Package 'robustfa' reference manual

Title:	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: 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.
Authors:	Frederic Bertrand [cre] , Ying-Ying Zhang (Robert) [aut]
Maintainer:	Frederic Bertrand <[email protected]>
License:	GPL (>= 2)
Version:	1.1-0
Built:	2025-03-07 03:03:43 UTC
Source:	https://github.com/cran/robustfa

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

Package:	robustfa
Type:	Package
Version:	1.0-5
Date:	2013-11-09
License:	GPL (>= 2)
Depends:	methods

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

Author(s)

Ying-Ying Zhang (Robert)

Maintainer: Ying-Ying Zhang (Robert) <[email protected]>

References

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

Examples

library("robustfa")

library("robustfa")

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)
compute_cov_cor(x, control)

Arguments

x

A numeric matrix or an object that can be coerced to a numeric matrix.

control

A control object (S4) for one of the available control classes, e.g. CovControlMcd-class, CovControlOgk-class, CovControlSest-class, etc., containing estimation options. The class of this object defines which estimator will be used. Alternatively a character string can be specified which names the estimator - one of auto, sde, mcd, ogk, m, mve, sfast, surreal, bisquare, rocke. If "auto" is specified or the argument is missing, the function will select the estimator.

Value

A list with the following components:

`S_r`	The robust covariance matrix of cov_x.
`S_r_tilda`	The robust covariance matrix of cov_scale_x.
`R_r`	The robust correlation matrix of cov_x.
`R_r_tilda`	The robust correlation matrix of cov_scale_x.

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

Author(s)

Ying-Ying Zhang (Robert) [email protected]

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")

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

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

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

Arguments

`out`	The result of factorScorePca(), factorScorePfa(), or factanal(). It is a list.
`x`	A numeric matrix.
`covmat`	A list with components: cov, center, and n.obs.
`cor`	A logical value indicating whether the calculation should use the covariance matrix (`cor = FALSE`) or the correlation matrix (`cor = TRUE`).
`scoresMethod`	Type of scores to produce, if any. The default is `"none"`, `"regression"` gives Thompson's scores, `"Bartlett"` gives Bartlett's weighted least-squares scores.

Value

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

`scoringCoef`	The scoring coefficients.
`scores`	The matrix of scores.
`meanF`	The sample mean of the scores.
`corF`	The sample correlation matrix of the scores.
`eigenvalues`	The eigenvalues of the running matrix.
`covariance`	The covariance matrix.
`correlation`	The correlation matrix.
`usedMatrix`	The used matrix (running matrix) to compute `scoringCoef` etc..
`reducedCorrelation`	NULL. The reduced correlation matrix, reducedCorrelation is calculated in factorScorePfa.R.

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

Author(s)

Ying-Ying Zhang (Robert) [email protected]

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 = [email protected])

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

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

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

Show Details of an Object

Description

Show details of an object.

Usage

detail(x)
detail(x)

Arguments

`x`	Any `R` object to be tested.

Value

A list with components:

`x`	The argument `x`.
`isS4`	Logical, indicates whether `x` is an S4 object.
`isObject`	Logical, indicates whether `x` is an object, i.e., with a class attribute.
`class`	The class of `x`.
`attributes`	The attributes of `x`. Usually `result$attributes` is also a list.

Author(s)

Ying-Ying Zhang (Robert) [email protected]

References

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

Examples

data(stock611)
detail(stock611)

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

data(stock611)
detail(stock611)

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

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) [email protected]

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.

Examples

showClass("Fa")
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"), ...)
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

`x`	A formula or a numeric matrix or an object that can be coerced to a numeric matrix.
`...`	Arguments passed to or from other methods.
`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`.
`factors`	The number of factors to be fitted.
`cor`	A logical value indicating whether the calculation should use the covariance matrix (`cor = FALSE`) or the correlation matrix (`cor = TRUE`).
`method`	The method of factor analysis, one of "mle" (the default), "pca", and "pfa".
`scoresMethod`	Type of scores to produce, if any. The default is `"none"`, `"regression"` gives Thompson's scores, `"Bartlett"` gives Bartlett's weighted least-squares scores.

