Applied Structural Equation Modeling for Dummies by Dummies

Applied Structural Equation Modeling for Dummies, by Dummies February 22, 2013 Indiana University, Bloomington Joseph J. Sudano, Jr. , Ph. D Center for Health Care Research and Policy Case Western Reserve University at The Metro. Health System Adam T. Perzynski, Ph. D Center for Health Care Research and Policy Case Western Reserve University at The Metro. Health System

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Thanks So Much!! • Acknowledgements: – Bill Pridemore Ph. D – Adam Perzynski Ph. D – David W. Baker MD – Randy Cebul MD – Fred Wolinsky Ph. D – 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 = s 2 Standard deviation = s Correlation = r Covariance = s. XY = 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 D 1 Psychosocial health Hostility e 1 Hopelessness e 2 GHQ e 3 Self-rated health e 4 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 D 1 Psychosocial health Income Hostility e 1 Hopelessness e 2 GHQ e 3 Self-rated health e 4 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 b+c=indirect Income c Hostility e 1 Hopelessness e 2 GHQ e 3 Self-rated health e 4 Psychosocial health D 1 D 3 Occupation D 2 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 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? ? jsudano@metrohealth. org 28