From Wikiversity
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.
[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:
- Examine the inter-item correlations - are there at least several sizable correlations e.g., > .5?
- Examine the anti-image correlation matrix diagnals - they should be > ~.5.
- Examine the KMO (should be > ~.5) and Bartlett's test of sphericity (should be significant)
- 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.
- 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