Value

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

Author(s)

Ying-Ying Zhang (Robert) [email protected]

References

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

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)

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) [email protected]

References

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

Examples

showClass("FaClassic")
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"), ...)
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

`x`	A formula or a numeric matrix or an object that can be coerced to a numeric matrix.
`...`	Arguments passed to or from other methods.
`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`.
`factors`	The number of factors to be fitted.
`cor`	A logical value indicating whether the calculation should use the covariance matrix (`cor = FALSE`) or the correlation matrix (`cor = TRUE`).
`method`	The method of factor analysis, one of "mle" (the default), "pca", and "pfa".
`scoresMethod`	Type of scores to produce, if any. The default is `"none"`, `"regression"` gives Thompson's scores, `"Bartlett"` gives Bartlett's weighted least-squares scores.
`cov.control`	Specifies which covariance estimator to use by providing a `CovControl-class` object. The default is `CovControlMcd-class` which will indirectly call `CovMcd`. If `cov.control=NULL` is specified, the classical estimates will be used by calling `CovClassic`.

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) [email protected]

References

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

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

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) [email protected]

References

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

Examples

showClass("FaCov")
showClass("FaCov")

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

Arguments

`x`	A numeric matrix or an object that can be coerced to a numeric matrix.
`factors`	The number of factors to be fitted.
`covmat`	A covariance matrix, or a covariance list as returned by `cov.wt`. Of course, correlation matrices are covariance matrices.
`cor`	A logical value indicating whether the calculation should use the covariance matrix (`cor = FALSE`) or the correlation matrix (`cor = TRUE`).
`rotation`	character. "none" or "varimax": it will be called with first argument the loadings matrix, and should return a list with component `loadings` giving the rotated loadings, or just the rotated loadings.
`scoresMethod`	Type of scores to produce, if any. The default is `"none"`, `"regression"` gives Thompson's scores, `"Bartlett"` gives Bartlett's weighted least-squares scores.

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:

`call`	The matched call.
`loadings`	A matrix of loadings, one column for each factor. This is of class `"loadings"` if `rotation = "varimax"`: see `loadings` for its print method; It is a plain matrix if `rotation = "none"`.
`communality`	The common variance.
`uniquenesses`	The uniquenesses/specific variance computed.
`covariance`	The robust/classical covariance matrix.
`correlation`	The robust/classical correlation matrix.
`usedMatrix`	The used matrix (running matrix). It may be the covariance or correlation matrix according to the value of `cor`.
`reducedCorrelation`	NULL. The reduced correlation matrix, reducedCorrelation is calculated in factorScorePfa.R.
`factors`	The argument factors.
`method`	The method: always `"pca"`.
`scores`	If requested, a matrix of scores. NULL if `x` is missing.
`scoringCoef`	The scoring coefficients. NULL if `x` is missing.
`meanF`	The sample mean of the scores. NULL if `x` is missing.
`corF`	The sample correlation matrix of the scores. NULL if `x` is missing.
`scoresMethod`	The argument `scoresMethod`.
`n.obs`	The number of observations if available. NULL if `x` is missing.
`center`	The center of the data.
`eigenvalues`	The eigenvalues of the usedMatrix.

Author(s)

Ying-Ying Zhang (Robert) [email protected]

References

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

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), [email protected])
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

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

Arguments

`x`	A numeric matrix or an object that can be coerced to a numeric matrix.
`factors`	The number of factors to be fitted.
`covmat`	A covariance matrix, or a covariance list as returned by `cov.wt`. Of course, correlation matrices are covariance matrices.
`cor`	A logical value indicating whether the calculation should use the covariance matrix (`cor = FALSE`) or the correlation matrix (`cor = TRUE`).
`rotation`	character. "none" or "varimax": it will be called with first argument the loadings matrix, and should return a list with component `loadings` giving the rotated loadings, or just the rotated loadings.
`scoresMethod`	Type of scores to produce, if any. The default is `"none"`, `"regression"` gives Thompson's scores, `"Bartlett"` gives Bartlett's weighted least-squares scores.

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:

`call`	The matched call.
`loadings`	A matrix of loadings, one column for each factor. This is of class `"loadings"` if `rotation = "varimax"`: see `loadings` for its print method; It is a plain matrix if `rotation = "none"`.
`communality`	The common variance.
`uniquenesses`	The uniquenesses/specific variance computed.
`covariance`	The robust/classical covariance matrix.
`correlation`	The robust/classical correlation matrix.
`usedMatrix`	The used matrix (running matrix). It may be the covariance or correlation matrix according to the value of `cor`.
`reducedCorrelation`	The last reduced correlation matrix.
`factors`	The argument factors.
`method`	The method: always `"pfa"`.
`scores`	If requested, a matrix of scores. NULL if `x` is missing.
`scoringCoef`	The scoring coefficients. NULL if `x` is missing.
`meanF`	The sample mean of the scores. NULL if `x` is missing.
`corF`	The sample correlation matrix of the scores. NULL if `x` is missing.
`scoresMethod`	The argument `scoresMethod`.
`n.obs`	The number of observations if available. NULL if `x` is missing.
`center`	The center of the data.
`eigenvalues`	The eigenvalues of the usedMatrix.

