pfa | R Documentation |

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

```
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,
...
)
```

`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 |

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).

`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 |

Peter Filzmoser, Karel Hron, Matthias Templ

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.

```
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)))
```

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