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Scale Development

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**1. **Scale Development Chapter 6 – Factor Analysis

**2. **Overview Exploratory factor analysis (EFA)
Function
Process
Confirmatory factor analysis (CFA)
Function
Process

**3. **EFA Functions Determine how many latent variables underlie responses to a set of items
Define the factors underlying responses to a set of items
Represent the information in a set of items with a small number of factor scores

**4. **EFA Process Extracting factors
Rotating factors
Interpreting factors

**5. **Extracting Factors EFA first determines the linear combination of the items that best represents variability in the scale
Then determines the linear combination of the items that best represents whatever variability is left over
Keeps doing this until all variability is explained
For k items, will extract k factors

**6. **Extracting Factors (continued) Need to decide how many factors are needed
Scree plot: Look for “elbow”
Eigenvalues > 1
Percent variance explained

**7. **Rotating Factors Initial factor scores are often difficult to interpret.
Rotation relaxes some assumptions to provide more interpretable factors
What makes factors more interpretable?
Items clearly are or are not related to each factor
Each item is only related to one or a small number of factors

**8. **Rotating Factors (continued) Initial extraction has uncorrelated factors
Orthogonal rotations will also have uncorrelated factors
Oblique rotations allows for correlated factors
Important to intelligently decide whether you want an orthogonal or oblique rotation

**9. **Interpreting Factors Each factor has a set of “factor loadings” that indicate how strongly each item is related to that factor
Similar to regression coefficients
To interpret a factor
Identify items with strong factor loadings
See what all these items have in common
Interpreting factors is subjective

**10. **CFA functions Verifies that a proposed factor structure fits the observed data well
Allows you to compare the fit of different factor structures

**11. **Sample Size Issues EFA
5 to 10 subjects per item up to 300 subjects
After that point, ratio can be relaxed
CFA
5 subjects per parameter in the model with a minimum of 100 subjects

**12. **CFA process CFA is performed using structural equation modeling
Cannot be done in SPSS – requires SEM software such as AMOS or LISREL
Determines how well the correlations/covariances implied by your structural model match the observed correlations in the data