1. Graphs in HLM

2. Model setup, Run the analysis before graphing Sector = 0 public school Sector = 1 private school

3. Graph entire model

4. With level 1 predictor

5. Here it is the graph

6. Add level 2 categorical variable

7. And the graph

8. Add level 2 continuous variable

9. What happened if we choose 25 th and 75 th percentiles?

10. We can choose other options, say, 25 th /50 th /75 th percentiles

11. The graph with 3 MEANSES levels

12. More complicated graph

14. Graph level 1 equation

15. The graph with first 10 groups (schools)

16. What if we choose n=160 schools?

17. With level 2 predictor: sector

18. Add level 2 categorical variable

20. Add a level 2 continuous variable

22. Level 1 residual box-whisker To examine distributions of level-1 residuals. Normality assumption Homogeneity of variance

23. Level 1 residual box-whisker

24. Also could add a level 2 predictor

25. Level-1 residual vs predicted value

26. Observe the pattern of residual scatter Level-1 residual vs predicted value

27. Add level 2 - sector

28. One graph per group, multiple graphs per page

30. Level-2 EB/OLS coefficient confidence intervals Compare the estimated empirical Bayes (EB) and OLS estimates of randomly varying level-1 coefficients (intercept and other coefficients).

31. Intercept with level 2 sectors

32. Intercept with level 2 MEANSES

33. Slope of SES

35. Graph data

36. Math regressed on SES (10 schools)

37. One graph per group, multiple graphs per page

39. Longitudinal data

40. Whole model (CB- HLM Longitudinal Example)

42. With gender and year (level 2)

43. Graph data