Type:	Package
Title:	Object Oriented Solution for Robust Factor Analysis
Version:	1.1-0
Date:	2023-03-21
Author:	Frederic Bertrand [cre], Ying-Ying Zhang (Robert) [aut]
Maintainer:	Frederic Bertrand <frederic.bertrand@utt.fr>
Description:	Outliers virtually exist in any datasets of any application field. To avoid the impact of outliers, we need to use robust estimators. Classical estimators of multivariate mean and covariance matrix are the sample mean and the sample covariance matrix. Outliers will affect the sample mean and the sample covariance matrix, and thus they will affect the classical factor analysis which depends on the classical estimators (Pison, G., Rousseeuw, P.J., Filzmoser, P. and Croux, C. (2003) <doi:10.1016/S0047-259X(02)00007-6>). So it is necessary to use the robust estimators of the sample mean and the sample covariance matrix. There are several robust estimators in the literature: Minimum Covariance Determinant estimator, Orthogonalized Gnanadesikan-Kettenring, Minimum Volume Ellipsoid, M, S, and Stahel-Donoho. The most direct way to make multivariate analysis more robust is to replace the sample mean and the sample covariance matrix of the classical estimators to robust estimators (Maronna, R.A., Martin, D. and Yohai, V. (2006) <doi:10.1002/0470010940>) (Todorov, V. and Filzmoser, P. (2009) <doi:10.18637/jss.v032.i03>), which is our choice of robust factor analysis. We created an object oriented solution for robust factor analysis based on new S4 classes.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Depends:	rrcov, R (≥ 2.15.0)
Imports:	methods, stats4, stats
Suggests:	grid, lattice, cluster, mclust, MASS, ellipse, knitr, rmarkdown
LazyLoad:	yes
LazyData:	yes
Encoding:	UTF-8
RoxygenNote:	7.2.1
VignetteBuilder:	knitr, rmarkdown
NeedsCompilation:	no
Packaged:	2023-04-16 08:04:40 UTC; fbertran
Repository:	CRAN
Date/Publication:	2023-04-16 14:40:02 UTC

An Object Oriented Solution for Robust Factor Analysis

Description

Outliers virtually exist in any datasets of any application field. To avoid the impact of outliers, we need to use robust estimators. Classical estimators of multivariate mean and covariance matrix are the sample mean and the sample covariance matrix. Outliers will affect the sample mean and the sample covariance matrix, and thus they will affect the classical factor analysis which depends on the classical estimators (Pison, G., Rousseeuw, P.J., Filzmoser, P. and Croux, C. (2003) doi:10.1016/S0047-259X(02)00007-6). So it is necessary to use the robust estimators of the sample mean and the sample covariance matrix. There are several robust estimators in the literature: MCD, OGK, MVE, M, S, and Stahel-Donoho. The most direct way to robustify multivariate anal-ysis is to replace the sample mean and the sample covariance matrix of the classical estimators to robust estima-tors (Maronna, R.A., Martin, D. and Yohai, V. (2006) doi:10.1002/0470010940) (Todorov, V. and Filzmoser, P. (2009) doi:10.18637/jss.v032.i03), which is our choice of robust factor analysis. robustfa is an object oriented solution for robust factor analysis. In the solution, new S4 classes "Fa", "FaClassic", "FaRobust", "FaCov", "SummaryFa" are created.

Details

The most important functions are: FaClassic, FaCov, factorScorePca, factorScorePfa

Author(s)

Ying-Ying Zhang (Robert)

Maintainer: Ying-Ying Zhang (Robert) <robertzhangyying@qq.com>

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

Examples

library("robustfa")

Class "Fa"

Description

Class "Fa" is a virtual base class for all classical and robust FA classes. "Fa" searves as a base class for deriving all other classes representing the results of the classical and robust Factor Analysis methods.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

call:

Object of class "language" an unevaluated function call.

converged:

Object of class "Ulogical" a logical character indicates whether the iterations converged.

loadings:

Object of class "matrix" the matrix of variable loadings.

