Examples from Singer’s Using SAS Proc Mixed to Fit Multilevel Models…

1. Examples from Singer’s Using SAS Proc Mixed to Fit Multilevel Models… “To use the paper effectively, … in particular the reader must understand: • The difference between a fixed effect and a random effect • The notion of multiple levels with a hierarchy • The notion that error variance-covariance matrix can take on different structures • That centering can be a helpful way of parameterizing the models so that the results are more easily interpreted”

2. Example 1 in HLM: Unconditional Means Model • Focus on showing how to make .mdm file based on a single Stata file • Decomposition of variance into between and within variance • Intraclass correlation • Exploring the data graphically: • FileGraph Databox-whisker plots (outcome variable) • FileGraph Dataline plots, scatter plots (outcome variable on a predictor variable)

3. Example 2 in HLM: Include both level-1 and level-2 predictors • Level-1 variable SES is group-mean centered • Using level-2 variables to model random intercept and random slope • Showing the mixed model version

4. Continued… • Estimation method: REML vs. ML • Hypothesis testing

5. Example 3 in HLM: Unconditional Linear Growth Model • Use existing .mdm file to build up a model • Exploring the data graphically • Exploring the model graphically

6. Example 1 in MLwiN: Unconditional Means Model • Focus on showing how to input data • ASCII format file (tab delimited file)

7. Continued… • Stata2mlwin by Michael Mitchell (ATS), creating an ASCII data file and an MLwiN command file (.obe file) to read the ASCII file with variable names into MLwiN • stata2mlwin using hsb12, replace

8. Continued… • REML vs. ML • Decomposition of variance into between and within variance • Intraclass correlation

9. Example 2 in MLwiN: Include both level-1 and level-2 predictors

10. Example 3 in MLwiN: Unconditional Linear Growth Model

11. Model-based Graphics

12. Model-based Graphics