FA.Biplot: Biplot for Factor Analysis.

In MultBiplotR: Multivariate Analysis Using Biplots in R

Biplot for Factor Analysis.

Description

Biplot used as a graphical representation of Factor Analysis.

Usage

FA.Biplot(X, dimension = 3, Extraction="PC", Rotation="varimax", 
         InitComunal="A1", normalize=FALSE, Scores= "Regression",  
         MethodArgs=NULL, sup.rows = NULL, sup.cols = NULL, ...)

Arguments

X	Data Matrix
dimension	Dimension of the solution
Extraction	Method for the extraction of the factors. Can be "PC", "IPF" or "ML" ("Principal Components", "Iterated Principal Factor" or "Maximum Likelihood")
Rotation	Method for the rotation of the factors. Can be "PC", "IPF" or "ML"
InitComunal	Initial communalities for the iterated principal factor method. Can be "A1", "HSC" or "MC" ("All 1", "Highest Simple Correlation" or "Multiple Correlation")
normalize	Should the loadings be normalized
Scores	Method to calculate the Row Scores. Must be "Regression" or "Bartlett".
MethodArgs	Aditional arguments associated to the rotation method.
sup.rows	Supplementary or illustrative rows, if any.
sup.cols	Supplementary or illustrative rows, if any.
...	Additional arguments for the rotation procedure.

Details

Biplots represent the rows and columns of a data matrix in reduced dimensions. Usually rows represent individuals, objects or samples and columns are variables measured on them. The most classical versions can be thought as visualizations associated to Principal Components Analysis (PCA) or Factor Analysis (FA) obtained from a Singular Value Decomposition or a related method. From another point of view, Classical Biplots could be obtained from regressions and calibrations that are essentially an alternated least squares algorithm equivalent to an EM-algorithm when data are normal This routine Calculates a biplot as a graphical representation of a classical Factor Analysis alowing for different extraction methods and different rotations.

Value

An object of class "ContinuousBiplot" with the following components:

Title	A general title
Non_Scaled_Data	Original Data Matrix
Means	Means of the original Variables
Medians	Medians of the original Variables
Deviations	Standard Deviations of the original Variables
Minima	Minima of the original Variables
Maxima	Maxima of the original Variables
P25	25 Percentile of the original Variables
P75	75 Percentile of the original Variables
Gmean	Global mean of the complete matrix
Sup.Rows	Supplementary rows (Non Transformed)
Sup.Cols	Supplementary columns (Non Transformed)
Scaled_Data	Transformed Data
Scaled_Sup.Rows	Supplementary rows (Transformed)
Scaled_Sup.Cols	Supplementary columns (Transformed)
n	Number of Rows
p	Number of Columns
nrowsSup	Number of Supplementary Rows
ncolsSup	Number of Supplementary Columns
dim	Dimension of the Biplot
EigenValues	Eigenvalues
Inertia	Explained variance (Inertia)
CumInertia	Cumulative Explained variance (Inertia)
EV	EigenVectors
Structure	Correlations of the Principal Components and the Variables
RowCoordinates	Coordinates for the rows, including the supplementary
ColCoordinates	Coordinates for the columns, including the supplementary
RowContributions	Contributions for the rows, including the supplementary
ColContributions	Contributions for the columns, including the supplementary
Scale_Factor	Scale factor for the traditional plot with points and arrows. The row coordinates are multiplied and the column coordinates divided by that scale factor. The look of the plot is better without changing the inner product. For the HJ-Biplot the scale factor is 1.

Author(s)

Jose Luis Vicente Villardon

References

Gabriel, K.R.(1971): The biplot graphic display of matrices with applications to principal component analysis. Biometrika, 58, 453-467.

Gabriel, K. R. AND Zamir, S. (1979). Lower rank approximation of matrices by least squares with any choice of weights. Technometrics, 21(21):489–498, 1979.

Gabriel, K.R.(1998): Generalised Bilinear Regression. Biometrika, 85, 3, 689-700.

Gower y Hand (1996): Biplots. Chapman & Hall.

Vicente-Villardon, J. L., Galindo, M. P. and Blazquez-Zaballos, A. (2006). Logistic Biplots. Multiple Correspondence Analysis and related methods 491-509.

See Also

InitialTransform

Examples

data(Protein)
X=Protein[,3:11]
bip=FA.Biplot(X, Extraction="ML", Rotation="oblimin")
plot(bip, mode="s", margin=0.05, AddArrow=TRUE)

MultBiplotR documentation built on Nov. 21, 2023, 5:08 p.m.