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Welcome to
Data Science Course in
Bangalore
DataMites Part 10
Accredited by IABAC™

2. © DataMites™. All Rights Reserved | www.datamites.com DATA SCIENCE FOUNDATION 2
STRUCTURAL EQUATION MODEL
IN
DATA SCIENCE
Accredited by IABAC™

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Structural Equation Models
DATA SCIENCE FOUNDATION 3
Also known as:
Covariance structure models
Latent variable models
“LISREL” models
Structural Equations with Latent Variables
SEM is a most popularly used Non-Parametric model involving below cases:
• ANOVA
• Multiple regression
• Path analysis
• Confirmatory Factor Analysis
• Recursive and Nonrecursive systems

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DATA SCIENCE FOUNDATION
4
intelligence
test 1 test 2 test 3 test 4 test 5
δ1 δ2 δ3 δ4 δ5
Path diagram
Latent variables, factors, constructs
Observed variables, measures,
indicators, manifest variables
Direction of influence, relationship from
one variable to another
Association not explained within the
model
SEM Notations:

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Depress 1 Depress 2 Depress 3
Self rating MD rating # visits to MD
Self rated
closeness
Spousal
rating
Kids rating
Family support depression
Physical health
δ1 δ2 δ3
ε4 ε 5 ε 6
ε1 ε 2 ε 3
ζ1
ζ2

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What are Structural Equation Models?
• What can you do with these models?
– Latent and Observed Variables
– Multiple indicators of same concept
– Measurement error
– Restrictions on model parameters
– Tests of model fit

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What are Structural Equation Models?
• What can’t you do?
– Prove causation
– Prove a model is “correct”
All models
Models consistent with data
Models consistent
with reality
(Mueller 1997)

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Notation
ε1
y1
ε2
y2
ε3
y3
ε4
y4
ε5
y5
ε6
y6
ε7
y7
ε8
y8
δ1
x1
δ2
x2
δ3
x3
η1
ξ1
η2
ζ1 ζ2β21
γ21
γ11
λ1 λ2 λ3
λ4 λ5 λ6 λ7 λ8 λ9 λ10 λ11
ξ1= industrialization
η1 = democracy time 1
η2 = democracy time 2
x1-x3 = indus. indicators, e.g., energy
y1-y4 = democ. indicators time 1
y5-y8 = democ. indicators time 2

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Notation
• η Latent Endogenous Variable
• ξ Latent Exogenous Variable
• ζ Unexplained Error in Model
• x & y Observed Variables
• δ & ε Measurement Errors
• λ, β, & γ Coefficients

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Notation
• Two components to a SEM
– Latent variable model
• Relationship between the latent variables
ζΓξΒηη 
δξΛx x 
εηΛy y 
 Measurement model
• Relationship between the latent and observed variables

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