R: Factor analysis for compositional data

pfa {robCompositions} | 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)))

[Package robCompositions version 2.2.1 Index]