General information on
making the MDM file, model specification, graphing options
and output files, which is intended as an introduction to
HLM, can be found here. The discussion that follows assumes
the use of the Windows graphical user interface of HLM in
performing the analysis. It is, however, also possible to
run HLM in batch/interactive mode.
To run an analysis in HLM,
four steps are required:
- The type of
model to be fitted must be decided on.
- An appropriate
MDM file must be created.
- The model is
specified and various statistical and output options specified.
- The model is
run, after which model-based graphs can be obtained.
To fit models in HLM, 8
statistical applications are used: HLM2, which fits 2-level
linear and nonlinear (HGLM) models; HLM3, which fits 3-level
linear/nonlinear models; HLM4, which fits 4-level linear/nonlinear
models; HMLM, which fits hierarchical multivariate 2-level
linear models; HMLM2, which fits hierarchical multivariate
3-level models; HCM2, which fits 2-level crossed-and-nested
models, ; HCM3, which fits 3-level crossed-and-nested models;
and HLMHCM, which fits linear models with crossed-and-nested
random effects. For more on the types of models, please see
the type of model to be fitted.
For specific examples of each step for the different modules,
please see below.
HLM analyses are based
on Multivariate Data Matrix (MDM) files. Making the MDM file
is the first step in analyzing data using HLM. Users may construct
the MDM directly from different types of input files including
SPSS, ASCII, SAS, SYSTAT and STATA, or indirectly from many
additional types of data file formats through the third-party
software module included in the HLM program.
For more detail, please
select one of the following:
Examples for HLM3 and HMLM2
were not included, as it would, to a very large extent, be
a duplication of the material for HLM2 and HMLM. SPSS input
was used as this is the most common approach used by HLM users.
Fully annotated examples
of a 2-level linear (HLM2) model, a 2-level crossed-and-nested
model (HCM2) and a hierarchical multivariate linear model
(HMLM) are available. A similar approach as in 2 was followed
for model specification, due to the close similarity between
2-level (HLM2) and 3-level (HLM3) models, and 2-level multivariate
linear (HMLM) and 3-level multivariate linear (HMLM2) models.
HLM also offers data-and
model-based graphing options. Data-based graphing options
include group-specific scatter plots, line plots, and cubic
splines that can be color coded by values of predictor variables;
box-plots displayed for overall data and data grouped within
higher-level units. For examples of the data-based graphs,
please select one of the following links:
- Box and whisker plots, which
can be used to display univariate distributions of level-1
variables for each level-2 unit, with and without a level-2
- Line plots, where, for example,
level-1 repeated measures observations are joined by lines
to describe changes or developments over time during the
course of the research study.
- Scatter plots, which can
be used to explore bivariate relationships between level-1
variables for individual or a group of level-2 units, with
and without controlling level-2 variables.
HLM provides graphing options
to display the relationships between the outcome and the predictor(s)
based on the final analytic results. The options allow us
to visually represent the results of the models for the whole
or a subset of population, and to graphically examine underlying
model assumptions as well. These options are available after
running an analysis - for data-based graphics that can be
obtained prior to analysis, please see data-based graphs options
Model-based graphing options
available in HLM include graphing of group-specific equations,
box-plots of level-1 residuals for each group, plots of residuals
by predicted values for each group, posterior credibility
intervals for random coefficients. For three-level models,
level-1 trajectories are displayed in separate graphs or grouped
by level-3 units. Graphs can be color coded by values of predictor
Five options are available:
In addition, HLM offers
the user the option to specify a variety of outcome variable
types and a choice of estimation method. As data analyzed
with HLM are frequently from complex surveys, the option to
include weights at the various levels of the model is also
offered. For more on these additional features of HLM please