pfa: Factor analysis for compositional data

In robCompositions: Compositional Data Analysis

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,
  robust = TRUE,
  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
robust	default value is TRUE
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

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).

Value

loadings	A matrix of loadings, one column for each factor. The factors are ordered in decreasing order of sums of squares of loadings.
uniqueness	uniqueness
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

Author(s)

Peter Filzmoser, Karel Hron, Matthias Templ

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
res.rob <- pfa(x, factors=1)
res.cla <- pfa(x, factors=1, robust=FALSE)


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

robCompositions documentation built on Aug. 25, 2023, 5:13 p.m.