##### https://github.com/cran/nFactors
Tip revision: 4de3e28
nFactors-parameters.rd
\name{nFactors-parameters}
\alias{nFactors-parameters}
\alias{nFactors-parameters}
\docType{package}
\title{ Argument and Value Parameters Common to the Different Functions Available in Package nFactors}

\description{
This help file describes the argument and value parameters used in the different functions
available in package \pkg{nFactors}.  \cr

\emph{Arguments}:
\enumerate{
\item{\emph{adequacy}:}{          logical: if \code{TRUE} prints the recovered
population matrix from the factor structure
(\code{structureSim})}
\item{\emph{all}:}{               logical:   if \code{TRUE} computes he Bentler and Yuan
index (very long computing time to consider)
(\code{structureSim, studySim})}
\item{\emph{alpha}:}{             numeric: statistical significance level
(\code{nBartlett, nBentler})}
\item{\emph{aparallel}:}{         numeric: results of a parallel analysis
(\code{nScree}) }
\item{\emph{cent}:}{              depreciated numeric (use quantile instead):
quantile of the distribution
(\code{moreStats, parallel})}
\item{\emph{communalities}:}{     character: initial values for communalities
(\code{"component"},
\code{"ginv"}, \code{"maxr"}, or \code{"multiple"})
(\code{iterativePrincipalAxis, principalAxis})}
\item{\emph{cor}:}{               logical: if \code{TRUE} computes eigenvalues
from a correlation
matrix, else from a covariance matrix
(\code{eigenComputes, nBartlett, nBentler,
nCng, nMreg, nScree, nSeScree})}
\item{\emph{correction}:}{        logical: if \code{TRUE} uses a correction
for the degree
of freedom after the first eigenvalue (\code{nBartlett})}
\item{\emph{criteria}:}{          numeric: by default fixed at \eqn{\hat{\lambda}}.
When the \eqn{\lambda}s are computed from a principal components
analysis on a correlation matrix, it corresponds to the
usual Kaiser \eqn{\lambda >= 1} rule. On a covariance matrix
or from a factor analysis, it is simply the mean.
To apply the \eqn{\lambda >= 0} sometimes used with factor
analysis, fixed the criteria to \eqn{0} (\code{nScree})}
\item{\emph{details}:}{           logical: if \code{TRUE} also returns details about the
computation for each eigenvalues (\code{nBartlett, nBentler,
nCng, nMreg, structureSim})}
\item{\emph{diagCommunalities}:}{ logical: if \code{TRUE}, the correlation between
the initial
solution and the estimated one will use a
correlation of one in the diagonal.
If \code{FALSE} (default) the diagonal is not
used in the computation of
this correlation or covariance matrix
(\code{rRecovery})}
\item{\emph{dir}:}{               character:  directory where to save output
(\code{studySim})}
\item{\emph{eig}:}{               depreciated parameter (use x instead): eigenvalues to analyse
(\code{nScree,  plotParallel})}
\item{\emph{Eigenvalue}:}{        depreciated parameter (use x instead): eigenvalues to analyse
(\code{plotuScree})}
\item{\emph{graphic}:}{           logical: specific plot (\code{bentlerParameters, structureSim})}
\item{\emph{index}:}{             numeric: vector of the index of the selected indices
(\code{plot.structureSim, print.structureSim, summary.structureSim}}
\item{\emph{iterations}:}{        numeric: maximum number of iterations to obtain a solution
(\code{iterativePrincipalAxis})}
\item{\emph{legend}:}{            logical indicator of the presence of a legend (\code{plotnScree, plotParallel}) }
\item{\emph{log}:}{               logical: if \code{TRUE} does the minimization on the log values  (\code{bentlerParameters, nBentler})}
\item{\emph{main}:}{              character: main title (\code{plotnScree, plotParallel, plotuScree, boxplot.structureSim,
plot.structureSim}) }
\item{\emph{maxPar}:}{            numeric: maximums for the coefficient of the linear trend
(\code{bentlerParameters, nBentler})}
\item{\emph{minPar}:}{            numeric: minimums for the coefficient of the linear trend
(\code{bentlerParameters, nBentler})}
\item{\emph{method}:}{            character: actually only \code{"giv"} is supplied to compute the
approximation of the communalities by  maximum correlation
(\code{corFA, nCng, nMreg, nScree, nSeScree})}
\item{\emph{mjc}:}{               numeric: number of major factors (factors with practical significance)
(\code{generateStructure}) }
\item{\emph{pmjc}:}{              numeric: number of variables that load significantly on each major factor
(\code{generateStructure})}
\item{\emph{model}:}{             character: \code{"components"} or \code{"factors"}  (\code{nScree, parallel, plotParallel,
plotuScree, structureSim, eigenBootParallel, eigenBootParallel, studySim})}
\item{\emph{N}:}{                 numeric:  number of subjects (\code{nBartlett, bentlerParameters, nBentler, studySim})}
\item{\emph{nboot}:}{             numeric: number of bootstrap samples (\code{eigenBootParallel}) }
\item{\emph{nFactors}:}{          numeric: number of components/factors to retained (\code{componentAxis,
iterativePrincipalAxis, principalAxis, bentlerParameters, boxplot.structureSim, studySim})}
\item{\emph{nScree}:}{            results of a previous nScree analysis (\code{plotnScree})}
\item{\emph{option}:}{            character: \code{"permutation"} or \code{"bootstrap"} (\code{eigenBootParallel})}
\item{\emph{object}:}{            nScree: an object of the class nScree \code{is.nScree, summary.nScree} }
\item{\emph{object}:}{            structureSim: an object of the class structureSim (\code{is.structureSim,
summary.structureSim})}

