Introduction to Structural Equation Modelling
Todd K. Hartman
Lecturer in Quantitative Methods
Sheffield Methods Institute
26 January, 2017
Todd K. Hartman, SMI
Introduction to SEM
What is SEM?
Broad class of statistical techniques
Todd K. Hartman, SMI
Introduction to SEM
What is SEM?
Broad class of statistical techniques
Causal Modelling or Path Analysis (Structural Model)
X→Y→Z
Todd K. Hartman, SMI
Introduction to SEM
What is SEM?
Broad class of statistical techniques
Causal Modelling or Path Analysis (Structural Model)
X→Y→Z
Factor Analysis (Measurement Model of Latent Constructs)
Confirmatory Factor Analysis (CFA)
Todd K. Hartman, SMI
Introduction to SEM
What is SEM?
Broad class of statistical techniques
Causal Modelling or Path Analysis (Structural Model)
X→Y→Z
Factor Analysis (Measurement Model of Latent Constructs)
Confirmatory Factor Analysis (CFA)
Models with Structural and Measurement Components
Uses CFA to account for measurement error
Yet, models causal relationships
Todd K. Hartman, SMI
Introduction to SEM
What is SEM?
Broad class of statistical techniques
Causal Modelling or Path Analysis (Structural Model)
X→Y→Z
Factor Analysis (Measurement Model of Latent Constructs)
Confirmatory Factor Analysis (CFA)
Models with Structural and Measurement Components
Uses CFA to account for measurement error
Yet, models causal relationships
Basic statistic is the covariance (but can handle means)
Todd K. Hartman, SMI
Introduction to SEM
What is SEM?
Broad class of statistical techniques
Causal Modelling or Path Analysis (Structural Model)
X→Y→Z
Factor Analysis (Measurement Model of Latent Constructs)
Confirmatory Factor Analysis (CFA)
Models with Structural and Measurement Components
Uses CFA to account for measurement error
Yet, models causal relationships
Basic statistic is the covariance (but can handle means)
Covariance is strength of association between X and Y and
their variabilities
covXY = rrXY SDX SDY
(unlike correlation, covariance has no upper or lower bounds)
Todd K. Hartman, SMI
Introduction to SEM
Pros and Cons of SEM
Pros
Todd K. Hartman, SMI
Introduction to SEM
Pros and Cons of SEM
Pros
SEMs are very flexible
Todd K. Hartman, SMI
Introduction to SEM
Pros and Cons of SEM
Pros
SEMs are very flexible
Simultaneously models a system of relationships
Todd K. Hartman, SMI
Introduction to SEM
Pros and Cons of SEM
Pros
SEMs are very flexible
Simultaneously models a system of relationships
Multiple dependent variables (outcomes)
Todd K. Hartman, SMI
Introduction to SEM
Pros and Cons of SEM
Pros
SEMs are very flexible
Simultaneously models a system of relationships
Multiple dependent variables (outcomes)
Accounts for measurement error (latent variables)
Todd K. Hartman, SMI
Introduction to SEM
Pros and Cons of SEM
Pros
SEMs are very flexible
Simultaneously models a system of relationships
Multiple dependent variables (outcomes)
Accounts for measurement error (latent variables)
Cons
Todd K. Hartman, SMI
Introduction to SEM
Pros and Cons of SEM
Pros
SEMs are very flexible
Simultaneously models a system of relationships
Multiple dependent variables (outcomes)
Accounts for measurement error (latent variables)
Cons
Requires a priori specification
Todd K. Hartman, SMI
Introduction to SEM
Pros and Cons of SEM
Pros
SEMs are very flexible
Simultaneously models a system of relationships
Multiple dependent variables (outcomes)
Accounts for measurement error (latent variables)
Cons
Requires a priori specification
‘Large’ sample technique
Todd K. Hartman, SMI
Introduction to SEM
Pros and Cons of SEM
Pros
SEMs are very flexible
Simultaneously models a system of relationships
Multiple dependent variables (outcomes)
Accounts for measurement error (latent variables)
Cons
Requires a priori specification
‘Large’ sample technique
‘Small’ is N < 100
‘Medium’ is 100 ≤ N ≤ 200
‘Large’ is N > 200
(Depends on the complexity of model and estimator used)
Todd K. Hartman, SMI
Introduction to SEM
Pros and Cons of SEM
Pros
SEMs are very flexible
Simultaneously models a system of relationships
Multiple dependent variables (outcomes)
Accounts for measurement error (latent variables)
Cons
Requires a priori specification
‘Large’ sample technique
‘Small’ is N < 100
‘Medium’ is 100 ≤ N ≤ 200
‘Large’ is N > 200
(Depends on the complexity of model and estimator used)
Infinite number of possible models
Todd K. Hartman, SMI
Introduction to SEM
Pros and Cons of SEM
Pros
SEMs are very flexible
Simultaneously models a system of relationships
Multiple dependent variables (outcomes)
Accounts for measurement error (latent variables)
Cons
Requires a priori specification
‘Large’ sample technique
‘Small’ is N < 100
‘Medium’ is 100 ≤ N ≤ 200
‘Large’ is N > 200
(Depends on the complexity of model and estimator used)
Infinite number of possible models
Correlation 6= Causation
Todd K. Hartman, SMI
Introduction to SEM
Software
Many different software packages for SEM (each with their
own quirks)
Mplus
LISREL
EQS
AMOS
Mx and OpenMx
Stata
R
Todd K. Hartman, SMI
Introduction to SEM
Software: lavaan Package in R: http://lavaan.ugent.be/
Todd K. Hartman, SMI
Introduction to SEM
lavaan in R
lavaan is (relatively) easy and intuitive
Todd K. Hartman, SMI
Introduction to SEM
lavaan in R
lavaan is (relatively) easy and intuitive
lavaan in R is free (as in beer!)
