Package 'rrr'

All Pairs Plots

Description

All Pairs Plots

Usage

allpairs_plot(x, y, type = "pca", rank, k = 0)

Arguments

x	data frame or matrix of predictor variables
y	data frame or matrix of response variables
type	type of reduced-rank regression model to fit. type = "identity", the default, uses $\mathbf{\Gamma} = \mathbf{I}$ to fit a reduced-rank regression. type = "pca" fits a principal component analysis model as a special case of reduced-rank regression. type = "cva" fits a canonical variate analysis model as a special case of reduced-rank regression. type = "lda" fits a linear discriminant analysis model as a special case of reduced-rank regression.
rank	rank of coefficient matrix.
k	small constant added to diagonal of covariance matrices to make inversion easier.

Value

scatterplot matrix.

Examples

data(pendigits)
digits_features <- pendigits[, -35:-36]
digits_class <- pendigits[,35]
allpairs_plot(digits_features, digits_class, type = "pca", rank = 3)

---

MMST COMBO17 DATA

Description

COMBO-17 galaxy photometric catalogue, 216, 219, 235

Usage

COMBO17

Format

A data frame with 3462 observations on 65 numeric variables.

References

A. Izenman (2008). Modern Multivariate Statistical Techniques. Springer.

Wolf, C. Meisenheimer, M., Kleinheinrich, M., Borch, A., Dye, S., Gray, M., Wisotski, L., Bell, E.F., Rix, H., W. Cimatti, A., Hasinger, G., and Szokoly, G. (2004). A catalogue of the Chandra Deep Field South with multi-colour classification and photometric redshifts from COMBO-17, Astronomy & Astrophysics. https://arxiv.org/pdf/astro-ph/0403666.pdf

---

Pairwise Plots

Description

Pairwise Plots

Usage

pairwise_plot(x, y, type = "pca", pair_x = 1, pair_y = 2, rank = "full",
  k = 0, interactive = FALSE, point_size = 2.5)

Arguments

x	data frame or matrix of predictor variables
y	data frame or matrix of response variables
type	type of reduced-rank regression model to fit. type = "identity", the default, uses $\mathbf{\Gamma} = \mathbf{I}$ to fit a reduced-rank regression. type = "pca" fits a principal component analysis model as a special case of reduced-rank regression. type = "cva" fits a canonical variate analysis model as a special case of reduced-rank regression. type = "lda" fits a linear discriminant analysis model as a special case of reduced-rank regression.
pair_x	variable to be plotted on the $X$-axis
pair_y	variable to be plotted on the $Y$-axis
rank	rank of coefficient matrix.
k	small constant added to diagonal of covariance matrices to make inversion easier.
interactive	logical. If interactive = FALSE, the default, plots a static pairwise plot. If interactive = FALSE plots an interactive pairwise plot.
point_size	size of points in scatter plot.

Value

ggplot2 object if interactive = FALSE; plotly object if interactive = TRUE.

References

Izenman, A.J. (2008) Modern Multivariate Statistical Techniques. Springer.

Examples

data(pendigits)
digits_features <- pendigits[,1:34]
digits_class <- pendigits[,35]
pairwise_plot(digits_features, digits_class, type = "pca", pair_x = 1, pair_y = 3)

library(dplyr)
data(COMBO17)
galaxy <- as_data_frame(COMBO17)
galaxy <- select(galaxy, -starts_with("e."), -Nr, -UFS:-IFD)
galaxy <- na.omit(galaxy)
galaxy_x <- select(galaxy, -Rmag:-chi2red)
galaxy_y <- select(galaxy, Rmag:chi2red)
pairwise_plot(galaxy_x, galaxy_y, type = "cva")

data(iris)
iris_x <- iris[,1:4]
iris_y <- iris[5]
pairwise_plot(iris_x, iris_y, type = "lda")

---

MMST PENDIGITS DATA

Description

pen-based handwritten digit recognition, 211, 234, 274, 348, 391, 631

Usage

pendigits

Format

a data frame with 10992 observations on 36 unnamed variables

Source

http://archive.ics.uci.edu/ml/datasets.html

References

A. Izenman (2008) Modern Multivariate Statistical Techniques. Springer.

---

Rank Trace Plot

Description

rank_trace is a plot used to determine the effective dimensionality, i.e., $t = \mathrm{rank}\left(\mathbf{C}\right)$, of the reduced-rank regression equation.

