1.
Structural Equation Modelling
(SEM)
An Introduction (Part 2)

2.
SEM: Basic Concepts
• Measured Variable or Indicator Variable
• Latent Variable
• Measurement Model
• Structural Model

3.
Basic Concepts: Measured Variable/Indicator
• Measured variable(s) are the variables that are actually measured in the
study.
Latent Variable
Measured Variable 1
Measured Variable 2
Measured Variable 3

4.
Basic Concepts: Latent Variable
• Intangible constructs that are measured by a variety of indicators
(more is better!)
Latent Variable
Measured Variable 1
Measured Variable 2
Measured Variable 3

5.
Basic Concepts: Measurement Model
• The measurement model can be described as follows. It shows the
relationship between a latent variable and its measured
items(variables).
Latent Variable
Measured Variable 1
Measured Variable 2
Measured Variable 3

6.
Basic Concepts: Structural Models
• Often used to specify models in SEM
 Causal flow is from left to right; top to bottom
• Straight arrows represent direct effects
• Curved arrows represent bidirectional “correlational”
relationships
• Ellipses represent latent variables
• Boxes/rectangles represent observed variables

7.
Example: Structural Models

8.
Variants of Structural Equation Modelling
• Confirmatory Factor Analysis (CFA)
• Path Analysis with observed variables
• Path analysis with latent variables

9.
Confirmatory Factor Analysis
“Measurement Model”
• Tests model that specifies relationships between variables (items) and
factors
 And relationships among factors
• Confirmatory
 Because model is specified a priori

10.
Example: Oblique CFA Model

11.
Confirmatory vs. Exploratory Factor
Analysis
• In CFA the model is specified a priori
 Based on theory
• EFA is not a member of the SEM family
 Includes a class of procedures involving centroids, principal components, and
principal axis factor analysis
 Does not require a priori hypothesis about relationships within your model
 Inductive vs. deductive approach
 More restrictions on the relationships between indicators and latent factors

12.
Example: Oblique EFA Model

13.
Observed Variable Path Analysis (OVPA)
• Tests only a structural model
 Relationships among constructs represented by direct measured
(observed variables)
 i.e., each “box” in model is an idem, subscale, or scale
• Analogous to a series of multiple regressions
 But, with MR, we would need k different analyses, where k is # of
DVs
 With SEM, can test entire model at once

14.
Example: OVPA

15.
Latent Variable Path Analysis (LVPA)
• Simultaneous test of measurement and structural parameters
• CFA and OVPA at same time
• LVPA models incorporate….
• Relationships between observed and latent variables (i.e., measures and factors)
• Relationships between latent variables
• Error & disturbances/residuals

16.
Example: LVPA

17.
Data Considerations
Sample Size
• SEM is a large-sample technique
• The required Sample size needed depends on….
Complexity of model
 Ratios of sample size to estimated parameters ranging from
5:1 to 20:1 (Bentler & Chou, 1987; Kline, 2005)
Data Quality
 Larger samples for non-normal data

18.
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Training?
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