1. Psychology 202b Advanced Psychological Statistics, II April 5, 2011

2. The Plan for Today Homework and exam remediation Recap of path analysis by hand Assumptions Path analysis using SEM Introducing Mplus Estimating disturbances Assessing model fit

3. Homework Update on where we are. The disk system on faculty.ucmerced.edu thinks it is full. I cannot post sadistic Homework 5. Substitute: one more chance to submit a late homework; your choice which one, but only one.

4. Exam remediation A one-week take-home exam will be available Tuesday. Students who elect to take it to improve their scores will be on their honor to work alone.

5. Path Analysis So far, we have learned that manual path analysis is hard unless the model is saturated. To avoid the pain of the past, I did not make us suffer through unsaturated models by hand. Now that you have learned something about path analysis, what should you ask next?

6. Assumptions Linear relationships. Independence. Normal errors. No reverse causation. Exogenous variables are without error. State of equilibrium. Correct model specification.

7. Path analysis with SEM What if we had a way to select the best solution from the many possible solutions for an over-identified model? Maximum likelihood using the idea that the covariance matrix follows a Wishart distribution. That’s what SEM software does.

8. Software for SEM Lisrel Amos EQS Mplus (free demo version available) R’s sem package

9. Introducing Mplus A free demonstration version can be downloaded here.here Demo version is limited to 2 exogenous and 6 endogenous variables. Otherwise, fully functional.

10. Using Mplus Simple example: multiple regression. A saturated path analysis. An unsaturated path analysis. That is much easier than manual path analysis.

11. Estimating disturbances So far, we haven’t bothered adding disturbances to our path models. Using SEM output, it’s easy. Disturbances are just the square root of the residual variances.

12. Assessing model fit Indices of model fit: –The chi-square (compares the model to the saturated model). –The RMSEA –CFI and TLI Useful reference here.here Comparing models: –The likelihood-ratio test

13. Next time Exploratory factor analysis.