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Overview of Factor Analysis

Overview of Factor Analysis. Construct combinations of quantitative variables. Reduce a large set of variables to a smaller number of factors. Uses of Factor Analysis. Develop and test theories Describe differences between individuals

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Overview of Factor Analysis

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  1. Overview of Factor Analysis • Construct combinations of quantitative variables. • Reduce a large set of variables to a smaller number of factors.

  2. Uses of Factor Analysis • Develop and test theories • Describe differences between individuals • Determine which variables/measurements may be dropped from a scale or battery

  3. Extraction of Factors • Based on correlations among variables • The first factor will explain the most variance in the original scores, with each factor explaining less variance.

  4. Factor Rotation • Transform the loadings to make it easier to interpret what the factors represent. • A loading indicates how important a variable is for that particular factor. • VARIMAX is the most popular method: • Maximizes variability in factor loadings within factors • Maintains orthogonal factors

  5. Assumptions for Factor Analysis • Linear relationships among variables • Multivariate normal distributions

  6. Reporting Factor Analysis • Decide on number of factors based on factor extraction (principal components analysis). • The eigenvalue for a factor represents the amount of variance in the original scores explained by the factor. • Also look at percentage of variance explained.

  7. Reporting Factor Analysis • One way to decide on the number of factors is to only use those with eigenvalues greater than one. • The other way is to examine the scree plot and discard factors after the plot flattens out.

  8. Reporting Factor Analysis • Look at the rotated factor loadings to interpret and name the factors. • A confirmatory factor analysis can be done as a follow-up.

  9. Review Question! What are the two steps in factor analysis?

  10. Choosing Stats A business school obtains a sample of students who have taken an emotional intelligence test and a leadership inventory. They would like to use information from this data set to develop a way of predicting leadership ability for students who have known scores on the emotional intelligence test.

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