communality:

Object of class "Uvector" the communality.

uniquenesses:

Object of class "vector" the uniquenesses computed.

cor:

Object of class "Ulogical" A logical value indicating whether the calculation should use the covariance matrix (cor = FALSE) or the correlation matrix (cor = TRUE).

covariance:

Object of class "matrix" The robust/classical covariance matrix.

correlation:

Object of class "matrix" The robust/classical correlation matrix.

usedMatrix:

Object of class "matrix" The used matrix (running matrix). It may be the covariance or correlation matrix according to the value of cor.

reducedCorrelation:

Object of class "Umatrix" The last reduced correlation matrix. reducedCorrelation is only calculated in factorScorePfa.R.

criteria:

Object of class "Unumeric". The results of the optimization: the value of the negative log-likelihood and information on the iterations used.

factors:

Object of class "numeric" the number of factors.

dof:

Object of class "Unumeric". The number of degrees of freedom of the factor analysis model.

method:

Object of class "character". The method: one of "mle", "pca", and "pfa".

scores:

Object of class "Umatrix". If requested, a matrix of scores.

scoresMethod:

Object of class "character". The scores method: one of "none", "regression", and "Bartlett".

scoringCoef:

Object of class "Umatrix" the matrix of scoring coefficients.

meanF:

Object of class "Uvector" the column means of scores.

corF:

Object of class "Umatrix" the correlation matrix of the scores.

STATISTIC:

Object of class "Unumeric". The significance-test statistic, if it can be computed.

PVAL:

Object of class "Unumeric". The significance-test P value, if it can be computed.

n.obs:

Object of class "numeric". The number of observations.

center:

Object of class "Uvector". The center of the data.

eigenvalues:

Object of class "vector" the eigenvalues.

cov.control:

Object of class "UCovControl". Record the cov control method.

Methods

getCenter

signature(obj = "Fa"): center of the data

getEigenvalues

signature(obj = "Fa"): the eigenvalues of the covariance/correlation matrix

getFa

signature(obj = "Fa"): returns an S3 list of class fa for compatibility with the function factanal(). Thus the standard screeplot() can be used.

getLoadings

signature(obj = "Fa"): returns the matrix loadings

getQuan

signature(obj = "Fa"): returns the number of observations used in the computation, i.e., n.obs

getScores

signature(obj = "Fa"): if requested, a matrix of scores.

getSdev

signature(obj = "Fa"): returns the standard deviations of the factor analysis, i.e., the square roots of the eigenvalues of the covariance/correlation matrix

plot

signature(x = "Fa", y = "missing"): produces a scatterplot of the factor scores (if which = "factorScore") or shows the eigenvalues plot (if which = "screeplot")

predict

signature(object = "Fa"): calculates prediction using the results in object. The newdata argument is an optional data frame or matrix in which to look for variables with which to predict. If newdata is omitted, the scores are used.

print

signature(x = "Fa"): prints the results. obj = print(obj)

summary

signature(object = "Fa"): produce result summaries of an object of class "Fa".

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Bartlett, M. S. (1937) The statistical conception of mental factors. British Journal of Psychology, 28, 97–104.

Bartlett, M. S. (1938) Methods of estimating mental factors. Nature, 141, 609–610.

Joreskog, K. G. (1963) Statistical Estimation in Factor Analysis. Almqvist and Wicksell.

Lawley, D. N. and Maxwell, A. E. (1971) Factor Analysis as a Statistical Method. Second edition. Butterworths.

Thomson, G. H. (1951) The Factorial Analysis of Human Ability. London University Press.

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

Zhang, Y. Y. (2014), Robust Factor Analysis and Its Applications in the CSI 100 Index, Open Journal of Social Sciences 2(07):12-18, doi:10.4236/jss.2014.27003.

See Also

FaClassic-class, FaCov-class, FaRobust-class, Fa-class

Examples

showClass("Fa")

Classical Factor Analysis

Description

Performs a classical factor analysis and returns the results as an object of class "FaClassic" (a.k.a. constructor).

