Teaching SEM using OpenMx

Week 6 of the course presents concepts in latent structure and measurement models. We take a look at 3 possible ways of using latent structure to test theories:

1. the number of factors problem, i.e., can we collapse two scales into one;
2. multiple regression using latent variables, i.e, how do we test the prediction of one latent variable from another and what are some limits on our abilities to test such theories; and
3. mediation models with latent variables and some of the limitations on the conclusions that one can draw from fitting mediation models.

This list is for general discussion of the workshop that doesn't neatly fit into one of the days 1-5

In the fifth week of the course, we turn our attention to latent variables.

The lecture begins with a review of transformation matrices and principal components from a theoretic standpoint.

We then see how models that include latent predictors can be estimated and gain an understanding of problems of identification.

Next we fit a bunch of OpenMx models to a simulated data set and see how simple structure can emerge.

This week we start with an introduction to R. Then we introduce the OpenMx data structures and syntax. Next, we work through the same models we used last week.

The third week of the class focuses on path analysis. We calculate the model-expected components of covariance for some regression models using both path analysis tracing rules and the RAM-style matrix calculation of the effects matrix. These same simple regression models will be used next week as we introduce the OpenMx software syntax.

The second week of the class is dedicated to reviewing concepts and definitions from matrix algebra that are useful in specifying, fitting, and -- most important -- understanding SEM models. These notes are derived from the course in matrix algebra taught by Ledyard Tucker and passed on by John Nesselroade. I adapted them and translated them into LaTeX for the slides you see here.