CFA multi-factor with cross-loadings allowed

Formula: X = Lambda F + eps; F ~ N(0, Phi)

Usage

Cfafm2(X, factor_pattern)

Arguments

X

An n x p data matrix, or a p x p item covariance matrix.

factor_pattern

p x k matrix of 0/1 flags: 1 where item i may load on factor j.

Value

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

Details

Fitted by the Rubin-Thayer EM algorithm with the loading pattern imposed: an entry of factor_pattern that is zero forces the corresponding loading to stay zero, so cross-loadings are estimated only where the confirmatory model allows them. Factors are standardised and orthogonal (Phi = I), the identification the EM E-step assumes.

References

Joreskog (1969), Psychometrika 34(2):183-202; Rubin & Thayer (1982), Psychometrika 47(1):69-76.

Examples

Cfafm2(X = c(1, 2, 3, 4, 5, 6, 7, 8), factor_pattern = 5L)
#> $estimate
#> [1] 1
#> 
#> $loadings
#>         [,1]
#> [1,] 2.44949
#> 
#> $uniquenesses
#> [1] 1e-06
#> 
#> $fml
#> [1] 1.265654e-14
#> 
#> $max_resid
#> [1] 9.383863e-07
#> 
#> $communality
#> [1] 6
#> 
#> $n_iter
#> [1] 5000
#> 
#> $p
#> [1] 1
#> 
#> $k
#> [1] 1
#> 
#> $method
#> [1] "CFA multi-factor with cross-loadings allowed"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"