Factor Analysis applying the eigen value > 1 'rule'

This is the same analysis as previously, except that the often-applied 'rule' of extracting only factors with eigen values > = 1.0 is used. In Minitab this is achieved by entering the required number in the "Number of factors to extract" box. The required number of factors is found from a preliminary analysis with all variables included.

The explanation of this rule, or more correctly the guideline, relates to the standardisation of variables. It is important to remember that the sum of the eigenvalues equals the sum of the variables' variances. When variables are standardised they have a variance of 1.0. This means that any component or factor, whose eigenvalue is less than one, retains less variance than one of the original variables. Consequently such components may be thought to convey less "information" than the original variables and should therefore be ignored. There are two aspects to this guideline that you should continually bear in mind.

  1. It is only a guideline and you should always inspect the analysis details to see if it should be overriden. For example, a component whose eigenvalue was 0.999 would not be extracted using the rule. This is clearly nonsense.

  2. The rule only applies when the analysis is based on standardised variables. If the analysis is carried out on the covariance matrix of unstandardised data (whose variance may be far in excess of 1.0) then the rule should not be applied.

In the previous analysis all of the communalities were 1.00. This is no longer true (see below). This is because only two factors are retained and hence not all of the common variance is retained. For example, the two components retain 75.9% of the v1's variance (the communality is 0.759). The remaining 24.1% is shared between the 3 factors that are discarded.

Variable Factor1  Factor2 Communality
  V1     -0.805   0.334   0.759
  V2     -0.946  -0.172   0.925
  V3     -0.919  -0.100   0.855
  V4     -0.188  -0.837   0.736
  V5      0.160  -0.893   0.823
Variance  2.4490  1.6497  4.0987
  % Var   0.490   0.330   0.820

Since the loadings are identical to those from the "full" analysis the conclusions remain the same.

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