1. Structural Equation Modeling Hossein Salehi Jenny Lehman Jacob Tenney October, 2015

2. L EARNING O BJECTIVES  Understand Latent Variables (Ghost Chasing)  Definition of Structural Equation Modeling (SEM)  SEM Model  Goals in PFP  SEM Assumptions  Basic Components of SEM  Calculate Implied Covariance Matrix  SEM Approach  SEM in R  SEM’s Advantages

3. G HOST C HASING  We are in the business of Chasing “Ghosts” “Ghost” diagnoses Measuring “Ghosts” Exchanging one “Ghost” for another “Ghost” (Ainsworth 2006)

4. LATENT VARIABLES ▪ Variables of Interest ▪ Not directly measured or manifest ▪ Common ▪ Intelligence ▪ Trust ▪ Democracy ▪ Disturbance variables (Paxton)

5. F AMILY T REE OF SEM  Factor Analysis  Exploratory Factor Analysis  Confirmatory Factor Analysis Now it is … Structural Equation Modeling (SEM)’s turn !!! (Hubona)

6. SEM M ODEL

7. … Risk Requirement … Risk Tolerance SEM IN PFP  Let’s run some data in R. (FinaMetrica)

8.  Observed (or manifest, measures, indicators)  Latent (or factor, constructs) P ATH D IAGRAM S YMBOLS  Direction of influence, relationship from one variable to another  Reciprocal effects  Correlation or covariance (Sudano & Perzvnski, 2013)

9. … Risk Requirement … … Risk Tolerance … Structural Model Two Measurement Models E STABLISHING P ATH D IAGRAM

10. G OALS OF SEM ▪ To determine whether the theoretical model is supported by sample data or the model fits the data well. ▪ To understand the complex relationships among constructs. ▪ To compare the covariance matrix from all manifest variables (from the data collected) to the model-implied covariance matrix of the manifest variables. (Oct. 1 Class Presentation)

11. SEM A SSUMPTIONS  Univariate and multivariate normality (In theory but never in practice)  Independence of observations  Linearity in the relationships between your variables  Adequate sample size  The factors and measurement errors are uncorrelated. Cov(F, ε) = 0 (Oct. 1 Class Presentation)

12. SEM M ODEL (Steiger)

13. SEM G ENERAL M ODEL (Steiger)

14.  Let’s unpack the structural model: SEM G ENERAL M ODEL  Let’s unpack the two measurement models: (Steiger)

15. ▪ Error terms covariance matrix SEM G ENERAL M ODEL (Steiger)

16. ▪ Implied covariance matrix SEM G ENERAL M ODEL (Steiger)

17. … Risk Requirement … … Risk Tolerance … E STABLISHING P ATH D IAGRAM

18. P OLITICAL D EMOCRACY (Bollen, 1989)

19. E XAMPLE: P OLITICAL D EMOCRACY M ODEL IND 60DEM 60 (Bollen, 1989)

20. SEM M ODEL FOR D EMOCRACY E XAMPLE

21. 2/20/2006LATENT VARIABLE MODELS21 I MPORTANT M ATRICES

22. 2/20/2006LATENT VARIABLE MODELS22 I MPORTANT M ATRICES

23. A PPROACH TO SEM  Model Specification Creating a hypothesized model that you think explains the relationships among multiple variables Converting the model to multiple equations  Model Estimation Technique used to calculate parameters E.G. - Maximum Likelihood (ML), Ordinary Least Squares (OLS), etc. (Stevens, 2009)

24.  SEM can address the directional effects between latent variables, whereas factor analysis does not model relations because it assumes factors are independent.  Unlike factor analysis, SEM allows you to restrict some of loadings to zero to see how this changes the outcome. (Dr. Westfall) SEM A DVANTAGES

25.  Missing data  Can be dealt with in the typical ways (e.g. regression, EM algorithm, etc.)  Most SEM programs will estimate missing data and run the model simultaneously C ONSIDERATION IN A PPLYING SEM

26. C ONCLUSION Now we know how to use SEM to find the ghosts !!!!!!

27. R EFERENCES ▪ Ainsworth, A. (2006). "Ghost Chasing": Demystifying Latent Variables and SEM. Retrieved from UCLA. ▪ Bollen, K.A. (1989). Structural Equations with Latent Variables. John Wiley & Sons. ▪ Hubona, G. (2015). Structural Equation Modeling (SEM) with Lavaan. Udem. ▪ Iacobucci, D. (2009). Everything you always wanted to know about SEM (structural equations modeling) but were afraid to ask. Journal of Consumer Psychology, 19(Oct), 673-680. ▪ Paxton, P. (n.d.). Structural Equation Modeling: An Overview. ▪ PIRE. (2007). Structural Equation Modeling Workshop. ▪ Rosseel, Y. (2012). Lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 47(May), 2-36. ▪ Stevens, J. (2009). Structural Equation Modeling (SEM). University of Oregon. ▪ Steiger, J.H. (n.d.). LISREL Models and Methods. ▪ Sudano, & Perzynski. (2013). Applied Structural Equation Modeling for Dummies, by Dummies. Retrieved from Indiana University, Bloomington. ▪ FinaMetrica ▪ Wikipedia ▪ Oct. 1 Group ▪ Dr. Westfall

28. THANK YOU QUESTIONS !?!