Author(s)

Ying-Ying Zhang (Robert) [email protected]

References

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

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 = [email protected])
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

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

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) [email protected]

References

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

Examples

showClass("FaRobust")
showClass("FaRobust")

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)
fsOrder(factorScores)

Arguments

factorScores

The original factor scores.

Value

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

`[[1]]`	The ordered factor scores with a decreasing first column.
`[[2]]`	The ordered factor scores with a decreasing second column.
`...`
`[[m]]`	The ordered factor scores with a decreasing m-th column.

Author(s)

Ying-Ying Zhang (Robert) [email protected]

References

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

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

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)
myFaPrint(object, print.x=FALSE)

Arguments

`object`	an object of class `"Fa"` or of a class derived from `"Fa"`.
`print.x`	Logical. If `print.x = TRUE`, then print the rotated variables (scores).

Value

An invisible argument object.

Author(s)

Ying-Ying Zhang (Robert) [email protected]

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())

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

faCovPcaRegMcd
print(faCovPcaRegMcd)
myFaPrint(faCovPcaRegMcd)

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)
myplotDD(x, cutoff, id.n)

Arguments

`x`	An S4 object of class `"CovRobust"`.
`cutoff`	The `cutoff` value used. If missing, `cutoff <- sqrt(qchisq(0.975, p))` by default.
`id.n`	Number of observations to identify by a label. If not supplied, the number of observations with robust distance larger than `cutoff` is used.

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:

`cutoff`	The `cutoff` value used. If missing, `cutoff <- sqrt(qchisq(0.975, p))` by default.
`id.n`	Number of observations to identify by a label. If not supplied, the number of observations with robust distance larger than `cutoff` is used.
`sort.y`	A list containing the sorted values of y (the robust distance)
`ind`	The indices of the largest `id.n` observations whose robust distances are larger than `cutoff`.

Author(s)

Ying-Ying Zhang (Robert) [email protected]

References

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

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")

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

Arguments

`x`	an object of class `"Fa"` or of a class derived from `"Fa"`
`which`	indicate what kind of plot. 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.
`choices`	an integer vector indicate which columns of the factor scores to plot

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) [email protected]

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")

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, ...)
predict(object, ...)

Arguments

`object`	an object of class `"Fa"` or of a class derived from `"Fa"`
`...`	additional arguments, e.g., newdata: an optional data frame or matrix in which to look for variables with which to predict. If newdata is not missing, newdata should be scaled before `"predict"`.

Methods

signature(object = "Fa"): generic functions - see print, summary, predict, plot, getCenter, getEigenvalues, getFa, getLoadings, getQuan, getScores, getSdev

Author(s)

Ying-Ying Zhang (Robert) [email protected]

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

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, ...)
print(x, ...)

Arguments

`x`	an object of class `"Fa"` or `"SummaryFa"` or of a class derived from `"Fa"` or of class or `"SummaryFa"`.
`...`	additional arguments, e.g., print.x=TRUE

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) [email protected]

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())

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

faCovPcaRegMcd
print(faCovPcaRegMcd)
myFaPrint(faCovPcaRegMcd)

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

Summary an Object

Description

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

Usage

summary(object, ...)
summary(object, ...)

Arguments

`object`	an object of class `"Fa"` or of a class derived from `"Fa"`.
`...`	additional arguments, e.g., print.x=TRUE.

Methods

signature(object = "Fa"): Summary an object of class "Fa".

Author(s)

Ying-Ying Zhang (Robert) [email protected]

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)

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)

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) [email protected]

References

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

Examples

showClass("SummaryFa")
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) [email protected]

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) [email protected]

References

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

Package 'robustfa'

Help Index

An Object Oriented Solution for Robust Factor Analysis

Description

Details

Author(s)

References

Examples

Compute the Robust Covariance and Correlation Matrix of A Numeric Matrix

Description

Usage

Arguments

Value

Author(s)

References

Examples

Compute Factor Scores

Description

Usage

Arguments

Value

Author(s)

References

Examples

Show Details of an Object

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Class "Fa"

Description

Objects from the Class

Slots

Methods

Author(s)

References

See Also

Examples

Classical Factor Analysis

Description

Usage

Arguments

Value

Author(s)

References

See Also

Examples

Class "FaClassic"

Description

Objects from the Class

Slots

Extends

Methods

Author(s)

References

See Also

Examples

Robust Factor Analysis

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Class "FaCov"

Description

Objects from the Class

Slots

Extends

Methods

Author(s)

References

See Also

Class `"Fa"`

Class `"FaClassic"`

Class `"FaCov"`

Class `"FaRobust"`