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

## Description

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

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10``` ```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 Jan. 13, 2021, 10:07 p.m.