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 specific examples for the different modules, please see below.

Two-level models based on the HSB data (download data and command files)

- Creating an MDM file and a command file for a 2-level model
- Checking homogeneity of level-1 variance assumption
- Modeling heterogeneous level-1 variance
- Exploratory analysis of potential level-2 predictors
- General linear hypothesis testing
- Constraining fixed effects

Two-level spatial analysis model (download data and command files)

Three-level models based on the EG data (download data and command files)

Four-level models based on the literacy data (download data and command files)

- Creating an MDM and command file for an unconditional four-level model for the literacy data
- Conditional four-level model for the literacy data

HGLM models based on the Thai data (download data and command files)

- Two-level Bernoulli model
- Two-level binomial model
- Two-level Poisson model (constant exposure)
- Two-level Poisson model (variable exposure)

HGLM models based on the Teacher data (download data and command files)

HMLM models based on the NYS data (download data and command files)

- HMLM model for the NYS data
- HMLM model with log-linear model for level-1 variance
- HMLM model with first-order autoregressive model for level-1 variance
- Latent variable analysis using HMLM

HMLM2 model based on the EG data (download data and command files)

HCM2 models based on the Scotland data (download data and command files)

HCM3 model for the Growth data (download data and command files)

HLMHCM models for the Growth data (download data and command files)

Graphing (download data and command files)

Data based graphs:

- 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 classification variable.
- 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.

Model based graphs

- Model-based graphs
- Plots for individual level-2 units using the level-1 equation instead of the entire model (Level-1 equation modeling)
- Level-1 residual box-and-whisker plots
- Level-1 residual vs predicted value plots
- Level-2 EB/OLS coefficient confidence intervals
- Three-level graphing

FIRC models (download data and command files)

Augmented imputation models (download data and command files)