CFA one factor, ML estimation — Cfaftr • rmorie

Formula: X = lambda * F + eps; ML estimation

Usage

Cfaftr(X, factor_structure = NULL)

Arguments

X: An n x p data matrix, or a p x p item covariance matrix.
factor_structure: Optional length-p 0/1 mask of which items load on the factor; NULL lets every item load.

Value

List with estimate (variance explained), loadings, uniquenesses, fml, max_resid, communality, spearman, n_iter, p, method.

Details

The single factor is standardised, so the model covariance is lambda lambda' + Psi and the ML solution is reached by the Rubin-Thayer EM algorithm. For three items the ML solution is the Spearman closed form lambda_i^2 = s_ij s_ik / s_jk, reported alongside as an independent read of the same data.

References

Joreskog (1969), Psychometrika 34(2):183-202; Spearman (1904), Am. J. Psychology 15(2):201-292.

Examples

# \donttest{
set.seed(1)
X <- matrix(rnorm(200), 50, 4)
Cfaftr(X)
#> $estimate
#> [1] 0.316366
#> 
#> $loadings
#> [1] -0.22736925 -0.02311606  0.19582942  1.00151477
#> 
#> $uniquenesses
#> [1] 0.63951456 0.93809310 0.77117853 0.01430035
#> 
#> $fml
#> [1] 0.01084405
#> 
#> $max_resid
#> [1] 0.06418943
#> 
#> $communality
#> [1] 0.0516967748 0.0005343525 0.0383491602 1.0030318375
#> 
#> $spearman
#> [1] -0.4471565
#> 
#> $n_iter
#> [1] 5000
#> 
#> $p
#> [1] 4
#> 
#> $method
#> [1] "one-factor CFA, ML by EM"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"             
# }