principalComponents: Principal Component Analysis

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

Principal Component Analysis

Description

The principalComponents function returns a principal component analysis. Other R functions give the same results, but principalComponents is customized mainly for the other factor analysis functions available in the nfactors package. In order to retain only a small number of components the componentAxis function has to be used.

Usage

principalComponents(R)

Arguments

R	numeric: correlation or covariance matrix

Value

values	numeric: variance of each component
varExplained	numeric: variance explained by each component
varExplained	numeric: cumulative variance explained by each component
loadings	numeric: loadings of each variable on each component

Author(s)

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

References

Joliffe, I. T. (2002). Principal components analysis (2th Edition). New York, NJ: Springer-Verlag.

Kim, J.-O. and Mueller, C. W. (1978). Introduction to factor analysis. What it is and how to do it. Beverly Hills, CA: Sage.

Kim, J.-O. and Mueller, C. W. (1987). Factor analysis. Statistical methods and practical issues. Beverly Hills, CA: Sage.

See Also

componentAxis, iterativePrincipalAxis, rRecovery

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)

# Factor analysis: Principal component -
# Kim et Mueller (1978, p. 21)
# Replace upper diagonal with lower diagonal
 RU <- diagReplace(R, upper=TRUE)
 principalComponents(RU)

# Replace lower diagonal with upper diagonal
 RL <- diagReplace(R, upper=FALSE)
 principalComponents(RL)
# .......................................................

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