Todd K. Hartman, SMI
Introduction to SEM
lavaan in R
lavaan is (relatively) easy and intuitive
lavaan in R is free (as in beer!)
Strong online support/community
Todd K. Hartman, SMI
Introduction to SEM
lavaan in R
lavaan is (relatively) easy and intuitive
lavaan in R is free (as in beer!)
Strong online support/community
Compact, readable R commands
Todd K. Hartman, SMI
Introduction to SEM
lavaan in R
lavaan is (relatively) easy and intuitive
lavaan in R is free (as in beer!)
Strong online support/community
Compact, readable R commands
Constant development of latest methods
Todd K. Hartman, SMI
Introduction to SEM
lavaan in R
lavaan is (relatively) easy and intuitive
lavaan in R is free (as in beer!)
Strong online support/community
Compact, readable R commands
Constant development of latest methods
Full support for categorical data!
Todd K. Hartman, SMI
Introduction to SEM
lavaan in R
lavaan is (relatively) easy and intuitive
lavaan in R is free (as in beer!)
Strong online support/community
Compact, readable R commands
Constant development of latest methods
Full support for categorical data!
Binary, Categorical, and Continuous DVs
Todd K. Hartman, SMI
Introduction to SEM
Lavaan Code: CFA Model
Todd K. Hartman, SMI
Introduction to SEM
Lavaan Code: Structural and Measurement Model
Todd K. Hartman, SMI
Introduction to SEM
Practical Example: Support for Social Welfare Spending
What affects preferences for government spending on social
welfare programs?
Todd K. Hartman, SMI
Introduction to SEM
Practical Example: Support for Social Welfare Spending
What affects preferences for government spending on social
welfare programs?
1 Attitudes toward Government
Ideology
Party Affiliation
2 Personal Experiences
Income
Generational Cohorts (Age)
3 Attitudes toward Beneficiaries
Racial stereotypes
Todd K. Hartman, SMI
Introduction to SEM
Practical Example: Support for Social Welfare Spending
What affects preferences for government spending on social
welfare programs?
1 Attitudes toward Government
Ideology
Party Affiliation
2 Personal Experiences
Income
Generational Cohorts (Age)
3 Attitudes toward Beneficiaries
Racial stereotypes
4 Pro-Social Orientations
Humanitarianism (value helping those in need)
Empathy (ability to understand/feel what another being is
experiencing)
Todd K. Hartman, SMI
Introduction to SEM
Practical Example: Support for Social Welfare Spending
Todd K. Hartman, SMI
Introduction to SEM
Practical Example: Support for Social Welfare Spending
American National Election Study 2008 - 2009 Panel Study
Monthly surveys with representative Internet panel
1,420 to 2,665 completed interviews per wave
Social Spending toward Social Security, Aid to the Poor, Job
Retraining, and Public Schools
8 Humanitarianism Items
’It is important to help one another so that the community in
general is a better place.’
21 Empathy Items
Other Demographic Controls
Todd K. Hartman, SMI
Introduction to SEM
Structural Equation Model Results
Structural Equation Model Results
Structural Equation Model Results
Lavaan Code
Todd K. Hartman, SMI
Introduction to SEM
My Favourite SEM Books
Todd K. Hartman, SMI
Introduction to SEM
Upcoming Training Workshop in SEM
Date:
Tuesday, 14 February 2017
Time:
9:00 to 17:00
Location:
ICOSS Bldg, Sheffield
Costs:
£30 MA/PhD; £60 academic staff, ESRC researchers, charities; £250 Others
Application:
27 January 2017 (noon tomorrow)
URL:
http://aqmen.ac.uk/events/Feb2017/SEM
Todd K. Hartman, SMI
Introduction to SEM