factor analysis ( psychometrics)

• why use factor analysis

  practical uses

  • scale development
  • scale validation
  • data reduction
  • understand the nature of psychological constructs
• types of factor analysis

  exploratory factor analysis

  • exploring something new
  • data driven approach
• types of factor analysis

  confirmatory factor analysis

  • often used to replicate findings from CFA in different data
  • theory driven approach
• the statistical model

  A) observed score

  B) true score on the latent construct

  C) factor loading

  D) measurement error

  
• lambda, the factor loading

  • range from -1 to +1
  • higher factor loadings demonstrate a higher degree of association between the latent variable and that indicator
  • more of the variance in responses to that indicate is attributable to the latent factor than to measurement error
  • higher factor loadings - item is a better indicator of your latent construct
• factor loadings lambda

  • factor loadings above .6 are desirable
  • factor loadings above .4 are acceptable
• factor analysis involves

  1. extraction
  2. rotation
  3. interpretation
• EFA - checks

  sample size

  • rule of thumb > 300

  correlations between variables

  • between 0.3 and 0.9 desirable
• EFA - checks

  KMO measure of sampling adequacy

  • values range 0-1 and you want >0.5 desirable

  bartlett's test of sphericity

  • tests whether R matrix is an identity matrix
  • should be significant (p <0.05)
• step 1 - extraction (how many factors are there)

  how many factors to extract

  • factor analysis will extract as many factors as there are items ( but obviously we don't want this - the point of doing an FA is to reduce our factors)
  • Kaiser-guttman rule: factors with eigenvalues greater than one should be retained
  • an eigenvalue is the sum of the squared factor loadings for a given factor
  • the eigenvalue associated with each factor gives us an idea of how much variance in the observed items it has explained (we want factors that explain a lot of variance)
• factor analysis

  • technique used to tell us how well we measure things and can be used for the following:
  • questionnaire development (e.g. carnism)
  • reduce the number of items in a questionnaire (e.g. getting rid of all the items you generated that don't reflect attitudes towards eating meat)
  • better understand the nature of psychological constructs (by telling us whether we are measuring 1 thing or multiple things
• lambda - the strength of association between the observed variable and underlying latent variable
• refresher: steps in running a factor analysis

  three important steps

  1. extraction - how many factors to extract
  2. rotation - iterative process to decide what questionnaire item goes to which factor
  3. interpretation - when you use theory ( and common sense) to label the final factors (dimension / latent constrcuts)
• step 1 - extraction

  1. kaiser-guttman rule: factors with eigenvalues greater than one
  2. the scree plot
• reliability

  stability

  • test-retest reliability

  inter-rater reliability

  • cohen's kappa

  internal consistency

  • split-half reliability
  • cronbacks coefficient
• cronbach's alpha

  problem with split-half reliability

  • variables can be split randomly in many ways - many have different results

  cronbach's alpha - basically accounts for every possible way to split the items up

  • ranges from 0-1 with higher values reflecting greater consistency
  • values > 0.7 desirable

  tells us participants are answering questions in the same way

  not a perfect measure of internal consistency

  • number of items can impact alpha
  • scoring direction of items