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# Structural Equation Modelling (SEM) Part 2

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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) Part 2

1. 1. Structural Equation Modelling (SEM) An Introduction (Part 2)
2. 2. SEM: Basic Concepts • Measured Variable or Indicator Variable • Latent Variable • Measurement Model • Structural Model
3. 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. 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. 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. 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. 7. Example: Structural Models
8. 8. Variants of Structural Equation Modelling • Confirmatory Factor Analysis (CFA) • Path Analysis with observed variables • Path analysis with latent variables
9. 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. 10. Example: Oblique CFA Model
11. 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. 12. Example: Oblique EFA Model
13. 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. 14. Example: OVPA
15. 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. 16. Example: LVPA
17. 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. 18. Looking for Online SEM Training? Contact us: info@costarch.com Visit: http://tinyurl.com/costarch-sem www.costarch.com