HLM Examples

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)

• Creating an MDM file and a command file for an unconditional 3-level model
• Linear growth model

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)

• Two-level multinomial model
• Two-level ordinal model

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)

• Unconditional model
• Conditional model
• Comparison of models

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

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

•  Unconditional linear growth model
• Level-2 and a row-factor prediction model

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)

• A 2-level FIRC model
• A 3-level FIRC model

Augmented imputation models (download data and command files)

• An annotated example of HLM2 analysis of incomplete data

Spatial dependence models (download data and command files)