An Introductory Tutorial Mixed Linear Models An Introductory Tutorial

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

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?

Longitudinal Data: Preliminaries Line Graphs

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

Longitudinal Data Linear The Data Assuming linear

SPSS

Longitudinal Data Quadratic The Data Assuming Quadratic

SPSS

Longitudinal Data Cubic The Data Assuming Cubic

SPSS

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

SPSS

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

SPSS

Longitudinal Data No Assumptions The Data Dummy coded

SPSS