Scale Development

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 gt 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