Usage

FaClassic(x, ...)
## S3 method for class 'formula'
FaClassic(formula, data = NULL, factors = 2, cor = FALSE, method = "mle", 
scoresMethod = "none", ...)
## Default S3 method:
FaClassic(x, factors = 2, cor = FALSE, method = c("mle", "pca", "pfa"), 
scoresMethod = c("none", "regression", "Bartlett"), ...)

Arguments

Value

An S4 object of class FaClassic-class which is a subclass of the virtual class Fa-class.

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

See Also

FaClassic-class, FaCov-class, FaRobust-class, Fa-class

Examples

data("hbk")
hbk.x = hbk[,1:3] 

## faClassicPcaReg uses the default method
faClassicPcaReg = FaClassic(x = hbk.x, factors = 2, method = "pca",
scoresMethod = "regression"); faClassicPcaReg
summary(faClassicPcaReg)

## faClassicForPcaReg uses the formula interface
## faClassicForPcaReg = faClassicPcaReg
faClassicForPcaReg = FaClassic(~., data=as.data.frame(hbk.x), factors = 2, 
method = "pca", scoresMethod = "regression"); faClassicForPcaReg
summary(faClassicForPcaReg)

Class "FaClassic"

Description

Contains the results of a classical Factor Analysis

Objects from the Class

Objects can be created by calls of the form new("FaClassic", ...). But the usual way of creating FaClassic objects is a call to the function FaClassic which serves as a constructor.

Slots

call:

Object of class "language" an unevaluated function call

converged:

Object of class "Ulogical" a logical character indicates whether the iterations converged

loadings:

Object of class "matrix" the matrix of variable loadings

uniquenesses:

Object of class "vector" the uniquenesses computed

covariance:

Object of class "matrix" the covariance matrix

correlation:

Object of class "matrix" the correlation matrix

usedMatrix:

Object of class "matrix" the used matrix (running matrix)

criteria:

Object of class "Unumeric". The results of the optimization: the value of the negative log-likelihood and information on the iterations used.

factors:

Object of class "numeric" the number of factors

dof:

Object of class "Unumeric". The number of degrees of freedom of the factor analysis model.

method:

Object of class "character". The method: one of "mle", "pca", and "pfa".

scores:

Object of class "Umatrix". If requested, a matrix of scores.

scoresMethod:

Object of class "character". The scores method: one of "none", "regression", and "Bartlett".

STATISTIC:

Object of class "Unumeric". The significance-test statistic, if it can be computed.

PVAL:

Object of class "Unumeric". The significance-test P value, if it can be computed.

n.obs:

Object of class "Unumeric". The number of observations if available.

center:

Object of class "Uvector". The center of the data.

eigenvalues:

Object of class "vector" the eigenvalues

cov.control:

Object of class "UCovControl". Record the cov control method.

Extends

Class "Fa", directly.

Methods

No methods defined with class "FaClassic" in the signature.

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

See Also

FaClassic-class, FaCov-class, FaRobust-class, Fa-class

Examples

showClass("FaClassic")

Robust Factor Analysis

Description

Robust factor analysis are obtained by replacing the classical covariance matrix by a robust covariance estimator. This can be one of the available estimators in rrcov, i.e., MCD, OGK, M, S, SDE, or MVE estimator.

Usage

FaCov(x, ...)
## S3 method for class 'formula'
FaCov(formula, data = NULL, factors = 2, cor = FALSE, method = "mle", 
scoresMethod = "none", ...)
## Default S3 method:
FaCov(x, factors = 2, cor = FALSE, cov.control = rrcov::CovControlMcd(), 
method = c("mle", "pca", "pfa"), 
scoresMethod = c("none", "regression", "Bartlett"), ...)

Arguments

Details

FaCov, serving as a constructor for objects of class FaCov-class is a generic function with "formula" and "default" methods.

Value

An S4 object of class FaCov-class which is a subclass of the virtual class Fa-class.

