As the purpose of factor analysis is data reduction and summarization, including all of the factors of a particular factor solution in one's research report would be non-productive. This is especially true when one considers that the number of factors naturally increase with the size of the original variable set.

As the researcher is usually able to choose the number of factors to be generated by his software program, he typically performs additional factor runs after an initial screening of the factors. These additional runs include some number of factors slightly higher (two to three) and lower (one) than that obtained after the initial screen, and require some form of factor rotation. The criteria for the initial screening of factors are provided below:

• Latent Root Criterion (factor analysis (factor extraction criteria) | top) - The most commonly used technique for selecting the number of factors for further analysis is the latent root criterion. One simply eliminates those factors whose eigen values (latent roots) are less than one. The principal behind this criterion is straight forward; one should not consider factors that account for less variance than any of the single variables included in the original variable set.
  
  Although the latent root criterion is well suited for principal component analysis for which all of the variance is included, it is less well suited for common factor analysis in which only the shared variance among all variables is included in the initial extraction procedure. Apparently this procedure works well when the initial number of variables is between 20 and 50.
  
  
• A Priori Criterion (factor analysis (factor extraction criteria) | top) - This criterion is useful when the researcher is testing an hypothesis about the number of factors that best describe a particular variable set, or when the researcher is seeking to replicate another researcher's work for which a particular number of factors was extracted. In effect the researcher decides before he begins his analysis how many factors he wishes to examine.
  
  
• Percentage of Variance Criterion (factor analysis (factor extraction criteria) | top) - With this criterion one considers the cumulative percentage of variance accounted for by successive factors. Where the cut-off point should be, however, is somewhat arbitrary in so far as it depends on the research objective and the desired degree of data precision. One must strike a balance between the amount of total variance that is taken into account and the ability to provide a clear interpretation of the factors.
  
  
• The Scree Test Criterion (factor analysis (factor extraction criteria) | top) - The Scree test is well suited for principal component analysis in so far as it is based on the relative amounts of common and unique variance employed to obtain a single factor. Factors that are dominated by unique variance are of little use for the purpose of data reductiton and summary.
  
  The Scree test is a visual test that looks for disjunctures in the pattern of eigen values as a function of factor succession. Since factors are extracted with increasingly less common variance as a basis for their determination, at some point unique variance dominates common variance, and disjunctures in the pattern of eigenvalues begin to form. A quick comparison of the the latent root and Scree test criteria in the sample diagram reveals a different number of factor selection outcomes. The Scree test would suggest either 5 or 10 factors depending upon the desired level of precision, whereas the latent root criterion yields 8.

Summary

Obviously which criterion one selects will depend on the individual research project and the researcher's objective. In the final analysis factors must be interpreted, if they are to provide meaningful results. The above criteria are simply guidelines for judgment -- not fast rules for factor number selection. (factor extraction criteria) | top)