% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/efa_ekc.R
\name{efa_ekc}
\alias{efa_ekc}
\title{Empirical Kaiser criterion}
\source{
Auerswald, M., & Moshagen, M. (2019). How to determine the number of
factors to retain in exploratory factor analysis: A comparison of extraction
methods under realistic conditions. Psychological Methods, 24(4), 468–491.
https://doi.org/10.1037/met0000200

Braeken, J., & van Assen, M. A. (2017). An empirical Kaiser criterion.
Psychological Methods, 22, 450 – 466. https://doi.org/10.1037/met0000074

Zwick, W. R., & Velicer, W. F. (1986). Comparison of five rules for
determining the number of components to retain. Psychological Bulletin, 99,
432–442. https://doi.org/10.1037/0033-2909.99.3.432
}
\usage{
efa_ekc(
  x,
  N = NA,
  use = c("pairwise.complete.obs", "all.obs", "complete.obs", "everything",
    "na.or.complete"),
  cor_method = c("pearson", "spearman", "kendall", "poly", "tetra"),
  type = lifecycle::deprecated()
)
}
\arguments{
\item{x}{data.frame or matrix. Dataframe or matrix of raw data or matrix with
correlations.}

\item{N}{numeric. The number of observations. Only needed if x is a correlation
matrix. Must be larger than the number of variables.}

\item{use}{character. Passed to \code{\link[stats:cor]{stats::cor()}} if raw
data is given as input. Default is "pairwise.complete.obs".}

\item{cor_method}{character. Correlation computed from raw data: \code{"pearson"},
\code{"spearman"}, or \code{"kendall"} (passed to \code{\link[stats:cor]{stats::cor()}}), or \code{"poly"} /
\code{"tetra"} for polychoric / tetrachoric correlations of ordinal / binary data
(a two-step estimator). Default is \code{"pearson"}. Note that the EKC reference
values rest on the Marchenko-Pastur law for the eigenvalues of a sample
correlation matrix of independent variables, which assumes the sampling
behaviour of product-moment correlations; with \code{"poly"} / \code{"tetra"} (and, to a
lesser degree, the rank-based methods) the reference series is therefore an
approximation.}

\item{type}{\ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#deprecated}{\figure{lifecycle-deprecated.svg}{options: alt='[Deprecated]'}}}{\strong{[Deprecated]}} Accepted and ignored. It selected
between two ways to compute the reference values. The \code{"AM2019"} reference values
do not depend on the observed eigenvalues, so they do not apply the empirical
correction that defines the criterion, and they are no longer computed.}
}
\value{
An object of class \code{efa_retention} (see \code{\link[=print.efa_retention]{print.efa_retention()}} and
\code{\link[=plot.efa_retention]{plot.efa_retention()}} for the print and plot methods). Its main fields are:
\item{n_factors}{A numeric vector of length one, named \code{"BvA2017"}, with the
suggested number of factors. The factors up to the first observed eigenvalue
that fails to exceed its reference value are retained. The "all-exceed"
convention of parallel analysis (\code{\link[=efa_parallel]{efa_parallel()}}), which retains all \emph{J} factors
when no such crossing is found, cannot be reached here: the reference values are
never below 1, while the eigenvalues of a correlation matrix sum to \emph{J} and are
sorted downwards, so the last of them is never above 1.}
\item{results}{A list with one record, holding the eigenvalues, the reference
eigenvalues, and the retained solution used for printing and plotting.}
\item{settings}{A list with the settings used.}
}
\description{
The empirical Kaiser criterion incorporates random sampling variations of the
eigenvalues from the Kaiser-Guttman criterion (\code{\link[=efa_kgc]{efa_kgc()}}; see Auerswald &
Moshagen, 2019; Braeken & van Assen, 2017). The implementation follows Braeken
and van Assen (2017).
}
\details{
The Kaiser-Guttman criterion was defined with the intend that a factor
should only be extracted if it explains at least as much variance as a single
factor (see \code{\link[=efa_kgc]{efa_kgc()}}). However, this only applies to population-level
correlation matrices. Due to sampling variation, the KGC strongly overestimates
the number of factors to retrieve (e.g., Zwick & Velicer, 1986). To account
for this and to introduce a factor retention method that performs well with
small number of indicators and correlated factors (cases where the performance
of parallel analysis, see \code{\link[=efa_parallel]{efa_parallel()}}, is known to deteriorate)
Braeken and van Assen (2017) introduced the empirical Kaiser criterion in
which a series of reference eigenvalues is created as a function of the
variables-to-sample-size ratio and the observed eigenvalues.

Braeken and van Assen (2017) showed that "(a) EKC performs about as well as
parallel analysis for data arising from the null, 1-factor, or orthogonal
factors model; and (b) clearly outperforms parallel analysis for the specific
case of oblique factors, particularly whenever factor intercorrelation is
moderate to high and the number of variables per factor is small, which is
characteristic of many applications these days" (p.463-464).
}
\examples{
efa_ekc(test_models$baseline$cormat, N = 500)
}
\seealso{
\code{\link[=efa_retain]{efa_retain()}} as a wrapper function for this and the other factor
retention criteria.

Other factor retention criteria:
\code{\link[=efa_cd]{efa_cd()}},
\code{\link[=efa_hull]{efa_hull()}},
\code{\link[=efa_kgc]{efa_kgc()}},
\code{\link[=efa_map]{efa_map()}},
\code{\link[=efa_nest]{efa_nest()}},
\code{\link[=efa_parallel]{efa_parallel()}},
\code{\link[=efa_retain]{efa_retain()}},
\code{\link[=efa_scree]{efa_scree()}},
\code{\link[=efa_smt]{efa_smt()}}
}
\concept{factor retention criteria}
