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  box-whisker plots (outcome variable) File  Graph Data  line plots, scatter plots (outcome variable on a predictor 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) 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 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