CJT 765: Structural Equation Modeling

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 LGMwithin 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 R2 • 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.