The weighted varimax rotation and the promax rotation

Abstract

Kaiser's iterative algorithm for the varimax rotation fails when (a) there is a substantial duster of test vectom near the middle of each bounding hyperplane, leading to non-bounding hyperplanes more heavily overdetermined than those at the boundaries of the configuration of test vectors, and/or (b) there are appreciably more than m (m factors) tests whose loadings on one o f the factors of the initial F-matrix, usually the first, are near-zero, leading to overdetermination of the hyperplane orthogonal to this initial F-axis before rotation. These difficulties are overcome by weighting the test vectors, giving maximum weights to those likely to be near the primary axes, intermediate weights to those likely to be near hyperptanes but not near primary axes, and near-zero weights to those almost collinear with or almost orthogonal to the first initial F-axis. Applications to the Promax rotation are discussed, and it is shown that these procedures solve Thurstone's hitherto intractable "invariant" box problem as well as other more common problems based on real data.

The LWDS-10J: Reliability and Validity of the Lebanon Waterpipe Dependence Scale Among University Students in Jordan

“…We examined eigenvalues, the scree plot, and proportion of the data explained by each factor in order to determine the ideal number of factors (DeVellis, 2003). We then reconducted principal-components analysis while forcing this number of factors and adjusting the factor weightings using Varimax rotation (Cureton & Mulaik, 1975). We examined the resulting factor loading pattern to characterize the resulting factors conceptually.…”

El análisis factorial exploratorio de los ítems: una guía práctica, revisada y actualizada

“…Por su parte, Equamax combina ambos criterios (un solo factor/varios factores) y lleva a soluciones intermedias. También se han formulado versiones ponderadas del criterio Varimax (e.g., Cureton y Mulaik, 1975).…”

Rotation to Simple Loadings Using Component Loss Functions: The Oblique Case

“…A three factor initial loading matrix A was extracted from data generated using these variables. For this we used the A given by Cureton and Mulaik (1975). Like the 24 psychological tests data in Harman this matrix has been used extensively to demonstrate and compare rotation methods.…”