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A corrmon problem encountered in the applied use of pr incipal components analysis (PCA) as a data reduction technique is the determination of the number of components to retain . This problem is particularly acute when some method of rotation is to be employed. This study examined the consequences of employing each of four decision methods upon PCA's of correlation matrices made up of systematically differing numbers of variables and subjects and based upon known systematically differing underlying component structures. Three levels of number of variables (36, 72, 144), sample size (75, 150, 450) and number of components (3, 6, 12) were examined at each of two (.50 and . 80) levels of component saturation. Within each example each component was defined by the same number of variables. No unique components nor complex variables were included in the set of computer generated data. It was found the different rules lead to dramatical ly different results . In general, the scree test (SCREE) and the minimum average partial test (MAP) were the most accurate. The Bartlett test (BART) was somewhat less accurate and the ei genvalue greater than one rule (Kl) was quite inaccurate. Increases in sample size and component saturation improved the performance of the rules . Increases in the number of variables examined increased the accuracy of SCREE and MAP, did not effect BART markedly but drasticly decreased Kl's accuracy. Kl often greatly overestimated the number of components to retain.

Factors Influencing Four Rules for Determining the Number of Principal Components to Retain