Applied Structural Equation Modeling for Dummies, by Dummies February 22, 2013 Indiana University, Bloomington Joseph J. Sudano, Jr., PhD Center for Health Care Research and Policy Case Western Reserve University at The MetroHealth System Adam T. Perzynski, PhD Center for Health Care Research and Policy Case Western Reserve University at The MetroHealth System 2 3 4 5 Thanks So Much!! • Acknowledgements: – Bill Pridemore PhD – Adam Perzynski PhD – David W. Baker MD – Randy Cebul MD – Fred Wolinsky PhD – No conflicts of interest (but I wish there were some major financial ones!) 6 Presentation Outline • Conceptual overview. – What is SEM? – Basic idea underpinning SEM – Major applications – Shared characteristics among SEM techniques • Terms, nomenclature, symbols, vocabulary • Basic SEM example • Sample size, other issues and model fit • Software and texts 7 What Is Structural Equation Modeling? • SEM: very general, very powerful multivariate technique. – Specialized versions of other analysis methods. • Major applications of SEM: • • • • • Causal modeling or path analysis. Confirmatory factor analysis (CFA). Second order factor analysis. Covariance structure models. Correlation structure models. 8 Advantages of SEM Compared to Multiple Regression • More flexible modeling • Uses CFA to correct for measurement error • Attractive graphical modeling interface • Testing models overall vs. individual coefficients 9 What are it’s Advantages? • Test models with multiple dependent variables • Ability to model mediating variables • Ability to model error terms 10 What are it’s Advantages? • Test coefficients across multiple betweensubjects groups • Ability to handle difficult data – Longitudinal with auto-correlated error – Multi-level data – Non-normal data – Incomplete data 11 Shared Characteristics of SEM Methods • SEM is a priori – Think in terms of models and hypotheses – Forces the investigator to provide lots of information • which variables affect others • directionality of effect 12 Shared Characteristics of SEM Methods • SEM allows distinctions between observed and latent variables • Basic statistic in SEM in the covariance • Not just for non-experimental data • View many standard statistical procedures as special cases of SEM • Statistical significance less important than for more standard techniques 13 Terms, Nomenclature, Symbols, and Vocabulary (Not Necessarily in That Order) • • • • • Variance = s2 Standard deviation = s Correlation = r Covariance = sXY = COV(X,Y) Disturbance = D •X Y D • Measurement error = e or E •A X E 14 Terms, Nomenclature, Symbols, and Vocabulary • Experimental research • independent and dependent variables. • Non-experimental research • predictor and criterion variables • Observed (or manifest) • Latent (or factors) 15 Terms, Nomenclature, Symbols, and Vocabulary • Exogenous • “of external origin” – Outside the model • Endogenous • “of internal origin” – Inside the model • Direct effects • Reciprocal effects • Correlation or covariance 16 Terms, Nomenclature, Symbols, and Vocabulary • Measurement model – That part of a SEM model dealing with latent variables and indicators. • Structural model – Contrasted with the above – Set of exogenous and endogenous variables in the model with arrows and disturbance terms 17 Measurement Model: Confirmatory Factor Analysis Observed or manifest variables D1 Psychosocial health Hostility e1 Hopelessness e2 GHQ e3 Self-rated health e4 Latent construct or factor Singh-Manoux, Clark and Marmot. 2002. Multiple measures of socio-economic position and psychosocial health: proximal and distal measures. 18 Structural Model with Additional Variables Observed or manifest variables Education Occupation D1 Psychosocial health Income Hostility e1 Hopelessness e2 GHQ e3 Self-rated health e4 Latent construct or factor Singh-Manoux, Clark and Marmot. 2002. Multiple measures of socio-economic position and psychosocial health: proximal and distal measures. 19 Causal Modeling or Path Analysis and Confirmatory Factor Analysis Education a= direct effect Hostility e1 Hopelessness e2 GHQ e3 Self-rated health e4 b+c=indirect Income c Psychosocial health D1 D3 Occupation D2 Singh-Manoux, Clark and Marmot. 2002. Multiple measures of socio-economic position and psychosocial health: proximal and distal measures. 20 What Sample Size is Enough for SEM? • The same as for regression* – More is pretty much always better – Some fit indexes are sensitive to small samples • *Unless you do things that are fancy! 21 What’s a Good Model? • Fit measures: – Chi-square test – CFI (Comparative Fit Index) – RMSE (Root Mean Square Error) – TLI (Tucker Lewis Index) – GFI (Goodness of Fit Index) – And many, many, many more –IFI, NFI, AIC, CIAC, BIC, BCC 22 How Many Indicators Do I Need? • That depends… • How many do you have? (e.g., secondary data analysis) • A prior concerns • Scale development standards • Subject burden • More is often NOT better 23 Software • LISREL 9.1 from SSI (Scientific Software International) • IBM’s SPSS Amos • EQS (Multivariate Software) • Mplus (Linda and Bengt Muthen) • CALIS (module from SAS) • Stata’s new sem module • R (lavaan and sem modules) 24 SPSS Amos Screenshot 25 Stata Screenshot 26 Texts (and a reference) • Barbara M. Byrne (2012): Structural Equation Modeling with Mplus, Routledge Press – She also has an earlier work using Amos • Rex Kline (2010): Principles and Practice of Structural Equation Modeling, Guilford Press • Niels Blunch (2012): Introduction to Structural Equation Modeling Using IBM SPSS Statistics and Amos, Sage Publications • James L. Arbuckle (2012): IBM SPSS Amos 21 User’s Guide, IBM Corporation (free from the Web) • Rick H. Hoyle (2012): Handbook of Structural Equation Modeling, Guilford Press • Great fit index site: – http://www.psych-it.com.au/Psychlopedia/article.asp?id=277 27 Thanks So Much Again!! Questions???? [email protected] 28