# pfa: Factor analysis for compositional data In robCompositions: Compositional Data Analysis

 pfa R Documentation

## 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.