PARALLEL: Parallel analysis

In EFAtools: Fast and Flexible Implementations of Exploratory Factor Analysis Tools

Parallel analysis

Description

PARALLEL() has been superseded by efa_parallel(), which is the recommended interface going forward. It remains available and unchanged so existing code keeps working.

Usage

PARALLEL(
  x = NULL,
  N = NA,
  n_vars = NA,
  n_datasets = 1000,
  percent = 95,
  eigen_type = c("PCA", "SMC", "EFA"),
  use = c("pairwise.complete.obs", "all.obs", "complete.obs", "everything",
    "na.or.complete"),
  cor_method = c("pearson", "spearman", "kendall", "poly", "tetra"),
  decision_rule = c("means", "percentile", "crawford"),
  n_factors = 1,
  ...
)

Arguments

x	matrix or data.frame. The real data to compare the simulated eigenvalues against. Must not contain variables of classes other than numeric. Can be a correlation matrix or raw data.
N	numeric. The number of cases / observations to simulate. Only has to be specified if x is either a correlation matrix or NULL. If x contains raw data, N is found from the dimensions of x. Must be larger than the number of variables.
n_vars	numeric. The number of variables / indicators to simulate. Only has to be specified if x is left as NULL as otherwise the dimensions are taken from x.
n_datasets	numeric. The number of datasets to simulate. Must be at least 1. Default is 1000.
percent	numeric. The percentile to take from the simulated eigenvalues. Default is 95.
eigen_type	character. On what the eigenvalues should be found. Can be either "SMC", "PCA", or "EFA". If using "SMC", the diagonal of the correlation matrix is replaced by the squared multiple correlations (SMCs) of the indicators. If using "PCA", the diagonal values of the correlation matrices are left to be 1. If using "EFA", eigenvalues are found on the correlation matrices with the final communalities of an EFA solution as diagonal. Default is c("PCA", "SMC", "EFA"), i.e. all three, which costs roughly six times a single non-EFA type: "EFA" fits an EFA to every simulated dataset and dominates that total. Pass a single type if the run is time-critical.
use	character. Passed to stats::cor() if raw data is given as input. Default is "pairwise.complete.obs".
cor_method	character. One of "pearson", "spearman", or "kendall", passed to stats::cor(). "poly" and "tetra" are not supported because PARALLEL compares the data against simulated continuous reference data. Default is "pearson".
decision_rule	character. Which rule to use to determine the number of factors to retain. Default is "means", which will use the average simulated eigenvalues. "percentile", uses the percentiles specified in percent. "crawford" uses the 95th percentile for the first factor and the mean afterwards (based on Crawford et al, 2010). All three rules retain the factors up to the first observed eigenvalue that fails to exceed its reference value; an eigenvalue further down the series that rises above its own reference again therefore adds no factor. Because the average simulated eigenvalue is a lower reference than the percentile, "means" tends to retain more factors than the more conservative "percentile" rule (Glorfeld, 1995).
n_factors	numeric. Number of factors to extract if "EFA" is included in eigen_type. Default is 1.
...	Further arguments passed on to the efa_fit() fits. For example, estimator, to change the estimator (default is "PAF"; PAF is more robust, but it will take longer compared to "ML" and "ULS"), or one of the estimation tuning knobs (type, init_comm, criterion, criterion_type, max_iter, abs_eigen, start_method), which are repacked into an estimate_control() object so that they tune the fits exactly as they always did.

Value

An object of class efa_retention, identical to the value of efa_parallel(); see there for the components.

See Also

efa_parallel()

EFAtools documentation built on Aug. 21, 2026, 5:16 p.m.