EFA: Exploratory factor analysis (EFA)

Description

EFA() has been superseded by efa_fit(), which is the recommended interface going forward. efa_fit() keeps the primary choices (data, factors, estimator, rotation, standard errors) as top-level arguments and collects the estimation and rotation tuning knobs into two control objects, estimate_control() and rotate_control(). EFA() remains available and unchanged -- its full flat argument list still works exactly as before -- so existing code keeps running.

Usage

EFA(
  x,
  n_factors,
  N = NA,
  method = c("PAF", "ML", "ULS", "MINRES", "DWLS"),
  rotation = c("none", "varimax", "equamax", "quartimax", "geominT", "bentlerT",
    "bifactorT", "promax", "oblimin", "quartimin", "simplimax", "bentlerQ", "geominQ",
    "bifactorQ"),
  se = c("none", "information", "sandwich", "np-boot"),
  type = c("EFAtools", "psych", "SPSS", "none"),
  max_iter = NA,
  init_comm = NA,
  criterion = NA,
  criterion_type = NA,
  abs_eigen = NA,
  use = c("pairwise.complete.obs", "all.obs", "complete.obs", "everything",
    "na.or.complete"),
  varimax_type = NA,
  k = NA,
  normalize = TRUE,
  p_type = NA,
  precision = 1e-05,
  order_type = NA,
  start_method = "psych",
  cor_method = c("pearson", "spearman", "kendall", "poly", "tetra", "fiml"),
  b_boot = 1000,
  ci = 0.95,
  random_starts = 100,
  seed = NULL,
  P_type = lifecycle::deprecated(),
  randomStarts = lifecycle::deprecated(),
  ...
)

Value

The value of efa_fit(), a list of class c("efa", "EFA"); see there for the components.

Arguments

x

data.frame or matrix. Dataframe or matrix of raw data or matrix with correlations. If raw data is entered, the correlation matrix is found from the data.

n_factors

numeric. Number of factors to extract. Must be at least 1 and smaller than the number of variables (the common factor model is not identified otherwise). Use efa_retain() to decide on a value.

N

numeric. The number of observations. Needs only be specified if a correlation matrix is used; with raw data, N is found from the data instead.

With N = NA, not all fit indices can be computed; a positive N that is very small relative to the number of variables leaves the chi-square-derived indices unavailable as well, with a warning.
With raw data, N is the number of cases the correlation matrix was actually computed from -- see use for the general rule and how missing values change it. Under cor_method = "fiml", use is ignored and N is instead the number of cases carrying at least one observed value.

method

character. The estimator used to fit the EFA; passed to efa_fit() as its estimator argument. One of "PAF", "ML", "ULS", "MINRES" (an accepted alias of "ULS"), or "DWLS"; see the efa_fit() documentation for their properties and data requirements.

rotation

character. Either perform no rotation ("none"; default), an orthogonal rotation ("varimax", "equamax", "quartimax", "geominT", "bentlerT", or "bifactorT"), or an oblique rotation ("promax", "oblimin", "quartimin", "simplimax", "bentlerQ", "geominQ", or "bifactorQ"). See the Rotations section in Details for their properties and known issues.

se

character. Whether and how to compute standard errors (and matching confidence intervals): "none" (default), "information" (analytic standard errors from the expected Fisher information of the ML solution), "sandwich" (robust "sandwich" standard errors from raw data, which stay reliable under non-normality or a misspecified estimator weight), or "np-boot" (non-parametric bootstrap). The methods differ in their assumptions, their data requirements, and which estimator, rotation, and cor_method combinations they support; see the Standard errors section in Details.

type

character. If one of "EFAtools" (default), "psych", or "SPSS" is used, and the following arguments with default NA are left with NA, these implementations are executed according to the respective program ("psych" and "SPSS") or according to the best solution found in Grieder & Steiner (2022; "EFAtools"). Individual properties can be adapted using one of the three types and specifying some of the following arguments. If set to "none" additional arguments must be specified depending on the method and rotation used (see details).

max_iter

numeric. The maximum number of iterations to perform after which the iterative PAF procedure is halted with a warning. If type is one of "EFAtools", "SPSS", or "psych", this is automatically specified if max_iter is left to be NA, but can be overridden by entering a number. Default is NA.