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

See Also

FaClassic-class, FaCov-class, FaRobust-class, Fa-class

Examples

data("hbk")
hbk.x = hbk[,1:3] 

##
## faCovPcaRegMcd is obtained from FaCov.default
##
faCovPcaRegMcd = FaCov(x = hbk.x, factors = 2, method = "pca",
scoresMethod = "regression", cov.control = rrcov::CovControlMcd()); faCovPcaRegMcd

##
## In fact, it is equivalent to use FaCov.formula
## faCovForPcaRegMcd = faCovPcaRegMcd
##
faCovForPcaRegMcd = FaCov(~., data = as.data.frame(hbk.x), 
factors = 2, method = "pca", scoresMethod = "regression", 
cov.control = rrcov::CovControlMcd()); faCovForPcaRegMcd

Class "FaCov"

Description

Robust FA based on a robust covariance matrix. Robust FA are obtained by replacing the classical covariance matrix by a robust covariance estimator. This can be one of the available in rrcov estimators, i.e., MCD, OGK, M, S, SDE, or MVE estimator.

Objects from the Class

Objects can be created by calls of the form new("FaCov", ...). But the usual way of creating FaCov objects is a call to the function FaCov which serves as a constructor.

Slots

call:

Object of class "language" an unevaluated function call

converged:

Object of class "Ulogical" a logical character indicates whether the iterations converged

loadings:

Object of class "matrix" the matrix of variable loadings

uniquenesses:

Object of class "vector" the uniquenesses computed

covariance:

Object of class "matrix" the covariance matrix

correlation:

Object of class "matrix" the correlation matrix

usedMatrix:

Object of class "matrix" the used matrix (running matrix)

criteria:

Object of class "Unumeric". The results of the optimization: the value of the negative log-likelihood and information on the iterations used.

factors:

Object of class "numeric" the number of factors

dof:

Object of class "Unumeric". The number of degrees of freedom of the factor analysis model.

method:

Object of class "character". The method: one of "mle", "pca", and "pfa".

scores:

Object of class "Umatrix". If requested, a matrix of scores.

scoresMethod:

Object of class "character". The scores method: one of "none", "regression", and "Bartlett".

STATISTIC:

Object of class "Unumeric". The significance-test statistic, if it can be computed.

PVAL:

Object of class "Unumeric". The significance-test P value, if it can be computed.

n.obs:

Object of class "Unumeric". The number of observations if available.

center:

Object of class "Uvector". The center of the data.

eigenvalues:

Object of class "vector" the eigenvalues

cov.control:

Object of class "UCovControl". Record the cov control method.

Extends

Class "FaRobust", directly. Class "Fa", by class "FaRobust", distance 2.

Methods

No methods defined with class "FaCov" in the signature.

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

See Also

FaClassic-class, FaCov-class, FaRobust-class, Fa-class

Examples

showClass("FaCov")

Class "FaRobust"

Description

Class "FaRobust" is a virtual base class for all robust FA classes. Currently the only available robust FA class is "FaCov". The class "FaRobust" serves as a base class for deriving all other classes representing the results of the robust Factor Analysis methods.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

call:

Object of class "language" an unevaluated function call

converged:

Object of class "Ulogical" a logical character indicates whether the iterations converged

loadings:

Object of class "matrix" the matrix of variable loadings

uniquenesses:

Object of class "vector" the uniquenesses computed

covariance:

Object of class "matrix" the covariance matrix

correlation:

Object of class "matrix" the correlation matrix

usedMatrix:

Object of class "matrix" the used matrix (running matrix)

criteria:

Object of class "Unumeric". The results of the optimization: the value of the negative log-likelihood and information on the iterations used.

factors:

Object of class "numeric" the number of factors

dof:

Object of class "Unumeric". The number of degrees of freedom of the factor analysis model.

method:

Object of class "character". The method: one of "mle", "pca", and "pfa".

scores:

Object of class "Umatrix". If requested, a matrix of scores.

scoresMethod:

Object of class "character". The scores method: one of "none", "regression", and "Bartlett".

