HULL: Hull method

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

Hull method

Description

HULL() has been superseded by efa_hull(), which is the recommended interface going forward.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

Usage

HULL(
  x,
  N = NA,
  n_fac_theor = NA,
  method = c("PAF", "ULS", "ML"),
  gof = c("CAF", "CFI", "RMSEA"),
  eigen_type = c("SMC", "PCA", "EFA"),
  use = c("pairwise.complete.obs", "all.obs", "complete.obs", "everything",
    "na.or.complete"),
  cor_method = c("pearson", "spearman", "kendall", "poly", "tetra"),
  n_datasets = 1000,
  percent = 95,
  decision_rule = c("means", "percentile", "crawford"),
  n_factors = 1,
  ...
)

Arguments

x	matrix or data.frame. Dataframe or matrix of raw data or matrix with correlations.
N	numeric. Number of cases in the data. This is passed to efa_parallel. Only has to be specified if x is a correlation matrix, otherwise it is determined based on the dimensions of x.
n_fac_theor	numeric. Theoretical number of factors to retain. One plus the larger of this number and the number of factors suggested by efa_parallel is used as the upper bound J of factors to extract in the Hull method.
method	character. The estimator to use; passed to efa_hull() as its estimator argument. One of "PAF", "ULS", or "ML".
gof	character. The goodness of fit index to use. Either "CAF", "CFI", or "RMSEA", or any combination of them. With the "PAF" estimator, only the CAF can be used as goodness of fit index. For details on the CAF, see Lorenzo-Seva, Timmerman, and Kiers (2011).
eigen_type	character. On what the eigenvalues should be found in the parallel analysis. Can be one of "SMC", "PCA", or "EFA". If using "SMC" (default), the diagonal of the correlation matrices 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. This is passed to efa_parallel().
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 HULL derives its factor-search bound from an internal parallel analysis against continuous reference data. Default is "pearson".
n_datasets	numeric. The number of datasets to simulate. Must be at least 1. Default is 1000. This is passed to efa_parallel().
percent	numeric. The percentile to take from the simulated eigenvalues. Default is 95. This is passed to efa_parallel().
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). This is passed to efa_parallel().
n_factors	numeric. Number of factors to extract if "EFA" is included in eigen_type. Default is 1. This is passed to efa_parallel().
...	Further arguments passed on to the efa_fit() fits, including 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. The estimator is selected with method.

Value

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

See Also

efa_hull()

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