HLM

What is HLM?

HLM adjusts the models to the result variables that generate a linear model with explanatory variables that account for variations at each level, using variables specified at each level. HLM not only estimates the model coefficients at each level, but also predicts the random effects associated with each sampling unit at each level. Although commonly used in educational research due to the prevalence of hierarchical structures in data in this field, it is suitable for use with data from any research field that has a hierarchical structure. This includes longitudinal analysis, in which repeated measurements of an individual can be nested in the individuals under study. In addition, although the above examples imply that members of this hierarchy at any of the levels are nested exclusively within a member at a higher level,

HLM allows continuous, countable, ordinal and nominal result variables and assumes a functional relationship between the expectation of the result and a linear combination of a set of explanatory variables. This relationship is defined by an appropriate link function, for example, the identity link (continuous results) or the logit link (binary results).

In HLM, unprecedented flexibility in multilevel and longitudinal data modeling was introduced with the inclusion of three new procedures that deal with binary response, counting, ordinal and multinomial (nominal) variables, as well as continuous response variables for hierarchical linear models of normal theory. HLM introduced nested four-level models for cross-sectional and longitudinal models and four-way cross-mixed and nested models. Hierarchical models with dependent random effects (spatial design) were added. Another new feature was the new flexibility in estimating hierarchical generalized linear models through the use of gauss-hermite adaptive squaring (AGH) and high-order Laplace approximations for maximum probability. It has been shown that the AGH approach works very well when cluster sizes are small and the variation components are large. The high-order Laplace approach requires slightly larger cluster sizes, but allows for an arbitrarily large number of random effects (important when cluster sizes are large).

In HLM, the ability to estimate an HLM from incomplete data was also added. This is a fully automated approach that generates and analyzes multiplied datasets from incomplete data. The model is fully multivariate and allows the analyst to strengthen the imputation through auxiliary variables. This means that the user specifies the HLM; the program automatically searches the data to find out which variables have missing values, and then estimates a multivariate hierarchical linear model ("imputation model") in which all variables with lost values are regressed on all variables with complete data. The program uses the resulting parameter estimates to generate M imputed datasets, each of which is analyzed successively. The results are combined using the "Rubin rules".

Another new feature of HLM is that flexible combinations of fixed interceptions and random coefficients (FIRC) are now included. One concern that may arise in multilevel causation studies is that random effects may be correlated with treatment assignment. For example, suppose treatments are assigned non-randomly to students nested in schools. Estimating a two-level model with random school interceptions will generate bias if random interceptions 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 mean effect of treatment, incorrect standard errors and inadequate interpretation. HLM allows the analyst to combine fixed interceptions with random coefficients into models that address these problems and facilitate a richer summary, including an estimate of the variation of treatment effects and empirical bayes estimates of the specific effects of treatment.

System requirements

Operating system: Windows 7, 8, 10

Min. CPU: Processor 486 or higher

Min. RAM: 16 MB the RAM

Disk space: 10 MB