The options available for each module are listed in the overview of modeling options in HLM modules. Methods of estimation offered are discussed in the overview of estimation methods used in HLM.

Getting started: Making the MDM file

The first task in using HLM is to construct the Multivariate Data Matrix (MDM) from raw data or from a statistical package.

Data file(s) must be sorted by the level-2 and, if using HLM3 or HMLM2, the level-3 ID. When creating an MDM file for HCM2, row and column IDs are needed. While it is possible to build the MDM file from a single data file, this option is not suggested when the data file is very large. Information on the rules ID variables have conform to, and the construction of format statements when ASCII files are used as input are given elsewhere.

After identifying the type of model required as described in Step 1, the appropriate option should be selected on the Select MDM type dialog box accessed via the Make new MDM file option on the File menu.

The procedure to create a MDM file consists of three major steps. The user needs to

• Inform HLM of the input and MDM file type.
• Supply HLM with the appropriate information for the data, the command and the MDM files.
• Check if the data have been properly read into HLM.

Once the MDM file is constructed, all subsequent analyses will be computed using the MDM file as input. It will therefore be unnecessary to read the larger (level-1) data file in computing these analyses. The efficient summary of data in the MDM file leads to faster computation. The MDM file is like a "system file" in a standard computing package in that it contains not only the summarized data but also the names of all of the variables.

Users of previous versions of HLM should note that the MDM file format replaces the previously used SSM file format entirely. As such, HLM6 is not downward compatible - to use previously analyzed data in HLM6, a new MDM file has to be created to replace the previously used SSM file.

For examples of the construction of the MDM files for some combinations of data type and HLM module, see the overview of constructing MDM files. Note that MDM files should preferably be given a name with a *.MDM file extension to facilitate easy retrieval at a later date. Specifications of the data used, missing data (if any), etc. are saved in a MDM template file (*.MDMT) file. The MDMT file can be retrieved later to remake or change the contents of the MDM file. Descriptive statistics on all variables included in an MDM file are saved to a file automatically placed in the same folder as the MDM file, with a *.STS file extension. This file can be opened in Notepad, Wordpad, etc. Inspection of this file prior to model specification is imperative.

Getting started: Model specification

Basic model specification has three steps:

• Specifying the level-1 model, which defines a set of level-1 coefficients to be computed for each level-2 unit.
• Specifying a level-2 structural model to predict each of the level-1 coefficients.
• Specifying the level-1 coefficients to be viewed as random or non-random.

After these three steps have been completed, a linear model is obtained. The next phase of model specification is to

• Select the type of outcome variable if running an HGLM model with HLM2 or HLM3.
• Select the level-1 error structure if running an HMLM/HMLM2 model.
• Provide names for the basic output file, the graphing equations file (if required) and to request residual files.

These selections are made using the modules' respective Basic Settings dialog boxes, which are accessed by clicking the Basic Settings option on the main menu bar or the Outcome button at the top left of the modeling window. Options available on this dialog box for the various modules are listed in the overview of modeling options in HLM modules, and the amount of output is controlled via the Output Settings option on the Other Settings menu.

In addition, various statistical options are available. Additionally, the iterative procedure and the amount and type of output can be controlled. Again, these differ by module. Access to the options are via the Other Settings option on the main menu bar. Options accessible via this option for the various modules are listed in the overview of modeling options in HLM modules.

Once model specification has been completed, the model can be saved to a command file (*.mlm file extension). This file can be retrieved for modification at a later stage, and contains all the information for a given model, including the name of the MDM file on which the analysis is based. To do so, use the Save As option on the File menu.

Data-based graphs, that can be used as a exploratory analysis tool prior to running the analysis, are accessed via the Graph Data option for HLM2 and HLM3 only. For more on data-based graphs, see the data based graphs page.

Getting started: Output and model-based graphing

The analysis is performed by clicking the Run Analysis option on the main menu bar after the model specification has been completed and/or the model has been saved.

The standard output file

By default, this file will be named hlm2.txt, hlm3.txt, hmlm.txt, hmlm2.txt or hcm2.txt and will contain the following:

• Ordinary least squares and generalized least squares results for the fixed coefficients defined in the level-2 model.
• Estimates of variance and covariance components and approximate chi-square tests for the variance components.
• A variety of auxiliary diagnostic statistics.
• Additional output for hypothesis-testing procedures and requested optional statistical features.
• Unit-specific and population-average results in the case of HGLM models.
• Output for a number of level-1 error structures, depending on model specification, for HMLM and HMLM2 models.

Residual files

Residual files are created during the analysis in the format specified during Step 2 above, and can be opened in the statistical package of choice for inspection and/or further analysis. Residual files are available for HLM2, HLM3, HGLM and HCM2 models but contents vary according to module.

The level-1 residual file will contain

• level-1 residuals (the differences between the observed and fitted values),
• the fitted values,
• the square root of sigma_squared,
• the values of the level-1 and level-2 predictors entered in the model, and those of other level-1 and level-2 variables selected by the user.
• A level-2 residual file will contain some or all of the following:
  
• EB residuals,
• OL residuals,
• and fitted values for each level-1 coefficient based on the estimated level-2 models
• posterior variances and covariances of the estimates of intercept and slopes
• level-2 predictors used in analysis plus additional level-2 predictors requested by the user for inclusion
• Mahanalobis distance of a unit's EB estimates from its fitted value
• Expected values of the order statistics for a sample of similar size from a population with chi-square(v) distribution
• Three estimates of the level-1 variability: the natural log of the total standard deviation within each unit, the natural log of the residual standard deviation within each unit based on its least squares regression, and the natural log of the residual standard deviation from the final fitted fixed effects model.

A three-level analysis will produce two residual files, one at level-2 and one at level-3. The 3-level residual file contains the EB residuals, the OL residuals, fitted values, posterior variance and covariances; listed by level-3 unit ID.

In the case of HGLM analyses using HLM2 or HLM3, residual file contents are based on the unit-specific model results.

In addition, level-2 predictors can be included in the level-2 residual file and level-3 predictors in the level-3 residual file. However, other statistics provided in the residual file of HLM2, for example the Mahalanobis distance measures, are
not available in the residual files produced by HLM3.

The row residual file (produced only by HCM2) contains the following the Empirical Bayes estimates and its associated posterior variances, and additional predictors as selected by the user for inclusion in the residual file.

The column residual file (produced only by HCM2) contains the Empirical Bayes estimates and its associated posterior variances, and additional predictors as selected by the user for inclusion in the residual file

Variance-covariance matrices of estimates:

In addition, HLM offers output files containing the variance-covariance matrices of estimates of fixed effects and variance-covariance parameters. These can be saved by checking the print variance-covariance matrices option (available for HLM2, HLM3 and HGLM models only) in the Output Settings dialog box accessed via the Other Settings menu. These files can be opened in Notepad, Wordpad etc. In the case of HGLM analyses using HLM2 or HLM3, contents are based on the unit-specific model results.

Model-based graphs:

Finally, HLM offers the option to make model-based graphs after completion of the analysis. HLM2 and HLM3 offers the complete range of graphs, while HMLM, HMLM2 and HCM2 offer a subset of options. Options available on this dialog box for the various modules are listed in the overview of modeling options in HLM modules. Examples can be viewed by looking at the model based graphs page.