Seth M. Noar, Ph.D.

1
Factor Analysis

• Seth M. Noar, Ph.D.
• Department of Communication
• University of Kentucky

2
Major Types of Analytical Techniques

• Mean difference tests
• T-test
• ANOVA
• Tests of relationships / associations
• Correlation
• Multiple Regression
• Structural Equation Modeling
• Factor analysis does not fall into either of
  these categories

3
Factor Analysis

• Purpose To reduce a larger number of variables
  to a smaller number of factors
• Commonly used when developing self-report scales
  / measures
• Here we examine whats called exploratory factor
  analysis (EFA)

4
EFA Example

• Example We wish to develop a self-report measure
  of decision making (pros and cons)
• Develop a number of items in both content domains
• Theory suggests that this should be represented
  by 2 factors
• We would calculate an EFA to examine if this is
  the case

5
X3
X1
Common Factor
X4
X2
6
EFA Example (contd)

• Input a correlation matrix (raw data in SPSS)
• A factor matrix is calculated
• We rotate the factor matrix to get an
  interpretable solution (rotated factor matrix)
• We examine our output

7
EFA Output

• For each factor we get
• variance accounted for
• Eigenvalue the sum of the squared factor
  loadings on a given factor
• Factor loadings (-1 to 1)
• Note 1st factor will always have greatest
  variance (and highest eigenvalue), followed by
  second, etc.

8
(No Transcript)
9
Rotated Factor Matrix

• Factor I
  Factor II
• P1 .58
  .03
• P2 .65
  .05
• P3 .81
  .02
• P4 .72
  .04
• C1 .06
  .77
• C2 .01
  .82
• C3 .06
  .59
• C4 .02
  .67

10
Factor Loadings

• Factor loadings fall between -1 and 1
• Factor loadings should be gt.30
• Items / variables that load strongly on multiple
  factors are called complex
• Complex items should be discarded
• Even .85 on one factor and .35 on another is not
  ideal

11
Logic of Factor Analysis

• Common variance variance that overlaps between
  variables and factors
• Unique variance non-overlapping variance
• Best interpretation of the data in terms of
• Underlying number of factors
• Strength of factor loadings (variable saturation)

12
X3
X1
Common Factor
X4
X2
13
FA Decisions

• Factor analysis involves a number of decisions
• Formative work on theory / data
• Method of estimation (maximum likelihood)
• Number of factors to retain
• Type of rotation

14
Number of Factors to Retain

• A number of decision rules exist
• of eigenvalues gt 1
• SPSS default
• A decent general rule but often overestimates
  factors
• Cattells scree plot
• Good method, though can be subjective
• of variance accounted for by variables (gt50)
  can be arbitrary
• Chi-square test not incredibly reliable.
• Conclusion Use multiple procedures

15
(No Transcript)
16
Factor Rotation

• Two major types of rotation exist
• Orthogonal generally assumes factors are
  uncorrelated
• Example Varimax
• Oblique generally assumes factors are correlated
• Example Promax
• Note Variables can load on more than one factor
  with any of these methods

17
Principal Components Analysis

• Principal Components Analysis (PCA)
• Very similar to factor analysis has same basic
  purpose
• Language is different components rather than
  factors
• With good data, procedures will produce similar
  results
• Mathematics are different
• You will see PCA in the literature as much as
  factor analysis

18
CFA

• Once EFA is used, confirmatory factor analysis
  (CFA) can be used to confirm the structure of
  your data
• CFA is a structural equation modeling technique
• Difference from EFA YOU impose the structure on
  your data with CFA.
• Combination of both techniques to explore and
  confirm is powerful combination.