Determining the number of interpretable factors

Bibliographic Data

ID4885576
AuthorsCharles B Crawford, Charles Crawford (0000-0002-9009-5271, corresponding author)
Year1975
Volume82
Issue2
Pages226-237
Publication date1975-03-01
Peer ReviewedYes
Open AccessNo
TypeARTICLE
VenuePsychological Bulletin (JOURNAL)
Journal identifiersISSN: 0033-2909 • E-ISSN: 1939-1455
PublisherAmerican Psychological Association (APA) (PUBLISHER)
DOI10.1037/h0076374
OpenAlexW2098949351
LanguageEN
Citations received15
References cited7

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 & Hamburger, 1967). The inclusion of too few factors in the rotation results in the loss of potentially interpretable factors. Orthogonally rotating too many factors causes factor splitting, resulting in pseudospecific factors (Cattell, 1966). Rotating too many oblique factors may produce high interfactor correlations or cause the factor space to collapse. One of the key issues in a recent dispute between Eysenck (1971) and Cattell (1972) about the nature of the extraversion and neuroticism factors involved a difference in views on the number of factors that should be rotated and interpreted. Many similar examples could be cited. Most tests for determining the number of factors are based on either statistical or psychometric principles. In the classical statistical approach (Lawley, 1963; 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

Cognitive psychology · Statistics · Advanced Statistical Modeling Techniques · Cognitive Abilities and Testing · Mathematics · Psychology · Psychometric Methodologies and Testing · Social Psychology

Tools

Open DOISci-Hub