Exploratory Factor Analysis

Fit one or more Exploratory Factor Analysis (EFA) model(s).

Usage

efa(data = NULL, nfactors = 1L, sample_cov = NULL, sample_nobs = NULL,
    rotation = "geomin", rotation_args = list(), ov_names = NULL,
    bounds = "pos.var", ..., output = "efa")

Arguments

data

A data frame containing the observed variables we need for the EFA. If only a subset of the observed variables is needed, use the ov.names argument.

nfactors

Integer, integer vector, or a list. The desired number of factors to extract. Can be a single number, or a vector of numbers (e.g., nfactors = 1:4); for each different number, a model is fitted. When the model has multiple blocks (because the data is multilevel and/or multigroup), the same number of factors is extracted in every block. To extract a different number of factors per block, supply a list: each element of the list is one fitted model and contains a vector with the number of factors per block (or a single number that is recycled to all blocks). Blocks are ordered group-major, level-minor, ie block \(= (g - 1) \times nlevels + level\). For example, for a twolevel model, nfactors = list(c(1, 2)) extracts one factor at the within level and two factors at the between level.

sample_cov

Numeric matrix. A sample variance-covariance matrix. The rownames and/or colnames must contain the observed variable names. Unlike sem and CFA, the matrix may be a correlation matrix.

sample_nobs

Number of observations if the full data frame is missing and only the sample variance-covariance matrix is given.

rotation

Character or a list with first element a character variable. The character variable is the rotation method to be used. Possible options are varimax, quartimax, orthomax, oblimin, quartimin, geomin, promax, entropy, mccammon, infomax, tandem1, tandem2, oblimax, bentler, simplimax, target.strict, target (alias for pst), pst (=partially specified target), cf, crawford-ferguson, cf-quartimax, cf-varimax, cf-equamax, cf-parsimax, cf-facparsim, biquartimin, bigeomin. The latter two are for bifactor rotation only. The rotation algorithms (except promax and target) are similar to those from the GPArotation package, but have been reimplemented for better control. The promax method is taken from the stats package. The target.strict method is equal to the target method in the GPArotation package. The target method is in fact the pst method where all non-zero elements (in the target matrix) are ignored. Options for the rotation algorithm can be provided in the list after the method. The default options (and their alternatives) are orthogonal = FALSE, row_weights = "default" (or "kaiser", "cureton.mulaik" or "none"), std_ov = TRUE, algorithm = "gpa" (or "pairwise"), rstarts = 30, gpa_tol = 1e-05, tol = 1e-08, max_iter = 10000L, warn = FALSE, verbose = FALSE, reflect = TRUE, order_lv_by = "index" (or "sumofsquares" or "none"). Other options are specific for a particular rotation criterion: geomin_epsilon = 0.001, orthomax_gamma = 1, promax_kappa = 4, cf_gamma = 0, and oblimin_gamma = 0.

For the target rotation methods (target.strict, target and pst), the target option (and, for pst, the optional target_mask option) can take three forms: 1) a single matrix, which is used for all groups and all efa blocks; 2) a nameless list of matrices, one per group; or 3) a named list of matrices, where the names are the efa block labels used in the model syntax (e.g., list(a = target.a, b = target.b) if the model contains the efa blocks efa("a") and efa("b")), so that each efa block gets its own target matrix (the same targets are then used in all groups). The latter is only relevant when the model syntax (of sem() or cfa()) defines multiple efa blocks (set-ESEM). Note that a named list must provide a target matrix for every efa block (with two or more factors) in the model; omitting a block results in an error, as the rotation criterion would be undefined for that block.

rotation_args

List. Options related to the rotation algorithm. DEPRECATED. The options should now be given in the rotation argument as a list.

ov_names

Character vector. The variables names that are needed for the EFA. Should be a subset of the variables names in the data.frame. By default (if NULL), all the variables in the data are used.

bounds

Per default, bounds = "pos.var" forces all variances of both observed and latent variables to be strictly nonnegative. See the entry in lavOptions for more options.

...

Additional options to be passed to lavaan, using 'name = value'. See lavOptions for a complete list.

output

Character. If "efa" (the default), the output mimics the typical output of an EFA. If "lavaan", a lavaan object is returned. The latter is only possible if nfactors contains a single (integer) number.

Details

The efa function is essentially a wrapper around the lavaan function. It generates the model syntax (for a given number of factors) and then calls lavaan() treating the factors (in each block) as a set that should be rotated. Each block is rotated independently. Categorical data is handled as usual by first computing an appropriate (e.g., tetrachoric or polychoric) correlation matrix, which is then used as input for the EFA. Multiple groups (via the group= argument) and twolevel data (via the cluster= argument) are supported, and these may be combined. By default, the same number of factors is extracted in every block, but a different number of factors per block can be requested by supplying nfactors as a list (see the nfactors argument). The promax rotation method (taken from the stats package) is only provided for convenience. Because promax is a two-step algorithm (first varimax, then oblique rotation to get simple structure), it does not use the gpa or pairwise rotation algorithms, and as a result, no standard errors are provided.

Value

If output = "lavaan", an object of class lavaan. If output = "efa", a list of class efaList for which a print(), summary() and fitMeasures() method are available. Because we added the (standardized) loadings as an extra element, the loadings function (which is not a generic function) from the stats package will also work on efaList objects.

Examples