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

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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!)

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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

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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.

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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

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

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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

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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

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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

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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

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

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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

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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

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Measurement Model: Confirmatory Factor Analysis
GHQ
Hostility
Hopelessness
Self-rated health
Psychosocial
health
D1
e4
e3
e2
e1
Singh-Manoux, Clark and Marmot. 2002. Multiple measures of socio-economic
position and psychosocial health: proximal and distal measures.
Latent construct or factor
Observed or manifest variables

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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. 2002. Multiple measures of socio-economic
position and psychosocial health: proximal and distal measures.
Latent construct or factor
Observed or manifest variables

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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. 2002. Multiple measures of socio-economic
position and psychosocial health: proximal and distal measures.
D1
D2
a= direct effect
c
b+c=indirect

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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!

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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

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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

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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)

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SPSS Amos Screenshot

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Stata Screenshot

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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

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Thanks So Much Again!!
Questions????
jsudano@metrohealth.org