Number of factors

• Scree Plot (Cattell) - Not a test

  • Look for bend in plot

  • Include factor located right at bend point

• Kaiser (or Latent Root) criterion

  • Eigenvalues greater than 1

  • Also, 1 is the amount of variance accounted for by a single item (r2 = 1.00). If eigenvalue < 1.00 then factor accounts for less variance than a single item.

• A priori hypothesized number of factors

Scree Plot (Cattell’s) method:

Look for bend in plot

• Imagine drawing a straight line that summarizes the vertical part of the plot,

• and another that summarizes the horizontal part.

• The point of inflexion is the data point at which these two lines meet.

  Rule-of-thumb:

  Retain (extract) the factors to the left of the point of inflexion

Kaiser’s (Latent Root) method:

Eigenvalues greater than 1.

• λ= 1.0 is the amount of variance accounted for by a single item (r2 = 1.0).

• If λ < 1.0, then factor accounts for less variance than a single item.

  Rule-of-thumb:

  Retain (extract) the factors greater than λ = 1.0

• Although this rule is the default in SPSS, studies have been unanimous in finding that it is the least accurate guideline available

• Zwick and Velicer (1986) “we cannot recommend the K1 rule for PCA [principal component analysis]” (p. 439)

• “The eigenvalue greater than one rule was extremely inaccurate and was the most variable of all the methods. Continued use of this method is not recommended” (Velicer, Eaton, & Fava, 2000, p. 68)

• Most studies have found that K1 consistently overestimates the true number of components/factors in the population

”We suggest researchers use a combination of SMT [sequential chi-square model tests] and either Hull, the EKC [empirical Kaiser criterion], or traditional PA [parallel analysis], because the number of factors was almost always correctly retrieved if those methods converged. When the results of this combination rule are inconclusive, traditional PA, CD [comparison data method], and the EKC performed comparatively well.” (Auerswald & Moshagen, 2019, p. 1)

=> These methods should be combined for a more refined analysis

1. Sequentical Chi-Square Model

Either

• Hull

• Empirical Kaiser criterion

• Traditional parallel analysis