init_comm

character. The method to estimate the initial communalities in PAF. "smc" will use squared multiple correlations, "mac" will use maximum absolute correlations, "unity" will use 1s (see details). Default is NA.

criterion

numeric. The convergence criterion used for PAF. If the change in communalities from one iteration to the next is smaller than this criterion the solution is accepted and the procedure ends. Default is NA.

criterion_type

character. Type of convergence criterion used for PAF. "max_individual" selects the maximum change in any of the communalities from one iteration to the next and tests it against the specified criterion. This is also used by SPSS. "sum" takes the difference of the sum of all communalities in one iteration and the sum of all communalities in the next iteration and tests this against the criterion. This procedure is used by the psych::fa() function. Default is NA.

abs_eigen

logical. Which algorithm to use in the PAF iterations. If FALSE, the loadings are computed from the eigenvalues. This is also used by the psych::fa() function. If TRUE the loadings are computed with the absolute eigenvalues as done by SPSS. Default is NA.

use

character. Passed to stats::cor() if raw data is given as input. Default is "pairwise.complete.obs". It is ignored when cor_method = "fiml" (which handles the missingness itself, so every case contributes), and it is overridden to listwise deletion whenever an asymptotic covariance is required (the "DWLS" estimator, or se = "sandwich"), because the covariance must describe the same cases as the correlation matrix.

varimax_type

character. The type of the varimax rotation performed. If "svd", singular value decomposition is used, as stats::varimax() does. If "kaiser", the varimax procedure performed in SPSS is used, following the original procedure from Kaiser (1958) (see details). Default is NA.

k

numeric. Either the power used for computing the target matrix P in the promax rotation or the number of 'close to zero loadings' for the simplimax rotation. If left to NA (default), the value for promax depends on the specified type. For simplimax, nrow(L), where L is the matrix of unrotated loadings, is used by default.

normalize

logical. If TRUE, a kaiser normalization is performed before the specified rotation. Default is TRUE.

p_type

character. This specifies how the target matrix P is computed in promax rotation. If "unnorm" it will use the unnormalized target matrix as originally done in Hendrickson and White (1964). This is also used in the psych and stats packages. If "norm" it will use the normalized target matrix as used in SPSS. Default is NA.

precision

numeric. The tolerance for stopping in the rotation procedure. Default is 10^-5 for all rotation methods.

order_type

character. How to order the factors. "eigen" reorders the factors by descending explained variance; "ss_factors" reorders the factors by descending (unweighted) sum of squared factor loadings per factor. Default is NA.

start_method

character. How to specify the starting values for the optimization procedure for ML. Default is "psych" which takes the starting values specified in psych::fa(). "factanal" takes the starting values specified in the stats::factanal() function.

cor_method

character. How the correlation is computed from raw data: "pearson", "spearman", or "kendall" (passed to stats::cor()); "poly" / "tetra" for polychoric / tetrachoric correlations of ordinal / binary data; or "fiml" for a two-stage full-information maximum-likelihood correlation from raw data with missing values. See the Correlation methods section in Details for their properties and the combinations they support. Default is "pearson".

b_boot

numeric. The number of bootstrap samples to draw. Default is 1000. Must be at least 2, the smallest number from which a standard error is defined. Under cor_method = "fiml" each bootstrap sample re-runs the EM moment estimation, so a smaller value may be advisable.

ci

numeric. The level of the confidence intervals: the percentile intervals from the bootstrap samples under se = "np-boot", and the analytic Wald intervals under se = "information" and se = "sandwich", the corrected two-stage intervals of cor_method = "fiml" included. Must be greater than 0 and smaller than 1. Default is .95 for 95% CIs.

random_starts

numeric. The number of random starts to use in the rotation to guard against local minima. Default is 100.

seed

numeric. An optional seed for the random-number generator.

P_type, randomStarts

Former names of p_type and random_starts. Still accepted (silently) for backwards compatibility; please use the new names.

...

Additional arguments passed to the rotation procedure (e.g., maxit for the maximum number of iterations).

Description

Usage

Value

Arguments

See Also