principalAxis {nFactors} | R Documentation |
The PrincipalAxis
function return a principal axis analysis without
iterated communalities estimates. Three different choices of communalities
estimates are given: maximum corelation, multiple correlation or estimates based
on the sum of the sqared principal component analysis loadings. Generally statistical
packages initialize the the communalities at the multiple correlation value (usual inverse or generalized inverse).
Unfortunately, this strategy cannot deal with singular correlation or covariance matrices.
If a generalized inverse, the maximum correlation or the estimated communalities based on the sum of loading
are used insted, then a solution can be computed.
principalAxis(R, nFactors=2, communalities="component")
R |
numeric: correlation or covariance matrix |
nFactors |
numeric: number of factors to retain |
communalities |
character: initial values for communalities
("component", "maxr", "ginv" or "multiple" ) |
values |
numeric: variance of each component/factor |
varExplained |
numeric: variance explained by each component/factor |
varExplained |
numeric: cumulative variance explained by each component/factor |
loadings |
numeric: loadings of each variable on each component/factor |
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/
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
# ....................................................... # 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 axis factoring # without iterated communalities - # Kim and Mueller (1978, p. 21) # Replace upper diagonal by lower diagonal RU <- diagReplace(R, upper=TRUE) principalAxis(RU, nFactors=2, communalities="component") principalAxis(RU, nFactors=2, communalities="maxr") principalAxis(RU, nFactors=2, communalities="multiple") # Replace lower diagonal by upper diagonal RL <- diagReplace(R, upper=FALSE) principalAxis(RL, nFactors=2, communalities="component") principalAxis(RL, nFactors=2, communalities="maxr") principalAxis(RL, nFactors=2, communalities="multiple") # .......................................................