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.
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