PcaNA: Classical or robust Principal Components for incomplete data

Description

Computes classical and robust principal components for incomplete data using an EM algorithm as descibed by Serneels and Verdonck (2008)

Usage

PcaNA(x, ...)
# S3 method for default
PcaNA(x, k = ncol(x), kmax = ncol(x), conv=1e-10, maxiter=100, 
    method=c("cov", "locantore", "hubert", "grid", "proj", "class"), cov.control=NULL,
    scale = FALSE, signflip = TRUE, crit.pca.distances = 0.975, trace=FALSE, ...)
# S3 method for formula
PcaNA(formula, data = NULL, subset, na.action, ...)

Value

An S4 object of class PcaNA-class which is a subclass of the virtual class Pca-class.

Arguments

formula: a formula with no response variable, referring only to numeric variables.
data: an optional data frame (or similar: see model.frame) containing the variables in the formula formula.
subset: an optional vector used to select rows (observations) of the data matrix x.
na.action: a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The default is na.omit.
...: arguments passed to or from other methods.
x: a numeric matrix (or data frame) which provides the data for the principal components analysis.
k: number of principal components to compute. If k is missing, or k = 0, the algorithm itself will determine the number of components by finding such k that \(l_k/l_1 >= 10.E-3\) and \(\Sigma_{j=1}^k l_j/\Sigma_{j=1}^r l_j >= 0.8\). It is preferable to investigate the scree plot in order to choose the number of components and then run again. Default is k=ncol(x).
kmax: maximal number of principal components to compute. Default is kmax=10. If k is provided, kmax does not need to be specified, unless k is larger than 10.
conv: convergence criterion for the EM algorithm. Default is conv=1e-10.
maxiter: maximal number of iterations for the EM algorithm. Default is maxiter=100.
method: which PC method to use (classical or robust) - "class" means classical PCA and one of the following "locantore", "hubert", "grid", "proj", "cov" specifies a robust PCA method. If the method is "cov" - i.e. PCA based on a robust covariance matrix - the argument cov.control can specify which method for computing the (robust) covariance matrix will be used. Default is method="locantore".
cov.control: control object in case of robust PCA based on a robust covariance matrix.
scale: a logical value indicating whether the variables should be scaled to have unit variance (only possible if there are no constant variables). As a scale function mad is used but alternatively, a vector of length equal the number of columns of x can be supplied. The value is passed to scale and the result of the scaling is stored in the scale slot. Default is scale = FALSE
signflip: a logical value indicating wheather to try to solve the sign indeterminancy of the loadings - ad hoc approach setting the maximum element in a singular vector to be positive. Default is signflip = FALSE
crit.pca.distances: criterion to use for computing the cutoff values for the orthogonal and score distances. Default is 0.975.
trace: whether to print intermediate results. Default is trace = FALSE

Author

Valentin Todorov valentin.todorov@chello.at

Details

PcaNA, serving as a constructor for objects of class PcaNA-class is a generic function with "formula" and "default" methods. For details see the relevant references.

References

Serneels S & Verdonck T (2008), Principal component analysis for data containing outliers and missing elements. Computational Statistics and Data Analisys, 52(3), 1712--1727 .

Todorov V & Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1--47. URL http://www.jstatsoft.org/v32/i03/.

Examples

Run this code

## 1. With complete data
## PCA of the bushfire data
    data(bushfire)
    pca <- PcaNA(bushfire)
    pca

## Compare with the classical PCA
    prcomp(bushfire)

## or  
    PcaNA(bushfire, method="class")
    
## If you want to print the scores too, use
    print(pca, print.x=TRUE)

## Using the formula interface
    PcaNA(~., data=bushfire)

## To plot the results:

    plot(pca)                    # distance plot
    pca2 <- PcaNA(bushfire, k=2)  
    plot(pca2)                   # PCA diagnostic plot (or outlier map)
    
## Use the standard plots available for for prcomp and princomp
    screeplot(pca)    
    biplot(pca)  

################################################################      
## 2. Now the same wit incomplete data - bush10
    data(bush10)
    pca <- PcaNA(bush10)
    pca

## Compare with the classical PCA
    PcaNA(bush10, method="class")
    
## If you want to print the scores too, use
    print(pca, print.x=TRUE)

## Using the formula interface
    PcaNA(~., data=as.data.frame(bush10))

## To plot the results:

    plot(pca)                    # distance plot
    pca2 <- PcaNA(bush10, k=2)  
    plot(pca2)                   # PCA diagnostic plot (or outlier map)
    
## Use the standard plots available for for prcomp and princomp
    screeplot(pca)    
    biplot(pca)

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