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PCA and EFA (differences (Principles components are linear relationships,…

- - - - components remain uncorrelated
      - types
        
        Quartimax
        
        simplifies the variable pattern of loadings
        
        varimax
        
        simplifies the factor pattern of loadings
        
        equamax
        
        simplifies variable and factor pattern
    - - components allowed to correlate
      - types
        
        direct oblimin
        
        promax
- - - - tends to arbitrarily chose 1/3 of the variables
  - - - calculate average partial correlation after each extraction
        
        eventually components that reflect noise get partialled out and av. partial correlation begins to rise
        
        choose no. of components corresponding to minimum average partial correlation
- - - - High factor loadings (greater than .4)
      - few cross loadings of greater than .32
      - more than 3 strongly loading items per factor
  - - - variance due to common parts
        
        should be near 1
    - - due to unique parts (should be near 0)
  - - - significance infers that there's at least one non-zero correlation at population level,
  - - - use when dat non-normal
      - ML assumes normlaity
- - - - scores may correlate with other factors too
- - - - common factors are standardised with a variance of 1
      - common factors are uncorrelated
      - specific factors are uncorrelated
      - common factors are uncorrelated with specific factors
- - - - finding optimal linear transformations
        
        finding new axes for data
        
        =components
        
        Line of best fit to minimise error
        
        Eigan value= variance of data points against line of best fit
        
        each component will explain as much of the variance in the data as possible
      - components are not correlated with one another even though the original variables are
      - number of principle components= no. of variables
        
        components will successively be able to explain less of the variance (1st PC will explain the most)