1. CJT 765: Structural Equation Modeling Class 12: Wrap Up: Latent Growth Models, Pitfalls, Critique and Future Directions for SEM

2. Outline of Class Issues related to Final Project Latent Growth Models using Mean Structures Pitfalls Critique Future Directions Concluding Thoughts

3. Issues related to Final Project Final draft due Monday Apr. 18, 9 a.m., but never has to be turned in understanding you then won’t get feedback for presentation. You do:  have to have measurement and structural components in model  need to talk about theoretical background, measures, and implications as well as model testing  have to test measurement components first, structural and measurement components combined second  have to consider improving your initial model, considering removing paths, removing variables, or adding correlations or paths You don’t:  have to test more than 1 model  have to test the most complex model possible  have to have an adequate model

4. Latent Growth Models Latent Growth Models in SEM are often structural regression models with mean structures

5. Mean Structures Means are estimated by regression of variables on a constant Parameters of a mean structure include means of exogenous variables and intercepts of endogenous variables. Predicted means of endogenous variables can be compared to observed means.

6. Principles of Mean Structures in SEM When a variable is regressed on a predictor and a constant, the unstandardized coefficient for the constant is the intercept. When a predictor is regressed on a constant, the undstandardized coefficient is the mean of the predictor. The mean of an endogenous variable is a function of three parameters: the intercept, the unstandardized path coefficient, and the mean of the exogenous variable.

7. Additional Mean Structure Principles The predicted mean for an observed variable is the total effect of the constant on that variable. For exogenous variables, the unstandardized path coefficient for the direct effect of the constant is a mean; for endogenous variables, the direct effect of the constant is an intercept but the total effect is a mean.

8. Requirements for LGM within SEM continuous dependent variable measured on at least three different occasions scores that have the same units across time, can be said to measure the same construct at each assessment, and are not standardized data that are time structured, meaning that cases are all tested at the same intervals (not need be equal intervals)

9. Steps for Latent Growth Models within SEM Evaluate a change model that involves just the repeated measures variables Add predictors to the model by regressing the latent growth factors on the predictors

10. Pitfalls--Specification Specifying the model after data collection Insufficient number of indicators. Kenny: “2 might be fine, 3 is better, 4 is best, more is gravy” Carefully consider directionality Forget about parsimony Add disturbance or measurement errors without substantive justification

11. Pitfalls--Data Forgetting to look at missing data patterns Forgetting to look at distributions, outliers, or non-linearity of relationships Lack of independence among observations due to clustering of individuals

12. Pitfalls—Analysis/Respecification Using statistical results only and not theory to respecify a model Failure to consider constraint interactions and Heywood cases (illogical values for parameters) Use of correlation matrix rather than covariance matrix Failure to test measurement model first Failure to consider sample size vs. model complexity

13. Pitfalls--Interpretation Suggesting that “good fit” proves the model Not understanding the difference between good fit and high R 2 Using standardized estimates in comparing multiple-group results Failure to consider equivalent or (nonequivalent) alternative models Naming fallacy Suggesting results prove causality

14. Critique The multiple/alternative models problem The belief that the “stronger” method and path diagram proves causality Use of SEM for model modification rather than for model testing. Instead:  Models should be modified before SEM is conducted or  Sample sizes should be large enough to modify the model with half of the sample and then cross-validate the new model with the other half

15. Future Directions Assessment of interactions Multiple-level models Curvilinear effects Dichotomous and ordinal variables

16. Final Thoughts SEM can be useful, especially to:  separate measurement error from structural relationships  assess models with multiple outcomes  assess moderating effects via multiple-sample analyses  consider bidirectional relationships But be careful. Sample size concerns, lots of model modification, concluding too much, and not considering alternative models are especially important pitfalls.