Kaiser-Guttman criterion

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The Kaiser-Guttman criterion , often just called the Kaiser criterion , is a method for determining the number of factors in exploratory factor analysis . The criterion was developed in the 1950s by Louis Guttman and Kaiser and Dickman and, due to its simplicity and clarity, is the predominant method in practice, although others have already established themselves.

Background to factor selection

The aim of exploratory factor analysis is to reduce the dimensionality of a set of variables by explaining / modeling their variance through so-called latent factors to be constructed. This means that the exploratory factor analysis belongs to the so-called hypothesis- generating statistical methods (in contrast to the hypothesis- testing statistical methods). Because the goal of an exploratory factor analysis is always to reduce the dimensionality, the result of a factor analysis must always show fewer latent factors than the number of output variables. The question therefore arises as to how many latent factors can be used to explain / model the variable variance most satisfactorily. There is no fixed single criterion / method for the number of latent factors to be extracted, because the latent factors are statistical-mathematical constructs with which one would like to map / model the reality of the data in a data-reducing manner. There can therefore not be a single, unambiguous, objectively "correct" factor analysis result. It depends very much on the application, but it is by no means arbitrary because it has to be statistically justified. However, there are criteria / procedures the application of which leads to the suggestion of a certain number of factors. The factor solutions should always be explained and justified in terms of content / theory.

One such criterion for determining the number of factors is the Kaiser-Guttman criterion, but it is very conservative and its application, at least in psychometrics, is out of date. It leads in almost all applications means that the dimensionality significantly above estimates is. However, it can serve as an instrument, in a sense the "upper limit", i. H. to determine the maximum number of factors that can be justified .

Basic assumption and procedure

Since the factor analysis is a data-reducing procedure , it makes sense to only keep those factors as the maximum number that explain more variance than the original variables. This is only the case for factors with eigenvalues ​​greater than one.

The possible factors (or eigenvectors ) and their eigenvalues ​​are determined on the basis of a correlation matrix (Pearson or polychoric correlations) . The Kaiser-Guttman criterion states that only factors with eigenvalues ​​greater than one (if the variables are standardized = factor analysis based on the correlation matrix of the variables) or greater than the mean value of the eigenvalues ​​(if the variables are unstandardized = factor analysis based on the covariance matrix) of the variables), but the others are discarded.

criticism

The Kaiser-Guttman criterion is very easy to use and always leads to a clear solution. It is therefore used as a standard in many statistics packages when performing a factor analysis. It often overestimates the dimensionality and is hardly helpful for gaining meaningful interpretable factors.

Alternatives

In addition to the Kaiser-Guttman criterion, there are various other criteria:

  • the scree test , also known as the elbow criterion, or
  • the parallel analysis according to Horn.

In principle, several criteria should be used. In case of doubt, in particular, it is advisable to calculate several factor numbers and check them with regard to charges and interpretability.

See also

The Kaiser-Meyer-Olkin criterion , which is also used in factor analysis, has nothing to do with the Kaiser-Guttman criterion and must not be confused with it.

Individual evidence

  1. ↑ Guttman, L .: "Some necessary conditions for common factor analysis" in Psychometrika 19, 149-161, 1954.
  2. ^ Kaiser, HF, Dickman, K .: "Analytic determination of common factors" in American Psychologist 14, 425, 1959. (Abstract)
  3. ↑ Horn, JL: "A rationale and test for the number of factors in factor analysis" in Psychometrika 30, 179-185, 1965. (Modification according to Horn)

literature

  • Bortz, J. & Schuster, C. (2010). Factor analysis. In: Statistics for human and social scientists . 7th edition (pp. 385-433). Berlin and Heidelberg: Springer, ISBN 978-3-642-12769-4 .