umx (version 4.20.0)

umxEFA: FIML-based Exploratory Factor Analysis (EFA)

Description

Perform full-information maximum-likelihood factor analysis on a data matrix.

Usage

umxEFA(
  x = NULL,
  factors = NULL,
  data = NULL,
  scores = c("none", "ML", "WeightedML", "Regression"),
  minManifests = NA,
  rotation = c("varimax", "promax", "none"),
  return = c("model", "loadings"),
  report = c("markdown", "html"),
  summary = FALSE,
  name = "efa",
  digits = 2,
  tryHard = c("no", "yes", "ordinal", "search"),
  n.obs = NULL,
  covmat = NULL
)

Value

• EFA mxModel()

Arguments

x

Either 1: data, 2: Right-hand-side ~ formula , 3: Vector of variable names, or 4: Name for the model.

factors

Either number of factors to request or a vector of factor names.

data

A dataframe you are modeling.

scores

Type of scores to produce, if any. The default is none, "Regression" gives Thompson's scores. Other options are 'ML', 'WeightedML', Partial matching allows these names to be abbreviated.

minManifests

The least number of variables required to return a score for a participant (Default = NA).

rotation

A rotation to perform on the loadings (default = "varimax" (orthogonal))

return

by default, the resulting MxModel is returned. Say "loadings" to get a fact.anal object.

report

Report as markdown to the console, or open a table in browser ("html")

summary

run umxSummary() on the underlying umxRAM model? (Default = FALSE)

name

A name for your model (default = efa)

digits

rounding (default = 2)

tryHard

Default ('no') uses normal mxRun. "yes" uses mxTryHard. Other options: "ordinal", "search"

n.obs

Number of observations in if covmat provided (default = NA)

covmat

Covariance matrix of data you are modeling (not implemented)

Details

As in factanal(), you need only specify the number of factors and offer up some manifest data, e.g:

umxEFA(factors = 2, data = mtcars)

Equivalently, you can also give a list of factor names:

umxEFA(factors = c("g", "v"), data = mtcars)

The factor model is implemented as a structural equation model, e.g.

You can request scores from the model. Unlike factanal, these can cope with missing data.

You can also rotate the factors using any rotation function.

In an EFA, all items may load on all factors.

Should work with rotations provided in library("GPArotation") and library("psych"), e.g

Orthogonal: "varimax", "quartimax", "bentlerT", "equamax", "varimin", "geominT" and "bifactor" Oblique: "Promax", "promax", "oblimin", "simplimax", "bentlerQ", "geominQ", "biquartimin" and "cluster"

For identification we need m² degrees of freedom. We get m(m+1)/2 from fixing factor variances to 1 and covariances to 0. We get another m(m-1)/2 degrees of freedom by fixing the upper-right hand corner of the factor loadings component of the A matrix at 0.

To aid optimization, manifest residual variances are lbounded at 0.

EFA reports standardized loadings: to do this, we scale the data.

note: Bear in mind that factor scores are indeterminate (can be rotated to an infinity of equivalent solutions).

Thanks to @ConorDolan for code implementing the rotation matrix and other suggestions!

References

• https://github.com/tbates/umx,

Hendrickson, A. E. and White, P. O. (1964). Promax: a quick method for rotation to orthogonal oblique structure. British Journal of Statistical Psychology, 17, 65–70. tools:::Rd_expr_doi("10.1111/j.2044-8317.1964.tb00244.x").

Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187–200. tools:::Rd_expr_doi("10.1007/BF02289233").

See Also

• factanal(), mxFactorScores()

Other Super-easy helpers: umxTwoStage(), umx

Examples

if (FALSE) {
myVars = c("mpg", "disp", "hp", "wt", "qsec")
m1 = umxEFA(mtcars[, myVars], factors =   2, rotation = "promax")
# By default, returns the model
umx_is_MxModel(m1) # TRUE
# The loadings are stashed in the model:
loadings(m1)

# Formula interface in umxEFA
m2 = umxEFA(~ mpg + disp + hp + wt + qsec, factors = 2, rotation = "promax", data = mtcars)
loadings(m2)

# base-R factanal Formula interface for comparison
m2 = factanal(~ mpg + disp + hp + wt + qsec, factors = 2, rotation = "promax", data = mtcars)
loadings(m2)

# Return the loadings object
x = umxEFA(mtcars[, myVars], factors = 2, return = "loadings")
names(x) # "loadings" "rotmat"

# scores requested, so these will be returned
x = umxEFA(name = "score", factors = "g", data = mtcars[, myVars], scores= "Regression")
head(x)
#       g
# 1  -0.48059346
# 2  -0.42354000
# 3  -0.87078110

m1 = umxEFA(myVars, factors = 2, data = mtcars, rotation = "promax")
m1 = umxEFA(name = "named", factors = "g", data = mtcars[, myVars])
m1 = umxEFA(name = "by_number", factors = 2, rotation = "promax", data = mtcars[, myVars])

}