Factor Analysis

1
Factor Analysis

• Sarah Babcock
• Multivariate Statistics
• Spring 2000

2
Variables
3
Self-Descriptions

• kind
• intelligent
• optimistic
• jealous
• attractive
• shy
• competitive
• loving
• humorous
• persistent

• honest
• sensitive
• generous
• aggressive
• influential
• stubborn
• creative
• active
• intense
• lazy

4
Factors
Each factor represents a cluster of variables
that correlate closely with one another
5
Factors
6
Factor Analysis family of data reduction
techniques used to summarize large amounts of
data and identify relationships among multiple
variables.
7
Why Factor Analysis?

• Often too many variables to manage
• Not always clear which variables are most
  important
• Variables are redundant
• Correlation coefficient analysis between
  variables is useful, but soon becomes unwieldy

8
(No Transcript)
9
When to use Factor Analysis?

• Exploratory research
• Identification of underlying factors
• Screening of variables
• Data summarization
• Sampling of variables
• Clustering of objects

10
Data Input Matrix

• Observational or raw data

Variables
v1
v2 .
O1
O2
Objects
O3
O4
11
Correlation Matrix

• Calculate all correlation coefficients between
  variables

Variables
v1
v2 .
v1
v2
Variables
v3
v4
12
Factors
13
Factor Matrix

• Factor loadings from -1.00 to 1.00 represent
  degree to which each variable correlates with
  each factor

14
Key Ideas

• Factor Loading - can be positive or negative and
  high or low
• Factor Scores (calculated for original objects as
  a weighted combination of the scores on each
  input variable)
• High factor loadings mean high weights in
  equation for calculating factor scores

15
Number of Factors to Extract?

• Latent Root Criterion (Eigenvalues)
• Represents variance accounted for by factor
• Retain factors with values above 1.0 only
• A Priori Criterion
• Percentage of Variance Criterion
• Scree Test Criterion
• Scree accumulation of stony rubble at the base
  of a hill or cliff
• Graph of data allows researcher to get the big
  factors and eliminate the scree

16
Rotation of Factors

• Redefinition of factors such that loadings are
  very high or very low
• Can help in data interpretation
• Methods of rotation
• orthogonal (90 degree) and oblique methods
• Varimax (simplifies columns)
• Quartimax (simplifies rows)
• Equimax (rows and columns)
• Oblimin (used in SPSS)

17
Factor Analysis Tables

• Tabular presentation (Factors with the associated
  variables listed below)
• GOODNESS Factor Loadings
• Kind .71
• Generous .66
• Jealous - .51
• Sensitive .31

18
Factor Analysis Graphs

• Graphical presentation of results

19
Criticism of Factor Analysis

• There is great danger of assigning misleading or
  subjective factor names
• Factors are often obvious, making complex
  computer analysis unnecessary
• Factor analysis is subject to researcher bias
  Garbage In...Garbage Out

20
The End

21
(No Transcript)