% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/pfa.R
\name{pfa}
\alias{pfa}
\title{Factor analysis for compositional data}
\usage{
pfa(
  x,
  factors,
  robust = TRUE,
  data = NULL,
  covmat = NULL,
  n.obs = NA,
  subset,
  na.action,
  start = NULL,
  scores = c("none", "regression", "Bartlett"),
  rotation = "varimax",
  maxiter = 5,
  control = NULL,
  ...
)
}
\arguments{
\item{x}{(robustly) scaled input data}

\item{factors}{number of factors}

\item{robust}{default value is TRUE}

\item{data}{default value is NULL}

\item{covmat}{(robustly) computed covariance or correlation matrix}

\item{n.obs}{number of observations}

\item{subset}{if a subset is used}

\item{na.action}{what to do with NA values}

\item{start}{starting values}

\item{scores}{which method should be used to calculate the scores}

\item{rotation}{if a rotation should be made}

\item{maxiter}{maximum number of iterations}

\item{control}{default value is NULL}

\item{\dots}{arguments for creating a list}
}
\value{
\item{loadings }{A matrix of loadings, one column for each factor.
The factors are ordered in decreasing order of sums of squares of loadings.}
\item{uniqueness }{uniqueness} \item{correlation }{correlation matrix}
\item{criteria}{The results of the optimization: the value of the negativ
log-likelihood and information of the iterations used.} \item{factors }{the
factors } \item{dof }{degrees of freedom} \item{method }{\dQuote{principal}}
\item{n.obs }{number of observations if available, or NA} \item{call }{The
matched call.} \item{STATISTIC, PVAL }{The significance-test statistic and
p-value, if they can be computed}
}
\description{
Computes the principal factor analysis of the input data which are
transformed and centered first.
}
\details{
The main difference to usual implementations is that uniquenesses are nor
longer of diagonal form. This kind of factor analysis is designed for
centered log-ratio transformed compositional data. However, if the
covariance is not specified, the covariance is estimated from isometric
log-ratio transformed data internally, but the data used for factor analysis
are backtransformed to the clr space (see Filzmoser et al., 2009).
}
\examples{

data(expenditures)
x <- expenditures
res.rob <- pfa(x, factors=1)
res.cla <- pfa(x, factors=1, robust=FALSE)


## the following produce always the same result:
res1 <- pfa(x, factors=1, covmat="covMcd")
res2 <- pfa(x, factors=1, covmat=robustbase::covMcd(pivotCoord(x))$cov)
res3 <- pfa(x, factors=1, covmat=robustbase::covMcd(pivotCoord(x)))

}
\references{
C. Reimann, P. Filzmoser, R.G. Garrett, and R. Dutter (2008):
Statistical Data Analysis Explained.  \emph{Applied Environmental Statistics
with R}.  John Wiley and Sons, Chichester, 2008.

P. Filzmoser, K. Hron, C. Reimann, R. Garrett (2009): Robust Factor Analysis
for Compositional Data.  \emph{Computers and Geosciences}, \bold{35} (9),
1854--1861.
}
\author{
Peter Filzmoser, Karel Hron, Matthias Templ
}
\keyword{multivariate}