This document provides an introduction to structural equation modeling (SEM) concepts. It defines key terms like measured variable, indicator variable, latent variable, measurement model and structural model. It explains that measured variables are directly observed, while latent variables are abstract constructs measured indirectly through multiple indicators. It describes measurement models as showing the relationships between latent variables and their measured items, and structural models as specifying relationships between latent and observed variables with arrows. It provides examples of confirmatory factor analysis (CFA), path analysis with observed and latent variables, and discusses data sample size considerations for SEM.

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

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Training?
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