Psychology 202bAdvanced Psychological

Statistics, II

April 5, 2011

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

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.

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.

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?

Assumptions

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

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.

Software for SEM

• Lisrel• Amos• EQS• Mplus (free demo version available)• R’s sem package

Introducing Mplus

• A free demonstration version can be downloaded here.

• Demo version is limited to 2 exogenous and 6 endogenous variables.

• Otherwise, fully functional.

Using Mplus

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

analysis.

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.

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.• Comparing models:

– The likelihood-ratio test

Next time

• Exploratory factor analysis.