 |
In social research
and other fields, research data often have a hierarchical
structure. That is, the individual subjects of study may be
classified or arranged in groups which themselves have qualities
that influence the study. In this case, the individuals can
be seen as level-1 units of study, and the groups into which
they are arranged are level-2 units. This may be extended
further, with level-2 units organized into yet another set
of units at a third level. Examples of this abound in areas
such as education (students at level 1, schools at level 2,
and school districts at level 3) and sociology (individuals
at level 1, neighborhoods at level 2). It is clear that the
analysis of such data requires specialized software. Hierarchical
linear and nonlinear models (also called multilevel models)
have been developed to allow for the study of relationships
at any level in a single analysis, while not ignoring the
variability associated with each level of the hierarchy.
The HLM program can
fit models to outcome variables that generate a linear model
with explanatory variables that account for variations at
each level, utilizing variables specified at each level. HLM
not only estimates model coefficients at each level, but it
also predicts the random effects associated with each sampling
unit at every level. While commonly used in education research
due to the prevalence of hierarchical structures in data from
this field, it is suitable for use with data from any research
field that have a hierarchical structure. This includes longitudinal
analysis, in which an individual's repeated measurements can
be nested within the individuals being studied. In addition,
although the examples above implies that members of this hierarchy
at any of the levels are nested exclusively within a member
at a higher level, HLM can also provide for a situation where
membership is not necessarily "nested", but "crossed", as
is the case when a student may have been a member of various
classrooms during the duration of a study period.
The HLM program allows
for continuous, count, ordinal, and nominal outcome variables
and assumes a functional relationship between the expectation
of the outcome and a linear combination of a set of explanatory
variables. This relationship is defined by a suitable link
function, for example, the identity link (continuous outcomes)
or logit link (binary outcomes).
 
|