| principalComponents {nFactors} | R Documentation |
The principalComponents function return a principal component analysis.
Other R functions give the same results, but principalComponents is mainly
customed for the other factor analysis functions available in the nfactors
package. To retain only a small number of components the componentAxis
function has to be used.
principalComponents(R)
R |
numeric: correlation or covariance matrix |
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 |
Gilles Raiche
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
raiche.gilles@uqam.ca, http://www.er.uqam.ca/nobel/r17165/
Joliffe, I. T. (2002). Principal components analysis (2th Edition). New York, NJ: Springer-Verlag.
Kim, J.-O., Mueller, C. W. (1978). Introduction to factor analysis. What it is and how to do it. Beverly Hills, CA: Sage.
Kim, J.-O., Mueller, C. W. (1987). Factor analysis. Statistical methods and practical issues. Beverly Hills, CA: Sage.
componentAxis,
iterativePrincipalAxis,
rRecovery
# .......................................................
# Exemple 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 components -
# Kim et Mueller (1978, p. 21)
# Replace upper diagonal by lower diagonal
RU <- diagReplace(R, upper=TRUE)
principalComponents(RU)
# Replace lower diagonal by upper diagonal
RL <- diagReplace(R, upper=FALSE)
principalComponents(RL)
# .......................................................