Determining the number of interpretable factors.

A major weakness of current methods of determining the number of factors is that they require this decision to be made before rotation; therefore, information on the possible interpretability of factors cannot be considered in determining the appropriate number. An objective, noninferential index for determining the number of interpretable factors is developed and applied to several examples selected from the literature. The effects of type of rotation, type of communality estimate, and statistical sampling on the index were investigated. Results indicate that this is a promising method for determining number of interpretable factors and that principal components factors are less interpretable than are squared multiple correlation and image factors. Determining the number of factors is one of the most important problems facing the researcher wishing to use factor analysis. Rotation procedures require a prior, independent estimate of the number of factors because the rotated loadings are dependent on the number of factors rotated (Cliff Rao, 1955), the N individuals are considered to be a sample from a population of individuals, and an attempt is made to make inferences about this population from the characteristics of the sample. Statistical tests are actually tests of the importance of the last (« — k) factors,