HLM - Hierarchical Linear and Nonlinear Modeling (HLM)

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).

Four-level nested models:

• Four-level nested models for cross-sectional data (for example, models for item response within students within classrooms within schools).
• Four-level models for longitudinal data (for example items within time points within persons within neighborhoods).

Four-way cross-classified and nested mixtures:

• Repeated measures on students who are moving across teachers within schools over time, or item responses nested within immigrants who are cross-classified by country of origin and country of destination.
• Repeated measures on persons who are simultaneously living in a given neighborhood and attending a given school.

Hierarchical models with dependent random effects: 

• Spatially dependent neighborhood effects.
• Social network interactions.

HLM 7 also offers new flexibility in estimating hierarchical generalized linear models through the use of Adaptive Gauss-Hermite Quadrature (AGH) and high-order Laplace approximations to maximum likelihood. The AGH approach has been shown to work very well when cluster sizes are small and variance components are large. the high-order Laplace approach requires somewhat larger cluster sizes but allows an arbitrarily large number of random effects (important when cluster sizes are large)

New HTML output that supplies elegant notation for statistical models including visually attractive tables is also now available, allowing the user to cut and paste output of interest into manuscripts.

HLM 7 manual

• A hard copy of the HLM 7 manual is not available.
• PDF copies of the HLM 7 manual are available via the HLM 7 Manual option on the Help menu of the full, rental, trial, and student editions of HLM 7 for Windows.