| % File src/library/stats/man/varimax.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2018 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{varimax} |
| \alias{promax} |
| \alias{varimax} |
| \title{Rotation Methods for Factor Analysis} |
| \description{ |
| These functions \sQuote{rotate} loading matrices in factor analysis. |
| } |
| \usage{ |
| varimax(x, normalize = TRUE, eps = 1e-5) |
| promax(x, m = 4) |
| } |
| \arguments{ |
| \item{x}{A loadings matrix, with \eqn{p} rows and \eqn{k < p} columns} |
| \item{m}{The power used the target for \code{promax}. Values of 2 to |
| 4 are recommended.} |
| \item{normalize}{logical. Should Kaiser normalization be performed? |
| If so the rows of \code{x} are re-scaled to unit length before |
| rotation, and scaled back afterwards.} |
| \item{eps}{The tolerance for stopping: the relative change in the sum |
| of singular values.} |
| } |
| \details{ |
| These seek a \sQuote{rotation} of the factors \code{x \%*\% T} that |
| aims to clarify the structure of the loadings matrix. The matrix |
| \code{T} is a rotation (possibly with reflection) for \code{varimax}, |
| but a general linear transformation for \code{promax}, with the |
| variance of the factors being preserved. |
| } |
| \value{ |
| A list with components |
| \item{loadings}{The \sQuote{rotated} loadings matrix, |
| \code{x \%*\% rotmat}, of class \code{"loadings"}.} |
| \item{rotmat}{The \sQuote{rotation} matrix.} |
| } |
| \references{ |
| Hendrickson, A. E. and White, P. O. (1964). |
| Promax: a quick method for rotation to orthogonal oblique structure. |
| \emph{British Journal of Statistical Psychology}, \bold{17}, 65--70. |
| \doi{10.1111/j.2044-8317.1964.tb00244.x}. |
| |
| Horst, P. (1965). |
| \emph{Factor Analysis of Data Matrices}. |
| Holt, Rinehart and Winston. |
| Chapter 10. |
| |
| Kaiser, H. F. (1958). |
| The varimax criterion for analytic rotation in factor analysis. |
| \emph{Psychometrika}, \bold{23}, 187--200. |
| \doi{10.1007/BF02289233}. |
| |
| Lawley, D. N. and Maxwell, A. E. (1971). |
| \emph{Factor Analysis as a Statistical Method}, second edition. |
| Butterworths. |
| } |
| \seealso{\code{\link{factanal}}, \code{\link{Harman74.cor}}.} |
| |
| \examples{ |
| ## varimax with normalize = TRUE is the default |
| fa <- factanal( ~., 2, data = swiss) |
| varimax(loadings(fa), normalize = FALSE) |
| promax(loadings(fa)) |
| } |
| \keyword{multivariate} |