Factor Analysis

1
Factor Analysis

• Measuring latent variables

2
Factor Analysis - Discussion

• Definition
• Vocabulary
• Simple Procedure
• SPSS example
• ICPSR and hands on

3
Definition

• Factor analysis is a process by which we take a
  large number of variables (read that
  measurements) and reduce them into a smaller
  number of factors, by extracting the shared
  variation among variables. The result is a
  factor loading for each variable on each factor
  

4
Vocabulary and Procedure

• Exploratory Factor Analysis uses all of the
  variance of each variable to establish factors.
  Such technique is called Principal Component
  Analysis.
• It establishes the number of factors by
  several techniques, the two most often used are
  1) recognizing only those whose eigenvalue is gt
  one (the Kaiser method) or 2) only those whose
  plot shows a vertical line (Scree method)

5
Vocabulary and Procedure (cont.)

• In examining the number of factors or components,
  we would need to rotate their loadings, either
  Orthogonally (resulting in a loading matrix),
  which is the correlation between variables and
  the factors
• Alternatively, we can rotate them Obliquely
  (which results in the factors being correlated
  with each other). This is referred to as a
  factor correlation matrix. Used only when we
  believe the factors themselves, are correlated.

6
Orthogonal Rotation
1.0
X2
X4
X1
-1.0
1.0
X3
-1.0
7
Vocabulary and Procedure (cont.)

• Interpreting loadings is quite subjective, but
  can be looked at largely by size.

Components 1 2 .879 .296 .846 .450 .7
63 .509 .279 .719 .480 .678
Variable X1 Variable X2 Variable X3 Variable
X4 Variable X5
8
Steps in the Analysis

• Input the data
• Analyze, Dimension Reduction, Factor
• Choose the extraction and rotation method
• Generate the Output
• Interpret the results

9
Input the data
10
Generate the Procedure
11
Produce the Output
12
Produce the Output (cont.)
13
Produce the Output (cont.)