fapa: Iterated Principal Axis Factor Analysis (fapa)

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/fapa.R

Description

This function applies the iterated principal axis factoring method to extract an unrotated factor structure matrix.

Usage

1
2
3
4
5
6
7
fapa(
  R,
  numFactors = NULL,
  epsilon = 1e-04,
  communality = "SMC",
  maxItr = 15000
)

Arguments

R

(Matrix) A correlation matrix to be analyzed.

numFactors

(Numeric) The number of factors to extract.

epsilon

(Numeric) A numeric threshold to designate whether the function has converged. The default value is 1e-4.

communality

(Character) The routine requires an initial estimate of the communality values. There are three options (see below) with "SMC" (i.e., squared multiple correlation) being the default.

  • "SMC": Initial communalities are estimated by taking the squared multiple correlations of each indicator after regressing the indicator on the remaining variables. The following equation is employed to find the squared multiple correlation: 1 - 1 / diag(R^-1).

  • "maxr": Initial communalities equal the largest (absolute value) correlation in each column of the correlation matrix.

  • "unity": Initial communalities equal 1.0 for all variables.

maxItr

(Numeric) The maximum number of iterations to reach convergence. The default is 15,000.

Details

Value

The main output is the matrix of unrotated factor loadings.

Author(s)

References

Widaman, K. F., & Herringer, L. G. (1985). Iterative least squares estimates of communality: Initial estimate need not affect stabilized value. Psychometrika, 50(4), 469-477.

See Also

Other Factor Analysis Routines: BiFAD(), Box26, GenerateBoxData(), Ledermann(), SLi(), SchmidLeiman(), faAlign(), faEKC(), faIB(), faLocalMin(), faMB(), faMain(), faScores(), faSort(), faStandardize(), faX(), fals(), fareg(), fsIndeterminacy(), orderFactors(), print.faMB(), print.faMain(), promaxQ(), summary.faMB(), summary.faMain()

Examples

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
## Generate an example factor structure matrix
lambda <- matrix(c(.62, .00, .00,
                   .54, .00, .00,
                   .41, .00, .00,
                   .00, .31, .00,
                   .00, .58, .00,
                   .00, .62, .00,
                   .00, .00, .38,
                   .00, .00, .43,
                   .00, .00, .37),
                 nrow = 9, ncol = 3, byrow = TRUE)

## Find the model implied correlation matrix
R <- lambda %*% t(lambda)
diag(R) <- 1

## Extract factors using the fapa function
Out1 <- fapa(R           = R,
             numFactors  = 3,
             communality = "SMC")

## Call fapa through the factExtract function
Out2 <- faX(R          = R,
            numFactors = 3,
            facMethod  = "fapa",
            faControl  = list(communality = "maxr",
                              epsilon     = 1e-4))

## Check for equivalence of the two results
all.equal(Out1$loadings, Out2$loadings)

fungible documentation built on Sept. 29, 2021, 1:06 a.m.

Related to fapa in fungible...