Biplot used as a graphical representation of Factor Analysis.
FA.Biplot(X, dimension = 3, Extraction="PC", Rotation="varimax",
InitComunal="A1", normalize=FALSE, Scores= "Regression",
MethodArgs=NULL, sup.rows = NULL, sup.cols = NULL, ...)An object of class "ContinuousBiplot" with the following components:
A general title
Original Data Matrix
Means of the original Variables
Medians of the original Variables
Standard Deviations of the original Variables
Minima of the original Variables
Maxima of the original Variables
25 Percentile of the original Variables
75 Percentile of the original Variables
Global mean of the complete matrix
Supplementary rows (Non Transformed)
Supplementary columns (Non Transformed)
Transformed Data
Supplementary rows (Transformed)
Supplementary columns (Transformed)
Number of Rows
Number of Columns
Number of Supplementary Rows
Number of Supplementary Columns
Dimension of the Biplot
Eigenvalues
Explained variance (Inertia)
Cumulative Explained variance (Inertia)
EigenVectors
Correlations of the Principal Components and the Variables
Coordinates for the rows, including the supplementary
Coordinates for the columns, including the supplementary
Contributions for the rows, including the supplementary
Contributions for the columns, including the supplementary
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.
Data Matrix
Dimension of the solution
Method for the extraction of the factors. Can be "PC", "IPF" or "ML" ("Principal Components", "Iterated Principal Factor" or "Maximum Likelihood")
Method for the rotation of the factors. Can be "PC", "IPF" or "ML"
Initial communalities for the iterated principal factor method. Can be "A1", "HSC" or "MC" ("All 1", "Highest Simple Correlation" or "Multiple Correlation")
Should the loadings be normalized
Method to calculate the Row Scores. Must be "Regression" or "Bartlett".
Aditional arguments associated to the rotation method.
Supplementary or illustrative rows, if any.
Supplementary or illustrative rows, if any.
Additional arguments for the rotation procedure.
Jose Luis Vicente Villardon
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.
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.
InitialTransform
data(Protein)
X=Protein[,3:11]
bip=FA.Biplot(X, Extraction="ML", Rotation="oblimin")
plot(bip, mode="s", margin=0.05, AddArrow=TRUE)
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