STATISTIC:

Object of class "Unumeric". The significance-test statistic, if it can be computed.

PVAL:

Object of class "Unumeric". The significance-test P value, if it can be computed.

n.obs:

Object of class "Unumeric". The number of observations if available.

center:

Object of class "Uvector". The center of the data.

eigenvalues:

Object of class "vector" the eigenvalues

cov.control:

Object of class "UCovControl". Record the cov control method.

Extends

Class "Fa", directly.

Methods

No methods defined with class "FaRobust" in the signature.

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

See Also

FaClassic-class, FaCov-class, FaRobust-class, Fa-class

Examples

showClass("FaRobust")

Class "SummaryFa"

Description

Summary of "Fa" objects. The "Fa" object plus some additional summary information.

Objects from the Class

Objects can be created by calls of the form new("SummaryFa", ...). But most often by invoking 'summary' on an "Fa" object. They contain values meant for printing by 'show'.

Slots

faobj:

Object of class "Fa"

importance:

Object of class "matrix". Matrix with additional information: importance of components.

Methods

show

signature(object = "SummaryFa"): display the object

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

See Also

Fa-class

Examples

showClass("SummaryFa")

Class "Ulogical"

Description

Define class unions for optional slots, e.g., for definition of slots which will be computed on demand.

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

No methods defined with class "Ulogical" in the signature.

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

Class "Unumeric"

Description

Define class unions for optional slots, e.g., for definition of slots which will be computed on demand.

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

No methods defined with class "Unumeric" in the signature.

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

Compute Factor Scores

Description

Compute factor scores on the result of factor analysis method, the method is one of "mle", "pca", and "pfa".

Usage

computeScores(out, x = data, covmat = covmat, cor = cor, scoresMethod = scoresMethod)

Arguments

Value

The output is a list. Except for the components of out, it also has components:

scoringCoef = F = meanF = corF = NULL if scoresMethod = "none".

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

Examples

data("stock611")
stock604 = stock611[-c(92,2,337,338,379,539,79), ]
data = as.matrix(stock604[, 3:12])

factors = 2
cor = TRUE
scoresMethod = "regression" 

covx = rrcov::Cov(data)
covmat = list(cov = rrcov::getCov(covx), center = rrcov::getCenter(covx), n.obs = covx@n.obs)

out = stats::factanal(factors = factors, covmat = covmat)

out = computeScores(out, x = data, covmat = covmat, cor = cor, scoresMethod = scoresMethod)
out

Compute the Robust Covariance and Correlation Matrix of A Numeric Matrix

Description

Compute the robust covariance and correlation matrix of a numeric matrix. The function is used to check whether S_r != S_r_tilda and R_r == R_r_tilda?

Usage

compute_cov_cor(x, control)

Arguments

Value

A list with the following components:

cov_x = rrcov::CovRobust(x = x, control = control) cov_scale_x = rrcov::CovRobust(x = scale(x), control = control)

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

Examples

data("hbk")
hbk.x = hbk[,1:3]

compute_cov_cor(x = hbk.x, control = "mcd")

Show Details of an Object

Description

Show details of an object.

Usage

detail(x)

Arguments

Value

A list with components:

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

See Also

isS4, is.object, class, attributes

Examples

data(stock611)
detail(stock611)

facovRegOgk=FaCov(x=scale(stock611[,3:12]), factors=3, cov.control = rrcov::CovControlOgk(), 
scoresMethod = "regression"); facovRegOgk
detail(facovRegOgk)

Factor Analysis by Principal Component Analysis (PCA)

Description

Perform principal component factor analysis on a covariance matrix or data matrix.

Usage

factorScorePca(x, factors = 2, covmat = NULL, cor = FALSE, 
rotation = c("varimax", "none"), 
scoresMethod = c("none", "regression", "Bartlett"))

Arguments

Details

Other feasible usages are:

factorScorePca(factors, covmat)

factorScorePca(x, factors, rotation, scoresMethod)

If x is missing, then the following components of the result will be NULL: scores, ScoringCoef, meanF, corF, and n.obs.

