DA.MRFA (version 1.1.2)

GreaterLowerBound:

Description

Estimates the communalities of the variables from a factor model where the number of factors is the number with positive eigenvalues.

Usage

GreaterLowerBound(C, conv = 0.000001, T, pwarnings = FALSE)

Arguments

C

Covariance/correlation matrix to be used in the analysis.

conv

Convergence criterion for glb step. The default convergence criterion will be conv=0.000001 . If the user determine a specific value, this will prevail.

T

Random matrix for start (can be omitted). If provided, it has to be the same size than the matrix provided in the C argument.

pwarnings

Determines if the possible warnings occurred during the computation will be printed in the console.

Value

gam

Optimal communalities for each variable

Details

Code adapted from a MATLAB function by Jos Ten Berge based on Ten Berge, Snijders & Zegers (1981) and Ten Berge & Kiers (1991).

References

Ten Berge, J.M.F., & Kiers, H.A.L. (1991). A numerical approach to the exact and the approximate minimum rank of a covariance matrix. Psychometrika, 56, 309-315.

Ten Berge, J.M.F., Snijders, T.A.B. & Zegers, F.E. (1981). Computational aspects of the greatest lower bound to reliability and constrained minimum trace factor analysis. Psychometrika, 46, 201-213.

Examples

## perform glb using the correlation matrix of the IDAQ dataset, and using severe convergence
## criterion.
GreaterLowerBound(cor(IDAQ), conv=0.000001)