Structural Equation Modeling Hossein Salehi Jenny Lehman Jacob

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

LEARNING OBJECTIVES § 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

GHOST CHASING § We are in the business of Chasing “Ghosts” • “Ghost” diagnoses • Measuring “Ghosts” • Exchanging one “Ghost” for another “Ghost” (Ainsworth 2006)

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

FAMILY TREE OF SEM § Factor Analysis § Exploratory Factor Analysis § Confirmatory Factor Analysis Now it is … Structural Equation Modeling (SEM)’s turn !!! (Hubona)

SEM MODEL ▪

SEM IN PFP Risk Requirement … … Risk Tolerance § Let’s run some data in R. (Fina. Metrica)

PATH DIAGRAM SYMBOLS § Direction of influence, relationship from one variable to another § Reciprocal effects § Correlation or covariance § Observed (or manifest, measures, indicators) § Latent (or factor, constructs) (Sudano & Perzvnski, 2013)

ESTABLISHING PATH DIAGRAM Two Measurement Models Risk Requirement Structural Model … … Risk Tolerance … …

GOALS OF SEM ▪ To determine whether 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)

SEM ASSUMPTIONS § 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)

SEM MODEL ▪ (Steiger)

SEM GENERAL MODEL ▪ (Steiger)

SEM GENERAL MODEL § Let’s unpack the structural model: § Let’s unpack the two measurement models: (Steiger)

SEM GENERAL MODEL ▪ Error terms covariance matrix (Steiger)

SEM GENERAL MODEL ▪ Implied covariance matrix (Steiger)

ESTABLISHING PATH DIAGRAM Risk Requirement … Risk Tolerance … …

POLITICAL DEMOCRACY ▪ (Bollen, 1989)

EXAMPLE: POLITICAL DEMOCRACY MODEL IND 60 DEM 60 (Bollen, 1989)

SEM MODEL FOR DEMOCRACY EXAMPLE ▪

IMPORTANT MATRICES ▪ 2/20/2006 LATENT VARIABLE MODELS 21

IMPORTANT MATRICES ▪ 2/20/2006 LATENT VARIABLE MODELS 22

APPROACH 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)

SEM ADVANTAGES § 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)

CONSIDERATION IN APPLYING SEM § 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

CONCLUSION Now we know how to use SEM to find the ghosts !!!!!!

REFERENCES ▪ 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. ▪ Fina. Metrica ▪ Wikipedia ▪ Oct. 1 Group ▪ Dr. Westfall

THANK YOU QUESTIONS !? !