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The performance of five methods for determi ning the number of components to retain (Horn' s parallel analy s is, Velicer 1 s MAP, Cattell 1 s SCREE, Bartlett's test and Kaiser ' s eigenvalu e greater than unity) was investigated across seven systematically varied factors (sample size, number of variables, number of component s, component saturation, equal or unequal numbers of var iables per component, and the presence or absence of unique and complex variables). Five sample correlation matrices were genera t ed at each of two levels of sample s ize from the 48 known population correlation matrices representing six levels of component patt ern complexit y. The performance of the parallel analysi s and the MAP methods was generally the best across all situati ons. The SCREE test was generally accurate but variable . Bartlett 's test was less accurate and more variable than the SCREE test. Kaiser ' s method tended to severely overestimate the number of components. Recommendations concerning the condi tions under which the methods are accurate and th e most effective and useful applications of combinations of methods are discuss ed.

A Comparison of Five Rules for Determining the Number of Components in Complex Patterns