PSYC214: Weeks 18-20: Principal Components Analysis

  • Principal components analysis
    • Introduction
    • Calculation
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Geometrical Explanation of Principal Components An

  • Each measure is represented by a line starting from a common point
  • Correlation between measures is represented by the cosine of the angle
  • The bigger the angle, the smaller the correlation and vice versa
  • With 3 or more variables, the plot becomes multidimensional

Zero order correlation: 90 degress or right angle

  • Variables clumps to form factors
  • First factor: attempts to capture all of the variance
    Second factor: attempts to capture the remaining variance, and so on
    Orthogonal to the first factor.
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Principal components analysis

Rotation: changes the loading between the measures and factors, making the factors more interpretable, however the variance remains the same.
Makes both high and low correlations with the factor clearer.

Communalities: proportion of the variance of each variable captured by the analysis

Eigenvalues: variance captured by the factor

Factor loadings: correlations between the variables and the factors

-ve, limitations of factor analysis:

  • factors that emerge are dependant on the measures entered
  • if there are few measures representing a factor, it may not emerge
  • based on corrrelations; only linear relationships are captured
  • need replications
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