Exploratory factor analysis

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Subject classification: this is a psychology resource .
Subject classification: this is a statistics resource .
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This page introduces and explains the use of exploratory factor analysis particularly for the purposes of psychometric instrument development in the context of developing psychological measurement tools.

Contents

[edit] Assumed knowledge

[edit] Purposes of factor analysis

There are two main purposes or applications of factor analysis:

[edit] Data reduction

  • Reducing data to a smaller set of summary variables.
  • For example, psychological questionnaire often aim to measure several psychological constructs, with each construct measured using multiple items (in order to enhance reliability and validity).

[edit] Exploring theoretical structure

  • Theoretical understandings of the underlying structure of phenomenon can be meaningfully explored and empirically tested using factor analysis.
  • For example, is intelligence better described as a single, general factor, or as consisting of multiple, independent dimensions?

[edit] History

[edit] Pros & cons

[edit] Assumptions

  • The main assumption is that there are linear relations between at least some sets of variables.
  • This can be tested by visually examining all or some of the bivariate scatterplots.
  • It can be explored by examining correlational statistics such as:
    1. Examine the inter-item correlations - are there at least several sizable correlations e.g., > .5?
    2. Examine the anti-image correlation matrix diagnals - they should be > ~.5.
    3. Examine the KMO (should be > ~.5) and Bartlett's test of sphericity (should be significant)
    4. Sample size: Ideally, there should be a ratio of > ~20:1 (cases per item), but factor analysis can still be reasonably done with > ~5:1 or for pilot study purposes, as low as 3:1.

[edit] Types

  • Principal components (PC): Analyses all variance in the items
  • Principal axis factoring (PAF): Analyses shared variance amongst the items

[edit] Establishing the number of factors

Consider:

  • Theory?
  • Eigen-values over 1?
  • Scree-plot?
  • Are all factors interpretable? (especially the last one?)
  • Have you tried several different models, with different numbers of factors?
  • Have you eliminated items which don't don't seem to belong? (this can change the structure/number of factors)?
  • Are the factor correlations not too high (e.g., not over ~.7?)

[edit] Criteria for selecting items

For a simple factor structure, consider each item with regard to:

  • Communality (ideally, above .5)
  • Primary (target) factor loading (should be above .5, preferably above .7)
  • Item cross-loadings (should be a gap of at least ~.2 between primary and cross-loadings), with cross-loadings above .3 being worrisome
  • Meaningful and useful membership to a factor (each item should make a meaningful (face validity) and useful (non-redundant) contribution to an identifiable factor)
  • Reliability (removal of the item wouldn't improve Cronbach's alpha)
  • See also: How do I eliminate items?

[edit] Data analysis exercises

[edit] See also

[edit] Wikipedia & Wikibooks

[edit] External links

[edit] References

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