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\name{DMFA}
\alias{DMFA}
\title{Dual Multiple Factor Analysis (DMFA)}
\description{
Performs Dual Multiple Factor Analysis (DMFA) with supplementary individuals, supplementary quantitative
variables and supplementary categorical variables.
}
\usage{
DMFA(don, num.fact = ncol(don), scale.unit = TRUE, ncp = 5,
quanti.sup = NULL, quali.sup = NULL, graph = TRUE, axes=c(1,2))}
\arguments{
\item{don}{a data frame with \emph{n} rows (individuals) and \emph{p} columns (numeric variables)}
\item{num.fact}{the number of the categorical variable which allows to make the group of individuals}
\item{scale.unit}{a boolean, if TRUE (value set by default) then data are scaled to unit variance}
\item{ncp}{number of dimensions kept in the results (by default 5)}
\item{quanti.sup}{a vector indicating the indexes of the quantitative supplementary variables}
\item{quali.sup}{a vector indicating the indexes of the categorical supplementary variables}
\item{graph}{boolean, if TRUE a graph is displayed}
\item{axes}{a length 2 vector specifying the components to plot}
}
\value{
Returns a list including:
\item{eig}{a matrix containing all the eigenvalues, the percentage of variance and the cumulative percentage of variance}
\item{var}{a list of matrices containing all the results for the active variables (coordinates, correlation between variables and axes, square cosine, contributions)}
\item{ind}{a list of matrices containing all the results for the active individuals (coordinates, square cosine, contributions)}
\item{ind.sup}{a list of matrices containing all the results for the supplementary individuals (coordinates, square cosine)}
\item{quanti.sup}{a list of matrices containing all the results for the supplementary quantitative variables (coordinates, correlation between variables and axes)}
\item{quali.sup}{a list of matrices containing all the results for the supplementary categorical variables (coordinates of each categories of each variables, and v.test which is a criterion with a Normal distribution)}
\item{svd}{the result of the singular value decomposition}
\item{var.partiel}{a list with the partial coordinate of the variables for each group}
\item{cor.dim.gr}{}
\item{Xc}{a list with the data centered by group}
\item{group}{a list with the results for the groups (cordinate, normalized coordinates, cos2)}
\item{Cov }{a list with the covariance matrices for each group}
Returns the individuals factor map and the variables factor map.
}
\author{Francois Husson \email{francois.husson@institut-agro.fr}}
\seealso{ \code{\link{plot.DMFA}}, \code{\link{dimdesc}}}
\examples{
## Example with the famous Fisher's iris data
res.dmfa = DMFA ( iris, num.fact = 5)
}
\keyword{multivariate}
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