\item{\emph{parallel}:}{          numeric: vector of the result of a previous parallel analysis (\code{plotParallel})}
\item{\emph{pmjc}:}{              numeric: number of major loadings on each factor factors (\code{generateStructure, studySim}) }
\item{\emph{quantile}:}{          numeric: quantile that will be reported (\code{parallel, moreStats,
eigenBootParallel, structureSim, studySim}) }
\item{\emph{R}:}{                 numeric: correlation or covariance matrix (\code{componentAxis, iterativePrincipalAxis,
principalAxis, principalComponents, rRecovery, corFA})}
\item{\emph{r2limen}:}{           numeric: R2 limen value for the R2 Nelson index (\code{structureSim, nSeScree, studySim})}
\item{\emph{rep}:}{               numeric: number of replications of the correlation or the covariance matrix (default is 100) (\code{parallel})}
\item{\emph{reppar}:}{            numeric: number of replications for the parallel analysis (\code{structureSim, studySim})}
\item{\emph{repsim}:}{            numeric: number of replications of the matrix correlation simulation (\code{structureSim, studySim})}
\item{\emph{resParx}:}{           numeric: restriction on the \eqn{\alpha} coefficient (x) to graph the function to minimize
(\code{bentlerParameters})}
\item{\emph{resolution}:}{        numeric: resolution of the 3D graph (number of points from \eqn{\alpha} and from \eqn{\beta}).}
\item{\emph{resPary}:}{           numeric: restriction on the \eqn{\beta} coefficient (y) to graph the function to minimize
(\code{bentlerParameters})}
\item{\emph{sd}:}{                numeric: vector of standard deviations of the simulated variables
(for a parallel analysis on a covariance matrix) \code{parallel})}
\item{\emph{show}:}{              logical: if \code{TRUE} prints the quantile chosen (\code{moreStats}) }
\item{\emph{stats}:}{             numeric:   vector of the statistics to return: mean(1),
median(2), sd(3), quantile(4), min(5), max(6)
(\code{studySim})}
\item{\emph{subject}:}{           numeric: number of subjects (default is 100) (\code{parallel})}
\item{\emph{tolerance}:}{         numeric: minimal difference in the estimated communalities after a given iteration
(\code{iterativePrincipalAxis})}
\item{\emph{trace}:}{             logical:   if \code{TRUE} gives details of the status of the simulations
(\code{studySim})}
\item{\emph{typePlot}:}{          character: plots the minimized function according to a 3D plot: \code{"wireframe"},
\code{"contourplot"} or \code{"levelplot"}  (\code{bentlerParameters})}
\item{\emph{unique}:}{            numeric: loadings on the non significant variables on each major factor
(\code{generateStructure, studySim}) }
\item{\emph{upper}:}{             logical: if \code{TRUE} upper diagonal is replaced with lower
diagonal. If \code{FALSE}, lower diagonal is replaced with upper diagonal
(\code{diagReplace})}
\item{\emph{use}:}{               character: how to deal with missing values, same as the
parameter from the \code{corr} function (\code{eigenBootParallel}) }
\item{\emph{var}:}{               numeric: number of variables (default is 10) (\code{parallel, generateStructure, studySim}) }
\item{\emph{vLine}:}{             character: color of the vertical indicator line in the eigen boxplot
(\code{boxplot.structureSim})}
\item{\emph{x}:}{                 numeric: a \code{vector} of eigenvalues, a \code{matrix} of
correlations or of covariances or a \code{data.frame} of data
(\code{eigenFrom, nBartlett, nCng, nMreg})}
\item{\emph{xlab}:}{              character: label of the x axis (\code{plotnScree, plotParallel, plotuScree,
boxplot.structureSim})}
\item{\emph{x}:}{                 data.frame: data from which a correlation or covariance matrix will be obtained (\code{eigenBootParallel})}
\item{\emph{x}:}{                 depreciated: (\code{plotParallel})}
\item{\emph{x}:}{                 nScree: an object of the class nScree (\code{plot.nScree, print.nScree})}
\item{\emph{x}:}{                 numeric: matrix (\code{makeCor})}
\item{\emph{x}:}{                 numeric: matrix or data.frame (\code{moreStats})}
\item{\emph{x}:}{                 structureSim: an object of the class structureSim (\code{boxplot.structureSim,
plot.structureSim, print.structureSim})}
\item{\emph{ylab}:}{              character: label of the y axis (\code{plotnScree, plotParallel, plotuScree,
boxplot.structureSim}) }
}