Value

An object of class "factorScorePca" with components:

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

See Also

factorScorePfa, factanal

Examples

data(stock611)
R611=cor(stock611[,3:12]); R611

## covmat is a matrix
fsPca1=factorScorePca(factors = 3, covmat = R611); fsPca1

## covmat is a list
covx <- rrcov::Cov(stock611[,3:12])
covmat <- list(cov=rrcov::getCov(covx), center=rrcov::getCenter(covx), n.obs=covx@n.obs)
fsPca2=factorScorePca(factors = 3, covmat = covmat); fsPca2

## fsPca3 contains scores etc.
fsPca3=factorScorePca(x = stock611[,3:12], factors = 2, cor = TRUE, rotation = "varimax", 
scoresMethod = "regression"); fsPca3

Factor Analysis by Principal Factor Analysis (PFA)

Description

Perform principal factor factor analysis on a covariance matrix or data matrix.

Usage

factorScorePfa(x, factors = 2, covmat = NULL, cor = FALSE, 
rotation = c("varimax", "none"), 
scoresMethod = c("none", "regression", "Bartlett"))

Arguments

Details

Other feasible usages are:

factorScorePfa(factors, covmat)

factorScorePfa(x, factors, rotation, scoresMethod)

If x is missing, then the following components of the result will be NULL: scores, ScoringCoef, meanF, corF, and n.obs.

Value

An object of class "factorScorePfa" with components:

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

See Also

factorScorePca, factanal

Examples

data(stock611)
R611 = cor(stock611[,3:12]); R611

## covmat is a matrix
fsPfa1 = factorScorePfa(factors = 3, covmat = R611); fsPfa1

## covmat is a list
covx = rrcov::Cov(stock611[,3:12])
covmat = list(cov = rrcov::getCov(covx), center = rrcov::getCenter(covx), n.obs = covx@n.obs)
fsPfa2 = factorScorePfa(factors = 3, cor = TRUE, covmat = covmat); fsPfa2

## fsPfa3 contains scores etc.
fsPfa3 = factorScorePfa(x = stock611[,3:12], factors = 2, 
cor = TRUE, rotation = "varimax", scoresMethod = "regression"); fsPfa3

Compute the Ordered Factor Scores

Description

Compute the ordered factor scores according to the first/second/third... column of the original factor scores.

Usage

fsOrder(factorScores)

Arguments

Value

A list with m (the number of factors) components:

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

See Also

order

Examples

data(stock611)
R611=cor(stock611[,3:12]); R611

## FS.pca contains scores etc.
fsPca=factorScorePca(x = stock611[,3:12], factors = 2, cor = TRUE, 
rotation = "varimax", scoresMethod = "regression"); fsPca

orderedFS=fsOrder(fsPca$scores); orderedFS

Access Center slot

Description

Accessor method to the Center slot of an object of class "Fa" and its subclasses.

Methods

signature(obj = "Fa")

Accessor method to the Center slot of an object of class "Fa" and its subclasses

Access Eigenvalues slot

Description

Accessor method to the Eigenvalues slot of an object of class "Fa" and its subclasses.

Methods

signature(obj = "Fa")

Accessor method to the Eigenvalues slot of an object of class "Fa" and its subclasses

Access slots of "Fa"

Description

Accessor method to some slots of an object of class "Fa" and its subclasses. Return a list of class "fa".

Methods

signature(obj = "Fa")

Accessor method to some slots of an object of class "Fa" and its subclasses. Return a list of class "fa".

Access Loadings slot

Description

Accessor method to the Loadings slot of an object of class "Fa" and its subclasses.

Methods

signature(obj = "Fa")

Accessor method to the Loadings slot of an object of class "Fa" and its subclasses

Access n.obs slot

Description

Accessor method to the n.obs slot of an object of class "Fa" and its subclasses.

