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Chapter 4 (Test dimensionality (3 key questions (how many dimensions? (one…

- - - - no
        
        dimensions do not reflect any one higher-order factor
        
        each subset is treated as its own test
        
        a total test score is not calculated
        
        number of composite scores reflects number of dimensions
      - yes
        
        total test score is computed
        
        multidimensional scale with correlated factors
    - - how do these dimensions tie together
      - examined with factor analysis
      - do they represent a higher-order psychological attribute?
    - - one
        
        conceptual homogeneity
        
        responses to items all come from one psychological attribute
        
        one single composite score (from items)
        
        unidimensional scale
      - multidimensional tests
      - two or more psychological attributes affect responses to items
      - groups of items represent a subset
        
        each subset represents one psychological dimension/attribute
        
        subsets have their own composite score
        
        all subset scores form a total composite score
      - higher order factor
        
        general attribute affecting more specific dimensions
      - simple structure
        
        certain items load mainly on one specific dimension
- - - - clear, pre-existing ideas about number of dimensions
      - used to CONFIRM a hypothesis about a test's dimensionality
    - - most commonly used form of factor analysis
      - finds factors that explain as much variance as possible
      - a regression line is fitted to a potential factor
      - factor loadings
        
        correlation between item and factor
      - Conducting an EFA
        
        choosing extraction method
        
        principal axis factoring
        
        maximum likelihood factor analysis
        
        principal component analysi
        
        correlation between each item score and factor score
        
        interpreting number of dimensions
        
        eigenvalues greater than 1
        
        amount of eigenvalues>1 is the number of dimensions
        
        most commonly used
        
        inaccurate because eigenvalues depend on amount of items
        
        many items likely gives many eigenvalues>1
        
        large eigenvalues explain a lot of variance --> possible dimension
        
        relative sizes of eigenvalues
        
        large differences between eigenvalues suggest separate factors
        
        point where differences between subsequent eigenvalues become relatively small
        
        scree plots
        
        eigenvalues plotted on graph
        
        look for a large 'drop' in eigenvalues
        
        point before the drop is the amount of dimensions
        
        after this 'drop', gradient of eigenvalues becomes less steep
        
        in reality this is often very ambiguous
        
        no clear drop, leads to different interpretations
      - unclear about the number of dimensions a test reflects
  - - - varimax procedure
      - generates uncorrelated factors
      - maximal loadings on one factor
    - - promax, direct oblimin
      - factors may be correlated or uncorrelated to each other
      - correlation between factors
        
        represents higher-order attributes
    - - factor loadings between -1 and 1
        
        correlations between each item and factor
      - in oblique rotation
        
        structure coefficients
        
        item responses and their levels of underlying factors
        
        pattern coefficients
        
        unique association between item and factor
      - interpreting factor loadings
        
        size of loadings
        
        degree of association between item and factor
        
        direction of loading
        
        positive
        
        high score on item indicates high level of factor
        
        negative
        
        high score on item indicates low level of factor
        
        items which load weakly on all factors
        
        item not well related to other items
        
        does not represent same psychological construct
        
        items which load strong on multiple factors
        
        suggests that these items may reflect multiple dimensions