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This presentation is an introduction to the concept and theory of Structural Equation Modelling.
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Structural Equation Modelling(SEM)
An Introduction (Part 2)
SEM: Basic Concepts
• Measured Variable or Indicator Variable
• Latent Variable
• Measurement Model
• Structural Model
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
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
Basic Concepts: Measurement Model• The measurement model can be described as follows. It shows the
relationship between a latent variable and its measureditems(variables).
Latent Variable
Measured Variable 1 Measured Variable 2 Measured Variable 3
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
Example: Structural Models
Variants of Structural Equation Modelling
•Confirmatory Factor Analysis (CFA)
•Path Analysis with observed variables
•Path analysis with latent variables
Confirmatory Factor Analysis “Measurement Model”
• Tests model that specifies relationships between variables (items) andfactors
And relationships among factors
• Confirmatory
Because model is specified a priori
Example: Oblique CFA Model
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, andprincipal 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
Example: Oblique EFA Model
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 # ofDVs
With SEM, can test entire model at once
Example: OVPA
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
Example: LVPA
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 from5:1 to 20:1 (Bentler & Chou, 1987; Kline, 2005)
Data Quality
Larger samples for non-normal data
Looking for Online SEM Training?
Contact us: info@costarch.com
Visit: http://tinyurl.com/costarch-sem
www.costarch.com
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