Applied Structural Equation Modeling for Dummies, by Dummies Borrowed gratefully from slides from 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 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.

3 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

4 What are it’s Advantages? Test models with multiple dependent variables Ability to model mediating variables Ability to model error terms

5 What are it’s Advantages? Test coefficients across multiple between- subjects groups Ability to handle difficult data –Longitudinal with auto-correlated error –Multi-level data –Non-normal data –Incomplete data

6 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

7 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

8 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

9 Terms, Nomenclature, Symbols, and Vocabulary Observed (or manifest) Latent (or factors) Experimental research independent and dependent variables. Non-experimental research predictor and criterion variables

10 Terms, Nomenclature, Symbols, and Vocabulary “of external origin” –Outside the model “of internal origin” –Inside the model Exogenous Endogenous Direct effects Reciprocal effects Correlation or covariance

11 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

12 Measurement Model: Confirmatory Factor Analysis GHQ Hostility Hopelessness Self-rated health Psychosocial health D1 e4 e3 e2 e1 Singh-Manoux, Clark and Marmot Multiple measures of socio-economic position and psychosocial health: proximal and distal measures. Latent construct or factor Observed or manifest variables

13 Structural Model with Additional Variables GHQ Hostility Hopelessness Income Occupation Education Self-rated health Psychosocial health D1 e4 e3 e2 e1 Singh-Manoux, Clark and Marmot Multiple measures of socio-economic position and psychosocial health: proximal and distal measures. Latent construct or factor Observed or manifest variables

14 Causal Modeling or Path Analysis and Confirmatory Factor Analysis GHQ Hostility Hopelessness Occupation Income Education Self-rated health Psychosocial health D3 e4 e3 e2 e1 Singh-Manoux, Clark and Marmot Multiple measures of socio-economic position and psychosocial health: proximal and distal measures. D1 D2 a= direct effect c b+c=indirect

15 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!

16 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

17 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

18 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)

19 SPSS Amos Screenshot

20 Stata Screenshot

21 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: –