The Varimax Criterion for Analytic Rotation in Factor Analysis
1958/09/01 by Henry F. Kaiser · 7,625 citations
Agricultural and Biological Sciences · Decision Sciences · Mathematics · #Algorithm #Applied mathematics #Factorial #Generalization #Geometry #Mathematical analysis #Mathematics #Optimal Experimental Design Methods #Psychometric Methodologies and Testing #Psychometrics #Rotation (mathematics) #Rotational invariance #Sensory Analysis and Statistical Methods #Simple (philosophy) #Statistics #Varimax rotation
paper · doi:10.1007/bf02289233
published in Psychometrika 23(3), 187-200 (Springer Science+Business Media)
openalex publication_date 1958/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract
An analytic criterion for rotation is defined. The scientific advantage of analytic criteria over subjective (graphical) rotational procedures is discussed. Carroll's criterion and the quartimax criterion are briefly reviewed; the varimax criterion is outlined in detail and contrasted both logically and numerically with the quartimax criterion. It is shown that the normal varimax solution probably coincides closely to the application of the principle of simple structure. However, it is proposed that the ultimate criterion of a rotational procedure is factorial invariance, not simple structure –although the two notions appear to be highly related. The normal varimax criterion is shown to be a two-dimensional generalization of the classic Spearman case, i.e., it shows perfect factorial invariance for two pure clusters. An example is given of the invariance of a normal varimax solution for more than two factors. The oblique normal varimax criterion is stated. A computational outline for the orthogonal normal varimax is appended.
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