1. An Introductory Tutorial
Mixed Linear Models
An Introductory Tutorial

2. Other random effects Random slope Example:
If subjects in a group therapy trial are split into classes of size 10 with different therapists, we would expect that group dynamics, and therapist would effect how well the group therapy treatment worked. Thus treatment is a random effect, dependant on which therapist is drawn from the population of all therapists to teach the class, and which peers are drawn from the population to take part in the class.
Outcome at last time point
Intercept
Treatment Effect
Random effect of Treatment
Random intercept
Individual Error

3. Longitudinal Data: Preliminaries
The Citalopram study (PI Dr. Zisook)
Does Citalopram reduce the depression in schizophrenic patients with subsyndromal depression
Two Groups: Citalopram vs. Placebo
8 time points: baseline, week 1, 2, 4, 6, 8, and 12
Outcome measures: CDRS, and HAM-17
There were two sites, but we will only look at the Cincinnati site.
First thing’s first, what does our data look like over time?

4. Longitudinal Data: Preliminaries
Line Graphs

5. Longitudinal Data Mean Structures
What kind of treatment trajectory do your subjects take?
Mean Structures
Linear
Assumes that subjects improve steadily aX+b
Quadratic
Subjects’ follow a part of or a parabola cX^2+bX+a
Cubic
Subjects’ follow a part of or a cubic dX^3+cX^2+bX+a
Log
Decreases/Increases quickly, then slows
1/x
Decreases/increases to a floor/ceiling
Dummy coding
Assumes no particular treatment progression

6. Longitudinal Data
Linear
The Data Assuming linear

7. SPSS

8. Longitudinal Data
Quadratic
The Data Assuming Quadratic

9. SPSS

10. Longitudinal Data
Cubic
The Data Assuming Cubic

11. SPSS

12. Longitudinal Data
logarithmic
The Data Assuming Log(week+1)

13. SPSS

14. Longitudinal Data
Inverse
The Data Assuming 1/ (week+1)

15. SPSS

16. Longitudinal Data
No Assumptions
The Data Dummy coded

17. SPSS