Regression and Multilevel Modeling Approaches

1. Regression and Multilevel Modeling Approaches • Primer on regression analysis and multilevel modeling • Single-case applications of these procedures • Conceptual and procedural issues

2. Regression Imagine a scatter plot showing the relationship between motivation and achievement.

3. Regression allows us to summarize the relationship between the variables.

4. Often when we think of regression we think of each data point coming from a different individual, but all the observations could come from the same individual.

5. Now imagine we have multiple observations on multiple individuals. Cindy George John Lucy

6. A separate regression could be obtained for each of the individuals. Would the slopes (π1) be the same for everyone? Would the intercepts (π0) be the same for everyone?

7. Research Questions There are a variety of questions we may seek to answer. What is Cindy’s initial status on the outcome of interest? π0

8. How much does Cindy change? Rise rise/run = π1 Run

9. What is the average initial status of the participants?

10. What is the average change of the participants?

11. To what extent do participants vary in their initial status?

12. To what extent do participants vary in their growth?

13. To what extent does initial status relate to growth?

14. To what extent does initial status relate to predictors of interest? Females Males

15. To what extent does growth relate to predictors of interest? Females Males

16. Multilevel Modeling Multilevel modeling provides a method for answering all these questions. average intercept average slope

17. Multilevel Modeling effect of predictor X on the intercept effect of predictor X on the slope

18. Single-Case Applications With single-case applications the questions may look a little different because the designs often have phases and the focus tends to be on the treatment effect.

19. Single-Case Research Questions What is the treatment effect of for Jody? Effect = π1

20. What is the average effect for the participants? Average Effect = β10 Average Baseline Level = β00

21. Does the size of the effect vary across participants?

22. To what extent is the effect related to predictors of interest? ADD Non-ADD

23. Issues to Keep in Mind There needs to be a match between the trajectory specified in the model and what is seen in the data Effect = b1? This seems incorrect

24. What is seen may require specification of a complex growth trajectory Do you think specification tends to be easier when there are more or less observations in a phase?

25. Correct model specification requires more than just correctly specifying the growth trajectory Should you assume the errors (e, r0, r1) are independent? Normally distributed?

26. Multilevel models were developed for large sample size conditions, but single-case applications tend to have a very small number of cases. Given small sample sizes the variances (e.g. variance in the treatment effect across participants) will generally be more poorly estimated than the averages (e.g. the average treatment effect).