting
for the effect of diet. The researcher may be interested in estimating
how much of the total variation comes from each source.
Split-plot and repeated measures experiments and longitudinal studies
are familiar designs that produce multilevel data. In the past,
analysis of data from such designs was problematic if there were
continuous factors or missing data. Specialized software for estimating
multilevel models has been made available over the past few years.
Multilevel models estimated using this software can account for
different factors and different sources of variability at each level.
A future newsletter will discuss and compare this software.
Statistical Consulting staff can help you develop and implement a model
for analyzing multilevel data. We have also researched a number of
publications that address this topic in more detail. A particularly
clear and non-technical article, "An Introduction to Hierarchical Linear
Models", by Carolyn L. Arnold (Measurement and Evaluation in Counseling
and Development, July 1992, pp. 58-90), is available from anyone in the
Statistical Consulting office.
Author: Cara Olsen
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