A Comparison of Methods for Determining the Number of Factors to Retain in Exploratory Factor Analysis for Categorical Indicator Variables

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Abstract
Exploratory factor analysis (EFA) is a widely used tool in the social sciences. Researchers employ it to identify the latent structure underlying observed indicator variables during the process of scale development, theory construction, and comparison of various constructs. One of the most important aspects of conducting EFA is determining the number of factors to retain. There exist a number of techniques for this purpose, but none have been identified as uniformly optimal in all situations. The purpose of this simulation study is to compare several such techniques in the context of dichotomous and ordinal indicator variables (corresponding to items on an instrument). Some of the methods investigated in this study include well-established techniques, such as parallel analysis and the minimum average partial correlation, as well as newly developed ones, such as out-of-sample prediction error and the next eigenvalue sufficiency test. The results of the study demonstrate that a Bayesian estimation approach and the out-of-sample prediction error method are particularly effective for identifying the number of factors to retain. The implications for practice are discussed.

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