Usage

rank_trace(x, y, type = "identity", k = 0, plot = TRUE,
  interactive = FALSE)

Arguments

x	data frame or matrix of predictor variables
y	data frame or matrix of response variables
type	type of reduced-rank regression model to fit. type = "identity", the default, uses $\mathbf{\Gamma} = \mathbf{I}$ to fit a reduced-rank regression. type = "pca" fits a principal component analysis model as a special case of reduced-rank regression. type = "cva" fits a canonical variate analysis model as a special case of reduced-rank regression. type = "lda" fits a linear discriminant analysis model as a special case of reduced-rank regression.
k	small constant added to diagonal of covariance matrices to make inversion easier.
plot	if FALSE, returns data frame of rank trace coordinates.
interactive	if TRUE, creates an interactive plotly graphic.

Value

plot of rank trace coordinates if plot = TRUE, the default, or data frame of rank trace coordinates if plot = FALSE.

References

Izenman, A.J. (2008) Modern Multivariate Statistical Techniques. Springer.

Examples

data(tobacco)
tobacco_x <- tobacco[,4:9]
tobacco_y <- tobacco[,1:3]
gamma <- diag(1, dim(tobacco_y)[2])
rank_trace(tobacco_x, tobacco_y)
rank_trace(tobacco_x, tobacco_y, plot = FALSE)
rank_trace(tobacco_x, tobacco_y, type = "cva")

data(pendigits)
digits_features <- pendigits[, -35:-36]
rank_trace(digits_features, digits_features, type = "pca")

library(dplyr)
data(COMBO17)
galaxy <- as_data_frame(COMBO17)
galaxy <- select(galaxy, -starts_with("e."), -Nr, -UFS:-IFD)
galaxy <- na.omit(galaxy)
galaxy_x <- select(galaxy, -Rmag:-chi2red)
galaxy_y <- select(galaxy, Rmag:chi2red)
rank_trace(galaxy_x, galaxy_y, type = "cva")

---

Reduced-Rank Regression Residuals

Description

residuals calculates the regression residuals for reduced-rank regression and canonical variate analysis.

Usage

residuals(x, y, type = "identity", rank = "full", k = 0, plot = TRUE)

Arguments

x	data frame or matrix of predictor variables
y	data frame or matrix of response variables
type	type of reduced-rank regression model to fit. type = "identity", the default, uses $\mathbf{\Gamma} = \mathbf{I}$ to fit a reduced-rank regression. type = "pca" fits a principal component analysis model as a special case of reduced-rank regression. type = "cva" fits a canonical variate analysis model as a special case of reduced-rank regression. type = "lda" fits a linear discriminant analysis model as a special case of reduced-rank regression.
rank	rank of coefficient matrix.
k	small constant added to diagonal of covariance matrices to make inversion easier.
plot	if FALSE, returns data frame of rank trace coordinates.

Value

scatterplot matrix of residuals if plot = TRUE, the default, or a data frame of residuals if plot = FALSE.

References

Izenman, A.J. (2008) Modern Multivariate Statistical Techniques. Springer.

Examples

data(tobacco)
tobacco_x <- tobacco[,4:9]
tobacco_y <- tobacco[,1:3]
tobacco_rrr <- rrr(tobacco_x, tobacco_y, rank = 1)
residuals(tobacco_x, tobacco_y, rank = 1, plot = FALSE)
residuals(tobacco_x, tobacco_y, rank = 1)

library(dplyr)
data(COMBO17)
galaxy <- as_data_frame(COMBO17)
galaxy <- select(galaxy, -starts_with("e."), -Nr, -UFS:-IFD)
galaxy <- na.omit(galaxy)
galaxy_x <- select(galaxy, -Rmag:-chi2red)
galaxy_y <- select(galaxy, Rmag:chi2red)
residuals(galaxy_x, galaxy_y, type = "cva", rank = 2, k = 0.001)

---

Fit Reduced-Rank Regression Model

Description

rrr fits a reduced-rank regression model.

