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
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
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
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
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
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. Looking for Online SEM
Training?
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