Applied Statistics Using SAS and SPSS

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Applied Statistics Using SAS and SPSS

• Topic Factor Analysis
• By Prof Kelly Fan, Cal State Univ, East Bay

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Outline

• Introduction
• Principal component analysis
• Rotations
• Using communalities other than one

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Introduction

• Reduce data
• Summarize many ordinal categorical factors by a
  few combinations of them (new factors)

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Example. 6 Questions

• Goal a measure of depression and a measure of
  paranoia (how pleasant)
• 6 questions with response using number 1 to 7.
  The smaller the number is, the stronger the
  subject agrees. 4 no opinion

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Example. 6 Questions

• I usually feel blue.
• People often stare at me.
• I think that people are following me.
• I am usually happy.
• Someone is trying to hurt me.
• I enjoy going to parties.
• Q. Which questions will a depressed person likely
  agree with? A happy person?

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Data Set
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Data Set
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Principal Component Analysis

• Analyze gtgt Data Reduction gtgt Factor

The bigger the eigenvalue is, the more
information this factor (component) carries.
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A Visual Tool Scree Plot
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Communalities

• Communalities represent how much variance in the
  original variables is explained by all of the
  factors kept in the analysis.

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SPSS Output
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Two Summary Factors
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A Visual Tool Component Plot
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Discussion

• Q4 Q6 should be at the same direction of factor
  1 2 (component 1 2)
• The other questions should be at the same
  direction of factor 1 2 (component 1 2)
• Need a rotation!!

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Rotation Varimax Rotation
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Varimax rotation
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Using Communalities Other Than One

• When the original factors are not equally
  important
• Different methods of extraction

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Un-weighted Least Squares
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Varimax rotation