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Causal Models and Structural Equations
1. Causal Models and Structural
Equations Day 1Equations Day 1
Peter Schmidt
2. Day 1: Overview
1. Course Overview
2. Notation
3. Philosophy of Science and SEM
4. Differences: Exploratory FA and CFA
2
4. Differences: Exploratory FA and CFA
5. Unidimensionality
6. Measurement Errors
7. Formative and reflective Indicators
8. Summary and Introduction of practical session
3. Overview of the Course
1st part: Confirmatory factor analysis
2nd part: Full structural equation model
Course procedure: Regular alternation
3
Course procedure: Regular alternation
between
4. Overview: Types of models 1:
Factor (measurement) Model
A
x1
x
e1
e
4
A x2
x3
e2
e3
5. Overview: Types of models 1:
Formative Indicator Model
A
x1
xe4
5
A x2
x3
e4
6. Overview: Types of models 1:
Feedback Model
A
x1
x
e1
ee4
6
A x2
x3
e2
e3
e4
7. Types of Models in the Course
Factor model (measurement model)
- Single or simultaneous analyses of the
measurement models
- Exploratory or confirmatory simultaneous
factor analysis
- Multiple group comparison, structured means
7
- Multiple group comparison, structured means
analyses
- Confirmation, rejection or modification of the
models.
- Reflective vs. Formative vs. Feedback
indicators
8. Overview: Types of models 2:
Structural Model
A B
x1
y1
e1
d1
d3
8
• What are the causal relationships among the
theoretical (latent) variables?
• How strong are these relationships?
• How strong is the stochastic error (d3)?
A
x2
y2 d2
e2
9. Types of Models in the Course
Structural model
- Analysis of the core theory: Is the explication of the
core hypotheses correct?
- MIMIC Model
- Confirmation, rejection or modifications of models
9
- Strictly Confirmatory (SC), Alternative Models (AM),
Model Generating (MG)
- Multiple Group Analysis, moderator and non-linear
effects
- Mediators and indirect effects compared to direct
effects
10. Overview: General Information about the
SEM approach and using AMOS
ADVANTAGES USING SEM
• Test complex hypotheses involving causal
relationships among constructs (latent
variables).
• Unifies several multivariate methods into one
10
• Unifies several multivariate methods into one
analytic framework.
• Effects of latent variables on each other and
on observed variables.
• Possibility: testing alternative hypotheses.
11. • Multivariate models without latent variables:
regression models, dummy regressions,
variance analyses and covariance analyses.
• Multivariate models with latent variables:
confirmatory factor analysis (CFA), second order
and nth-order factor analysis, MIMIC models,
canonical correlations, MTMM models, and
11
canonical correlations, MTMM models, and
structural equation models (SEM).
• Longitudinal dynamic models: CFA with panel
data, SEM with panel data, autoregressive
models, cross-lagged models, latent growth
curves and differential equations.
15. SEM and Philosophy of
Science
• Deductive power
• Transformation of substantive theory
• Operationalizations into confirmatory models
15
• Operationalizations into confirmatory models
with restrictions to be tested
• Simultaneous test of measurement theory
and substantive theory
16. The methodology provides behavioral
scientists with tools for:
• Stating theories more exactly
• Testing theories more precisely
• Testing alternative theories against each
16
• Testing alternative theories against each
other
• Generating a more thorough
understanding of observed data.
17. SEM and Philosophy of Science
Lakatos-Kuhn-Scheme:
- metaphysical Assumptions
- Propositions of Core Theory
17
- Propositions of Core Theory
- Correspondence Rules
18. Terminology from Philosophy
of science for theory
construction
Terminology of SEM
Core theory composed of
theoretical postulates (deductive
nomological explanation, a b)
Structural model- causal
relations between constructs
Assumptions of the core theory Assumptions of the structural
18
model
Operationalization of theoretical
constructs/dimensions (rules of
correspondence)
Assumptions of
operationalizations (linearity?