\emph{Values}:
\enumerate{
\item{\emph{cor}:}{          numeric: Pearson correlation between initial and recovered estimated
correlation or covariance matrix. Compution depend on the
logical value of the \code{communalities} argument (\code{rRecovery}) }
\item{\emph{details}:}{      numeric: matrix of the details for each index (\code{nBartlett, bentlerParameters, nCng, nMreg})}
\item{\emph{difference}:}{   numeric: difference between initial and recovered estimated
correlation or covariance matrix (\code{rRecovery})}
\item{\emph{iterations}:}{   numeric: maximum number of iterations to obtain a solution (\code{iterativePrincipalAxis})}
iterativePrincipalAxis, principalAxis, principalComponents}) }
\item{\emph{nFactors}:}{     numeric: vector of the number of components or factors retained by the
Bartlett, Anderson and Lawley procedures  (\code{nBartlett, bentlerParameters, nCng, nMreg}) }
\item{\emph{R}: }{           numeric: correlation or covariance matrix (\code{diagReplace, rRecovery})}
\item{\emph{recoveredR}:}{   numeric: recovered estimated correlation or covariance matrix (\code{rRecovery}) }
\item{\emph{tolerance}:}{    numeric: minimal difference in the estimated communalities after a given iteration
(\code{iterativePrincipalAxis})}
\item{\emph{values}:}{       numeric: data.frame of information (\code{nScree, parallel, plotnScree, plotParallel,
plotuScree, structureSim})}
\item{\emph{values}:}{       numeric: data.frame of statistics (\code{moreStats}) }
\item{\emph{values}:}{       numeric: full matrix of correlation or covariance (\code{makeCor}) }
\item{\emph{values}:}{       numeric: variance of each component or factor (\code{iterativePrincipalAxis, principalComponents}) }
\item{\emph{values}:}{       data.frame: mean, median, quantile, standard deviation,
minimum and maximum of bootstrapped eigenvalues (\code{eigenBootParallel})}
\item{\emph{values}:}{       numeric: matrix of correlation or covariance with communalities in the diagonal (\code{corFA})}
\item{\emph{values}:}{       numeric: variance of each component or factor retained (\code{componentAxis, principalAxis}) }
\item{\emph{values}:}{       numeric: matrix factor structure (\code{generateStructure})}
\item{\emph{varExplained}:}{ numeric: variance explained by each component or factor retained (\code{componentAxis, iterativePrincipalAxis,
principalAxis, principalComponents}) }
\item{\emph{varExplained}:}{ numeric: cumulative variance explained by each component or factor retained (\code{componentAxis,
iterativePrincipalAxis, principalAxis, principalComponents}) }
}
}

\author{
Gilles Raiche \cr
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI) \cr
Universite du Quebec a Montreal\cr
\email{raiche.gilles@uqam.ca}, \url{http://www.er.uqam.ca/nobel/r17165/} \cr \cr
David Magis \cr
Departement de mathematiques \cr
Universite de Liege \cr
\email{David.Magis@ulg.ac.be}
}

\references{
Raiche, G., Riopel, M. and Blais, J.-G. (2006). \emph{Non graphical solutions
for the Cattell's scree test}. Paper presented at the International Annual
meeting of the Psychometric Society, Montreal.
[\url{http://www.er.uqam.ca/nobel/r17165/RECHERCHE/COMMUNICATIONS/}]
}

\seealso{
Other packages are also very useful for principal component and factor analysis.
The \emph{R} psychometric view is instructive at this point.
See \url{http://cran.stat.sfu.ca/web/views/Psychometrics.html} for further details.
}

\keyword{ package }