HLM fits 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.

HLM 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).

Due to increased interest in multivariate outcome models, such as repeated measurement data, contributions by Jennrich & Schluchter (1986), and Goldstein (1995) led to the inclusion of multivariate models in most of the available hierarchical linear modeling programs. These models allow the researcher to study cases where the variance at the lowest level of the hierarchy can assume a variety of forms/structures. The approach also provides the researcher with the opportunity to fit latent variable models (Raudenbush & Bryk, 2002), with the first level of the hierarchy representing associations between fallible, observed data and latent, "true" data. An application that has received attention in this regard recently is the analysis of item response models, where an individuals "ability" or "latent trait" is based on the probability of a given response as a function of characteristics of items presented to an individual.

In HLM 7, unprecedented flexibility in the modeling of multilevel and longitudinal data was introduced with the inclusion of three new procedures that handle binary, count, ordinal and multinomial (nominal) response variables as well as continuous response variables for normal-theory hierarchical linear models. HLM 7 introduced four-level nested models for cross-sectional and longitudinal models and four-way cross-classified and nested mixture models. Hierarchical models with dependent random effects (spatial design) were added. Another new feature was 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).

In HLM 8, the ability to estimate an HLM from incomplete data was added. This is a completely automated approach that generates and analyses multiply imputed data sets from incomplete data. The model is fully multivariate and enables the analyst to strengthen imputation through auxiliary variables. This means that the user specifies the HLM; the program automatically searches the data to discover which variables have missing values and then estimates a multivariate hierarchical linear model (”imputation model”) in which all variables having missed values are regressed on all variables having complete data. The program then uses the resulting parameter estimates to generate M imputed data sets, each of which is then analysed in turn. Results are combined using the “Rubin rules”.

Another new feature of HLM 8 is that flexible combinations of Fixed Intercepts and Random Coefficients (FIRC) are now included in HLM2, HLM3, HLM4, HCM2, and HCM3. A concern that can arise in multilevel causal studies is that random effects may be correlated with treatment assignment. For example, suppose that treatments are assigned non-randomly to students who are nested within schools. Estimating a two-level model with random school intercepts will generate bias if the random intercepts are correlated with treatment effects. The conventional strategy is to specify a fixed effects model for schools. However, this approach assumes homogeneous treatment effects, possibly leading to biased estimates of the average treatment effect, incorrect standard errors, and inappropriate interpretation. HLM 8 allows the analyst to combine fixed intercepts with random coefficients in models that address these problems and to facilitate a richer summary including an estimate of the variation of treatment effects and empirical Bayes estimates of unit-specific treatment effects. This approach was proposed in Bloom, Raudenbush, Weiss and Porter (2017).

Compatibility