facSMC {FMradio}

Evaluate the determinacy of factor scores

Description

facSMC is a function with which one may evaluate the determinacy of factor scores.

Usage

facSMC(R, LM)

Arguments

R

(Regularized) correlation matrix.

LM

A (rotated) loadings matrix. Usually the $Loadings-slot object from the mlFA function output.

Details

The facSMC function calculates the squared multiple correlations between the observed features and the common latent factors. The closer to unity, the lesser the problem of factor-score indeterminacy and the better one is able to uniquely determine the factor scores. In practice, a squared multiple correlation equalling or exceeding .9 would be considered adequate. See Mulaik (2010, Chapter 13) and Peeters et al. (2019, Supplementary Materials) for further details.

Value

The function returns a numeric vector indicating, for each factor, the squared multiple correlation between the observed features and the common latent factor.

Note

Note that the computations assume an orthogonal factor model. Hence, only orthogonal rotations of the loadings matrix should be used (or no rotation at all).

Author(s)

Carel F.W. Peeters <[e-mail]>

References

Mulaik, S.A. (2010). Foundations of Factor Analysis. Boca Raton: Chapman & Hall/CRC, 2nd edition.

Peeters, C.F.W. et al. (2019). Stable prediction with radiomics data. arXiv:1903.11696 [stat.ML].

See Also

facScore

Examples

## Simulate some data according to a factor model with 5 latent factors
## Simulate high-dimensional situation in the sense that p > n
## $cormatrix gives the correlation matrix on the generated data
simDAT <- FAsim(p = 50, m = 5, n = 40, loadingvalue = .9)
simDAT$cormatrix

## Regularize the correlation matrix
RegR <- regcor(simDAT$data)

## Evaluate the Guttman bounds
## First Guttman bound indicates to retain 5 latent factors
GB <- dimGB(RegR$optCor)
print(GB)

## Produce ML factor solution under 5 factors
## Print loadings structure of this solution
fit <- mlFA(RegR$optCor, 5)
print(fit$Loadings, digits = 2, cutoff = .3, sort = TRUE)

## Obtain factor-scores
scores <- facScore(scale(simDAT$data), fit$Loadings, fit$Uniqueness)
print(scores)

## Evaluate determinacy of factor scores
fd <- facSMC(RegR$optCor, fit$Loadings)
print(fd)