robCompositions (version 1.9.1)

pfa: Factor analysis for compositional data

Description

Computes the principal factor analysis of the input data which are transformed and centered first.

Usage

pfa(x, factors, data = NULL, covmat = NULL, n.obs = NA, 
subset, na.action, start = NULL, 
scores = c("none", "regression", "Bartlett"), 
rotation = "varimax", maxiter = 5, control = NULL, ...)

Arguments

x

(robustly) scaled input data

factors

number of factors

data

default value is NULL

covmat

(robustly) computed covariance or correlation matrix

n.obs

number of observations

subset

if a subset is used

na.action

what to do with NA values

start

starting values

scores

which method should be used to calculate the scores

rotation

if a rotation should be made

maxiter

maximum number of iterations

control

default value is NULL

...

arguments for creating a list

Value

• loadings
  A matrix of loadings, one column for each factor. The factors are ordered in decreasing order of sums of squares of loadings.
• uniquness
  uniquness
• correlation
  correlation matrix
• criteria
  The results of the optimization: the value of the negativ log-likelihood and information of the iterations used.
• factors
  the factors
• dof
  degrees of freedom
• method
  principal
• n.obs
  number of observations if available, or NA
• call
  The matched call.
• STATISTIC, PVAL
  The significance-test statistic and p-value, if they can be computed

Details

The main difference to usual implementations is that uniquenesses are nor longer of diagonal form. This kind of factor analysis is designed for centered log-ratio transformed compositional data. However, if the covariance is not specified, the covariance is estimated from isometric log-ratio transformed data internally, but the data used for factor analysis are backtransformed to the clr space (see Filzmoser et al., 2009).

References

C. Reimann, P. Filzmoser, R.G. Garrett, and R. Dutter (2008): Statistical Data Analysis Explained. Applied Environmental Statistics with R. John Wiley and Sons, Chichester, 2008.

P. Filzmoser, K. Hron, C. Reimann, R. Garrett (2009): Robust Factor Analysis for Compositional Data. Computers and Geosciences, 35 (9), 1854--1861.

Examples

data(expenditures)
x <- expenditures
res0 <- pfa(x, factors=1, covmat="cov")

## the following produce always the same result:
res1 <- pfa(x, factors=1, covmat="covMcd")
res2 <- pfa(x, factors=1, covmat=covMcd(isomLR(x))$cov)
res3 <- pfa(x, factors=1, covmat=covMcd(isomLR(x)))