| principalComponents {nFactors} | R Documentation |
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
raiche.gilles@uqam.ca
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)
# .......................................................