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Factor Analysis I

Factor Analysis I. Principle Components Analysis. “Data Reduction”. Purpose of factor analysis is to determine a minimum number of “factors” or components that can explain a maximum amount of variance in a set of survey items.

dorothy-nicholson
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Factor Analysis I

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  1. Factor Analysis I Principle Components Analysis

  2. “Data Reduction” • Purpose of factor analysis is to determine a minimum number of “factors” or components that can explain a maximum amount of variance in a set of survey items. • In the absence of a conceptual model, the process can become entirely “machine driven” and uninteresting.

  3. Factors • X1 an observable response to a survey item. • Fs are unobservable factors determined from shared variance found with in the sample and the n items. • U is the unique variance attributable only to that survey item. • A factor analysis of n items will generate at least n factors.

  4. “Communalities” show the proportion of variance in each items explained by the factors (or shared with other items). • Extraction of .862 shows that response to ‘Count Per Box’ shows that 86.2% of the overall variance in the item can be explained by the principle components (or factors).

  5. Eigenvalues will sum to n, the number of items. • Three components have eigenvalues over 1.00, indicating they account for more an “expected amount” for completely independent items. • Subtotals of eigenvalues/n =% of Variance explained.

  6. Component Matrix • “Default” output with each extraction technique, of an “unrotated” set of factors.

  7. “Rotation” • You’re attempting to produce a set of factor loadings to fit your conceptual presentation of the factors. • Do you believe the factors to be completely independent or orthogonal: Varimax. • Do your believe that responses could indicate shared or correlated traits: Oblimim (“Oblique”)

  8. Rotated Solution: Varimax • New eigenvalues and % of variance explained—you have created new factors to meet your assumption of the rotation. • Here is how factor analysis sometime is treated with skepticism befitting paranormal psychic phenomena, such as “voodoo.”

  9. Rotated Solution “Oblimin” • Cannot make claims about % of variance explained, total of eigenvalues exceeds n.

  10. Varimax rotation Oblimin rotation “New component matrices”

  11. Additional “Oblimin” Output

  12. Two Major Extraction Methods • Principle Components—best for data reduction • Common Factor, or Principal Axis Factoring • SPSS includes: • Unweighted least squares • Generalized least squares • Maximum likelihood • Alpha factoring • Image factoring

  13. Farm Credit Services Results • The 17 questionnaire items were originally designed to capture unique dimensions of satisfaction a customer with a lender. • What does the explained variance of a factor analysis illustrate?

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