Further Issues for Full Structural Models

Now that we've learned the basics of full structural models, we'll be taking up the following topics in the coming weeks:

Maximum Likelihood Estimation

Equivalent models

Handling single-indicator variables

Negative variances (Heywood Cases)


Equality constraints (these lecture notes also touch briefly on longitudinal models and multiple-group analyses)

Longitudinal (panel) models

Multiple-Group Modeling (see notes on equality constraints above; Kyle Gillett dissertation in links section to the right; and this article, which we'll revisit from when we learned about measurement and structural models)

Dyadic analysis in SEM (Actor-Partner Interdependence Model)

Running an AMOS model off of a published correlation/covariance matrix from the literature

Software comparison: AMOS vs. Mplus

Advanced Applications

Latent Growth Modeling (here and here)

Compared to the more piecemeal/incremental cross-lagged panel models for longitudinal analysis, latent growth models test for predictors and correlates of respondents' long-term growth trajectories (see cannon-ball analogy). Thanks to Tim and Xiaohui for photographing the board after class on May 1, 2012. Some illustrative references on latent growth modeling are:

Barnes, G. M., Reifman, A. S., Farrell, M. P., & Dintcheff, B. A. (2000). The effects of parenting on the development of adolescent alcohol misuse: A six-wave latent growth model. Journal of Marriage and the Family, 62, 175-186.

Wampler, R. S., Munsch, J., & Adams, M. (2002). Ethnic differences in grade trajectories during the transition to junior high. Journal of School Psychology, 40, 213-237.

Partial Least Squares (Alternative to Conventional SEM for Small Samples)

University-Quality Assignment

The following is the model for the new assignment. You will run the model twice, once without the three red-dashed paths and once with them. We will learn about comparative model testing.

Here's a direct link to the figure we recently looked at regarding where variances are located in full structural models, as well as how degrees of freedom are determined in a full structural model.

The model also makes salient the issue of outliers, in particular that Harvard's endowment (and to a lesser extent those of a few other institutions) are so much larger than most others. Harvard and these other elite universities have endowments in the billions, whereas many other schools have endowments well under 1 billion. This document discusses approaches to handling outliers; in the past we've used winsorizing, but this year, we'll use a square-root transformation (already implemented in the data set).

There is some evidence that the depressed economy may be "winsorizing" Harvard's endowment, but this didn't occur early enough to be reflected in the data set.

UPDATE (2014): Here's an illustration of the terminology you should use, regarding measurement and structural portions of the model, and factor loadings vs. structural paths. (Thanks to Satabdi for the photo.)