rRecovery: Test of Recovery of a Correlation or a Covariance matrix from...

In nFactors: Parallel Analysis and Other Non Graphical Solutions to the Cattell Scree Test

Test of Recovery of a Correlation or a Covariance matrix from a Factor Analysis Solution

Description

The rRecovery function returns a verification of the quality of the recovery of the initial correlation or covariance matrix by the factor solution.

Usage

rRecovery(R, loadings, diagCommunalities = FALSE)

Arguments

R	numeric: initial correlation or covariance matrix
loadings	numeric: loadings from a factor analysis solution
diagCommunalities	logical: if TRUE, the correlation between the initial solution and the estimated one will use a correlation of one in the diagonal. If FALSE (default) the diagonal is not used in the computation of this correlation.

Value

R	numeric: initial correlation or covariance matrix
recoveredR	numeric: recovered estimated correlation or covariance matrix
difference	numeric: difference between initial and recovered estimated correlation or covariance matrix
cor	numeric: Pearson correlation between initial and recovered estimated correlation or covariance matrix. Computations depend on the logical value of the communalities argument.

Author(s)

Gilles Raiche
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
[e-mail]

See Also

componentAxis, iterativePrincipalAxis, principalAxis

Examples

# .......................................................
# Example from Kim and Mueller (1978, p. 10)
# Population: upper diagonal
# Simulated sample: lower diagnonal
 R <- matrix(c( 1.000, .6008, .4984, .1920, .1959, .3466,
                .5600, 1.000, .4749, .2196, .1912, .2979,
                .4800, .4200, 1.000, .2079, .2010, .2445,
                .2240, .1960, .1680, 1.000, .4334, .3197,
                .1920, .1680, .1440, .4200, 1.000, .4207,
                .1600, .1400, .1200, .3500, .3000, 1.000),
                nrow=6, byrow=TRUE)


# Replace upper diagonal with lower diagonal
 RU         <- diagReplace(R, upper=TRUE)
 nFactors   <- 2
 loadings   <- principalAxis(RU, nFactors=nFactors,
                             communalities="component")$loadings
 rComponent <- rRecovery(RU,loadings, diagCommunalities=FALSE)$cor

 loadings   <- principalAxis(RU, nFactors=nFactors,
                             communalities="maxr")$loadings
 rMaxr      <- rRecovery(RU,loadings, diagCommunalities=FALSE)$cor

 loadings   <- principalAxis(RU, nFactors=nFactors,
                             communalities="multiple")$loadings
 rMultiple  <- rRecovery(RU,loadings, diagCommunalities=FALSE)$cor

 round(c(rComponent = rComponent,
         rmaxr      = rMaxr,
         rMultiple  = rMultiple), 3)
# .......................................................

nFactors documentation built on Oct. 10, 2022, 5:07 p.m.