Mixed Linear Models

1. 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 • 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

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8. Longitudinal Data Quadratic The Data Assuming Quadratic

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10. Longitudinal Data Cubic The Data Assuming Cubic

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

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

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16. Longitudinal Data No Assumptions The Data Dummy coded

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