The Behavior Of Number-Of-Factors Rules With Simulated Data

issues related to the decision of the number of factors to retain in factor analysis are identified, and three widely-used decision rules -- the Kaiser-Guttman, scree, and likelihood ratio tests -- are isolated for empirical study. Using two differing structural models and incorporating a number of relevant independent variables (such as number of variables, ratio of number of factors to number of variables, variable communality levels, and factorial complexity), the authors simulated 144 population data sets and, then, from these, 288 sample data sets, each with a precisely known (or incorporated) number of factors. The Kaiser-Guttman and scree rules were applied to the population data in Part I of the study, and all three rules were applied to the sample data sets in Part II. Overall trends and interactive results, in terms of the independent variables examined, are discussed in detail, and methods are presented for assessing the quality of the number-of-factors indicated by a particular rule.