Additivity)
Measurement theory- relating
factors to indicators with a set
of assumptions (linearity?
Additivity)
22. Confirmatory Factor Analysis with correlated
factors (CFA) of the theory of planned behavior
(with a residual correlation-a non random error)
Pbc
PBC1
PBC2
PBC3
e1
e2
e3
22
Subjective
norms
Attitude
NORM1
NORM2
NORM3
Attitu1
Attitu2
Attitu3
e4
e5
e6
e7
e8
e9
23. Exercise
• Select a theory you are working with
• Select a construct from your theory
• Select some items which measure this
construct
23
construct
• Draw a measurement model with the
respective indicators and constructs
25. Types of measurement error
• 1) Random measurement error (e‘s): we can
control for it and estimate it if we have at least
two indicators
• 2) Non-random measurement errors (the
25
• 2) Non-random measurement errors (the
correlations between the random measurement
errors (e‘s), e.g. social desirability, method
effect): we can control for them and estimate
them if we have at least three indicators, and we
can partly control for them and estimate them
when we have two indicators
27. Summary and Lab Session:
Core theory: Path diagram of the theoretical
assumptions:
Age, gender,
education
27
Conformity/Tradition
Allowing immigrants
into the country
Universalism/
Benevolence
28. Hypotheses:
SH1) The higher the importance of conformity and
tradition, the lower the support for allowing
immigrants into the country.
SH2) The higher the importance of universalism
28
SH2) The higher the importance of universalism
and benevolence, the higher the support for
allowing immigrants into the country.
30. Core theory: Path diagram of the theoretical assumptions (Round 2):
P O A C
im p r ic h
e 1 0
1
1
ip r s p o t
e 1 1
1
ip s h a b t
e 1 2
1
ip s u c e s
e 1 3
1
H E
ip g d tim
e 1 4
1
1
im p f u n
e 1 5
1
S T
im p d iff e 1 61
1
ip a d v n t e 1 7
1
ip s tr g ve 2 1
1
E x 2 : S C F A in th e N e th e r la n d s , v a lu e s E S S R 2
30
U N B E
ip e q o p t e 1
1
1
ip u d r s t e 2
1
im p e n v e 3
1
ip h lp p l e 4
1
T R C O
ip m o d s t
e 6
1
1
im p t r a d
e 7
1
ip fr u le
e 8
1
ip b h p r p
e 9
1
S D
ip c r tiv e 1 81 1
im p fr e e e 1 9
1
S E C
im p s a f ee 2 0
11
ip s tr g ve 2 1
ip ly lfr e 5
1
31. An additional research question:
To what extent are the values as proposed
to be measured by Shalom Schwartz
(1992) equivalent across the three
countries Netherlands, Belgium and
31
countries Netherlands, Belgium and
Luxembourg?
And across a larger set of countries from the
ESS?
32. Summary and Lab Session
Exercise 1: Tradition_conformity in the Netherlands,
ESS R2
32
TRCO
ipmodst
e1
1
1
imptrad
e2
1
ipfrule
e3
1
ipbhprp
e4
1
33. Summary and Lab Session:
The Data
The data we will use in the course:
ESS 2004-2005, focusing on the value
questions
33
Sample Size:
• The Netherlands: N = 1,881
• Belgium: N = 1,778
• Luxembourg: N = 1,635
• Total sample size: N=5,294
34. Syntax for generating the
Correlation Matrix
CORRELATIONS
/VARIABLES=selected variables
/PRINT=TWOTAIL SIG
/STATISTICS DESCRIPTIVES
/MISSING=PAIRWISE
34
/matrix out (SPSS-file.sav).
Example:
CORRELATIONS
/VARIABLES=ipmodst imptrad ipfrule ipbhprp
/PRINT=TWOTAIL SIG
/STATISTICS DESCRIPTIVES
/MISSING=PAIRWISE
/matrix out (cov_nl.sav).
