semTools (version 0.5-7)

efa.ekc: Empirical Kaiser criterion

Description

Identify the number of factors to extract based on the Empirical Kaiser Criterion (EKC). The analysis can be run on a data.frame or data matrix (data), or on a correlation or covariance matrix (sample.cov) and the sample size (sample.nobs). A data.frame is returned with two columns: the eigenvalues from your data or covariance matrix and the reference eigenvalues. The number of factors suggested by the Empirical Kaiser Criterion (i.e. the sample eigenvalues greater than the reference eigenvalues), and the number of factors suggested by the original Kaiser Criterion (i.e. sample eigenvalues > 1) is printed above the output.

Usage

efa.ekc(data = NULL, sample.cov = NULL, sample.nobs = NULL,
  missing = "default", ordered = NULL, plot = TRUE)

Value

A data.frame showing the sample and reference eigenvalues.

The number of factors suggested by the Empirical Kaiser Criterion (i.e. the sample eigenvalues greater than the reference eigenvalues) is returned as an attribute (see Examples).

The number of factors suggested by the original Kaiser Criterion (i.e. sample eigenvalues > 1) is also printed as a header to the data.frame

Arguments

data

A data.frame or data matrix containing columns of variables to be factor-analyzed.

sample.cov

A covariance or correlation matrix can be used, instead of data, to estimate the eigenvalues.

sample.nobs

Number of observations (i.e. sample size) if is.null(data) and sample.cov= is used.

missing

If "listwise", incomplete cases are removed listwise from the data.frame. If "direct" or "ml" or "fiml" and the estimator= is maximum likelihood, an EM algorithm is used to estimate an unrestricted covariance matrix (and mean vector). If "pairwise", pairwise deletion is used. If `"default"``, the value is set depending on the estimator and the mimic option (see lavaan::lavCor() for details).

ordered

character vector. Only used if object is a data.frame. Treat these variables as ordered= (ordinal) variables. Importantly, all other variables will be treated as numeric (unless is.ordered == TRUE in data). (see also lavCor)

plot

logical. Whether to print a scree plot comparing the sample eigenvalues with the reference eigenvalues.

Author

Ylenio Longo (University of Nottingham; )

Terrence D. Jorgensen (University of Amsterdam; )

References

Braeken, J., & van Assen, M. A. L. M. (2017). An empirical Kaiser criterion. Psychological Methods, 22(3), 450--466. tools:::Rd_expr_doi("10.1037/met0000074")

Examples

## Simulate data with 3 factors
model <- '
  f1 =~ .3*x1 + .5*x2 + .4*x3
  f2 =~ .3*x4 + .5*x5 + .4*x6
  f3 =~ .3*x7 + .5*x8 + .4*x9
'
dat <- simulateData(model, seed = 123)
## save summary statistics
myCovMat <- cov(dat)
myCorMat <- cor(dat)
N <- nrow(dat)

## Run the EKC function
(out <- efa.ekc(dat))

## To extract the recommended number of factors using the EKC:
attr(out, "nfactors")

## If you do not have raw data, you can use summary statistics
(x1 <- efa.ekc(sample.cov = myCovMat, sample.nobs = N, plot = FALSE))
(x2 <- efa.ekc(sample.cov = myCorMat, sample.nobs = N, plot = FALSE))