# PSYC214: Weeks 18-20: Principal Components Analysis

• Principal components analysis
• Introduction
• Calculation
HideShow resource information

## 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.
1 of 2

## 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

-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
2 of 2