Methods

signature(obj = "Fa")

Accessor method to the n.obs slot of an object of class "Fa" and its subclasses

Access Scores slot

Description

Accessor method to the Scores slot of an object of class "Fa" and its subclasses.

Methods

signature(obj = "Fa")

Accessor method to the Scores slot of an object of class "Fa" and its subclasses

Access Standard Deviation slot

Description

Accessor method to the Standard Deviation slot of an object of class "Fa" and its subclasses.

Methods

signature(obj = "Fa")

Accessor method to the Standard Deviation slot of an object of class "Fa" and its subclasses

Show/Print/Display an Object

Description

Show/print/display an object, including the Call, Standard deviations, Loadings, and Rotated variables (if print.x = TRUE).

Usage

myFaPrint(object, print.x=FALSE)

Arguments

Value

An invisible argument object.

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

See Also

Fa-class

Examples

data("hbk")
hbk.x = hbk[,1:3] 

faCovPcaRegMcd = FaCov(x = hbk.x, factors = 2, method = "pca",
scoresMethod = "regression", cov.control = rrcov::CovControlMcd())

## you can use either object or print(object) or myFaPrint(object)
## since faCovPcaRegMcd is an object of class "Fa"

faCovPcaRegMcd
print(faCovPcaRegMcd)
myFaPrint(faCovPcaRegMcd)

Distance-Distance Plot

Description

"myplotDD" is a revised version of ".myddplot" in "plot-utils.R" in the package "rrcov". In "myplotDD", id.n and ind are printed out.

Usage

myplotDD(x, cutoff, id.n)

Arguments

Details

Distance-Distance Plot: Plot the vector y=rd (robust distances) against x=md (mahalanobis distances). Identify by a label the id.n observations with largest rd. If id.n is not supplied, calculate it as the number of observations larger than cutoff. Use cutoff to draw a horisontal and a vertical line. Draw also a dotted line with a slope 1.

"myplotDD(x)" is equivalent to "plot(x, which="dd")". which: indicate what kind of plot. If which = "dd", then a distance-distance Plot.

Value

A distance-distance plot is shown. Return a list with components:

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

See Also

plot, qchisq, CovClassic, getDistance

Examples

data(stock611)
covMcd=CovRobust(x=scale(stock611[,3:12]), control="mcd"); covMcd

## "myplotDD" shows id.n and ind.
## Note: id.n and ind change each time due to covMcd changes each time!
## However, the ind of largest robust distances do not change.
result = myplotDD(x=covMcd); result

## "myplotDD" is equivalent to "plot(x=covMcd, which="dd")".
plot(x=covMcd, which="dd")

Plot an object of class "Fa"

Description

Plot an object of class "Fa". If which = "factorScore", then a scatterplot of the factor scores is produced; if which = "screeplot", shows the eigenvalues and is helpful to select the number of factors.

Usage

## S4 method for signature 'Fa'
plot(x, which=c("factorScore", "screeplot"), choices=1:2)

Arguments

Details

The feasible usages are: plot(x, which="factorScore", choices=1:2) plot(x, which="screeplot")

Methods

signature(x = "Fa", y = "missing")

generic functions - see plot

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

Examples

data("hbk")
hbk.x = hbk[,1:3] 

faClassicPcaReg = FaClassic(x = hbk.x, factors = 2, method = "pca",
scoresMethod = "regression"); faClassicPcaReg
summary(faClassicPcaReg)

plot(faClassicPcaReg, which = "factorScore", choices = 1:2)
plot(faClassicPcaReg, which = "screeplot")

Calculates prediction

Description

Calculates prediction using the results in object. The newdata argument is an optional data frame or matrix in which to look for variables with which to predict. If newdata is omitted, the scores are used.

Usage

predict(object, ...)

