Factor analysis for compositional data
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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