HLM 8 for Windows是一套群昱公司代理的多層次模式分析軟體，HLM提供的模型包括2-level models、3-level models、Hierarchical Generalized Linear Models (HGLM)和Hierarchical Multivariate Linear Models (HMLM)等。HLM所發展的階層模型(Hierarchical Linear and Nonlinear Modeling)軟體，包含線性和非線性部分，HLM可以讀取大部份統計軟體的檔案如 SPSS, SAS, SYSTAT及STATA等等。HLM常用於社會科學和行為科學，因為它常有巢狀結構(Nested Structure)的資料，因此需用次模型(Sub-Model)或階層模型(Hierarchical Model)，HLM就是設計來專門解決此類問題的。
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 and with level-3 units organized into another set of units at a fourth level. Examples of this abound in areas such as education (students at level 1, teachers at level 2, schools at level 3, and school districts at level 4) 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).
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