1. Mixed Linear Models An Introductory Tutorial

2. What we have covered!!! The Linear model: Mean Structure or Fixed Effects Errors

3. What we have covered We learned to split the errors into within group, and between group components: Fixed effects Random effects

4. Fixed effects: Linear Including time as a covariate The Data Assuming linear

5. Fixed effects: Unstructured Time included as a fixed factor The Data Dummy coded

6. What about the Random effects Treat = 0,1 Time = 0,1,2… Fixed effects Time as covariate (linear) Treatment by time interaction. (linear, do the treatments progress differently over the study?) What about the errors? They can’t be independent.

7. Error Structures: possible assumptions 1. Each time point affects only the time point directly following it. 2. The correlation between consecutive time points is the same for all time points. (Expect this to be violated when the spacing between time points is unequal) 3. Equal variances across time (Expect this to be violated when there is a ceiling effect)

8. Which error structure should we use? Methods of selection Simple: 1. Use Unstructured -Good option when there are many subjects, and few time points 2. Use Auto-regressive -Good option when there are many equally spaced time points and/or few subjects Data based 1. Use AIC to find error structure -This is an elegant data driven model selection tool

9. Cont. Methods NOT to use: 1. Do not use tests of the significance of the covariance parameters: -Remember that testing the random effects parameters can not be done with SPSS 2. Do not pick the structure that makes your research findings significant!! -This is fraud

10. Akaike’s Information Criterion Akaike’s Information Criterion (AIC) is a measure of how well the model fits the data that penalizes models with lots of parameters.  A good model should fit the data closely (i.e. have little unaccounted for variance), with the fewest parameters possible. The principle is that the simplest model that provides a good accounting of the data is probably the best one.  The smaller the AIC the better.  So, if a model fit with an AR(1) structure has an AIC of 781.9, and when it is fit with TOEP it has an AIC of 780.5, then we should use TOEP. The extra parameters in the TOEP structure are worth it.

11. The AIC in SPSS This is the AIC for the model The BIC is also a similar measure that can be used

12. Our Dataset The Citalopram study (PI Dr. Zisook) Does Citalopram reduce the depression in schizophrenic patients with subsyndromal depression Two Groups: Citalopram vs. Placebo 3 time points: baseline, week 0, 8, and 12 Outcome measures: PANSS, CDRS, and HAM-17 There were two sites, but we will only look at the Cincinnati site.