Arguments

Methods

signature(object = "Fa")

generic functions - see print, summary, predict, plot, getCenter, getEigenvalues, getFa, getLoadings, getQuan, getScores, getSdev

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

Examples

data("hbk")
hbk.x = hbk[,1:3] 

faCovPcaRegMcd = FaCov(x = hbk.x, factors = 2, method = "pca",
scoresMethod = "regression", cov.control = rrcov::CovControlMcd()); faCovPcaRegMcd

## If missing newdata, the scores are used
predict(faCovPcaRegMcd)

##
## If not missing newdata, newdata should be scaled first.
##
newdata = hbk.x[1, ]
cor = FALSE # the default
newdata = { 
if (cor == TRUE)
	# standardized transformation
	scale(newdata, center = faCovPcaRegMcd@center, 
	scale = sqrt(diag(faCovPcaRegMcd@covariance)))
else # cor == FALSE
	# centralized transformation
	scale(newdata, center = faCovPcaRegMcd@center, scale = FALSE)
}

##
## Now, prediction = predict(faCovPcaRegMcd)[1,] = faCovPcaRegMcd@scores[1,]
##
prediction = predict(faCovPcaRegMcd, newdata = newdata)
prediction

Print/Display an Object

Description

Print/display an object, including the Call, Standard deviations, Loadings.

Usage

print(x, ...)

Arguments

Value

An invisible argument x.

Methods

x = "Fa"

generic functions - see print, summary, predict, plot, getCenter, getEigenvalues, getFa, getLoadings, getQuan, getScores, getSdev

x = "SummaryFa"

generic functions - see print, summary, predict, plot, getCenter, getEigenvalues, getFa, getLoadings, getQuan, getScores, getSdev

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

See Also

Fa-class, SummaryFa-class

Examples

data("hbk")
hbk.x = hbk[,1:3] 

faCovPcaRegMcd = FaCov(x = hbk.x, factors = 2, method = "pca",
scoresMethod = "regression", cov.control = rrcov::CovControlMcd())

## you can use either object or print(object) or myFaPrint(object)
## since faCovPcaRegMcd is an object of class "Fa"

faCovPcaRegMcd
print(faCovPcaRegMcd)
myFaPrint(faCovPcaRegMcd)

The Stocks Data - Year 2001

Description

This data set consists of 611 observations with 12 variables.

Usage

data(stock611)

Format

A data frame with 611 observations on the following 12 variables.

code

a numeric vector

name

a numeric vector: the Chinese stocks name is replaced by integer, it can be found by its code.

x1

a numeric vector: main business income (China Yuan)

x2

a numeric vector: main business profit (China Yuan)

x3

a numeric vector: total profit (China Yuan)

x4

a numeric vector: net profit (China Yuan)

x5

a numeric vector: earnings per share (EPS) (China Yuan)

x6

a numeric vector: net assets per share (China Yuan)

x7

a numeric vector: net return on assets (%)

x8

a numeric vector: total return on assets (%)

x9

a numeric vector: total assets (China Yuan)

x10

a numeric vector: equity

Details

The data set is from Chinese stock market in the year 2001. It was used in Wang X. M. (2009) to illustrate the factor analysis methods.

Source

Wang X. M. (2009) Applied Multivariate Analysis. Third edition. ShangHai University of Finance & Economics Press. (This is a Chinese book)

Note: In Wang X. M.'s homepage, he provided a link to download materials related to his book (including the data set stock611): http://bb.shufe.edu.cn/bbcswebdav/institution/

Examples

data(stock611)
str(stock611)
plot(stock611)

Summary an Object

Description

Produce result summaries of an object of class "Fa".

Usage

summary(object, ...)

Arguments

Methods

signature(object = "Fa")

Summary an object of class "Fa".

Author(s)

Ying-Ying Zhang (Robert) robertzhangyying@qq.com

References

Zhang, Y. Y. (2013), An Object Oriented Solution for Robust Factor Analysis.

Examples

data("hbk")
hbk.x = hbk[,1:3] 

faCovPcaRegMcd = FaCov(x = hbk.x, factors = 2, method = "pca",
scoresMethod = "regression", cov.control = rrcov::CovControlMcd()); faCovPcaRegMcd

faCovPcaRegMcd
summary(faCovPcaRegMcd)