Usage

rrr(x, y, type = "identity", rank = "full", k = 0)

Arguments

x	data frame or matrix of predictor variables
y	data frame or matrix of response variables
type	type of reduced-rank regression model to fit. type = "identity", the default, uses $\mathbf{\Gamma} = \mathbf{I}$ to fit a reduced-rank regression. type = "pca" fits a principal component analysis model as a special case of reduced-rank regression. type = "cva" fits a canonical variate analysis model as a special case of reduced-rank regression. type = "lda" fits a linear discriminant analysis model as a special case of reduced-rank regression.
rank	rank of coefficient matrix.
k	small constant added to diagonal of covariance matrices to make inversion easier.

Value

list containing estimates of coefficients and means, and eigenvalue-based diagnostics.

References

Izenman, A.J. (2008) Modern Multivariate Statistical Techniques. Springer.

Examples

data(tobacco)
tobacco_x <- tobacco[,4:9]
tobacco_y <- tobacco[,1:3]
rrr(tobacco_x, tobacco_y, rank = 1)

data(pendigits)
digits_features <- pendigits[, -35:-36]
rrr(digits_features, digits_features, type = "pca", rank = 3)

library(dplyr)
data(COMBO17)
galaxy <- as_data_frame(COMBO17)
galaxy <- select(galaxy, -starts_with("e."), -Nr, -UFS:-IFD)
galaxy <- na.omit(galaxy)
galaxy_x <- select(galaxy, -Rmag:-chi2red)
galaxy_y <- select(galaxy, Rmag:chi2red)
rrr(galaxy_x, galaxy_y, type = "cva", rank = 2)

data(iris)
iris_x <- iris[,1:4]
iris_y <- iris[5]
rrr(iris_x, iris_y, type = "lda")

---

Compute Latent Variable Scores

Description

Compute Latent Variable Scores

Usage

scores(x, y, type = "pca", rank = "full", k = 0)

Arguments

x	data frame or matrix of predictor variables
y	data frame or matrix of response variables
type	type of reduced-rank regression model to fit. type = "identity", the default, uses $\mathbf{\Gamma} = \mathbf{I}$ to fit a reduced-rank regression. type = "pca" fits a principal component analysis model as a special case of reduced-rank regression. type = "cva" fits a canonical variate analysis model as a special case of reduced-rank regression. type = "lda" fits a linear discriminant analysis model as a special case of reduced-rank regression.
rank	rank of coefficient matrix.
k	small constant added to diagonal of covariance matrices to make inversion easier.

References

Izenman, A.J. (2008) Modern Multivariate Statistical Techniques. Springer.

Examples

data(pendigits)
digits_features <- pendigits[, -35:-36]
scores(digits_features, digits_features, type = "pca", rank = 3)

library(dplyr)
data(COMBO17)
galaxy <- as_data_frame(COMBO17)
galaxy <- select(galaxy, -starts_with("e."), -Nr, -UFS:-IFD)
galaxy <- na.omit(galaxy)
galaxy_x <- select(galaxy, -Rmag:-chi2red)
galaxy_y <- select(galaxy, Rmag:chi2red)
scores(galaxy_x, galaxy_y, type = "cva", rank = 4)

data(iris)
iris_x <- iris[,1:4]
iris_y <- iris[5]
scores(iris_x, iris_y, type = "lda")

---

3-D Reduced Rank Regression Plots

Description

Create three-dimensional, interactive plotly graphics for exploration and diagnostics.

Usage

threewise_plot(x, y, type = "pca", pair_x = 1, pair_y = 2, pair_z = 3,
  rank = "full", k = 0, point_size = 2.5)

Arguments

x	data frame or matrix of predictor variables
y	data frame or matrix of response variables
type	type of reduced-rank regression model to fit. type = "identity", the default, uses $\mathbf{\Gamma} = \mathbf{I}$ to fit a reduced-rank regression. type = "pca" fits a principal component analysis model as a special case of reduced-rank regression. type = "cva" fits a canonical variate analysis model as a special case of reduced-rank regression. type = "lda" fits a linear discriminant analysis model as a special case of reduced-rank regression.
pair_x	variable to be plotted on the $X$-axis
pair_y	variable to be plotted on the $Y$-axis
pair_z	variable to be plotted on the $Z$-axis
rank	rank of coefficient matrix.
k	small constant added to diagonal of covariance matrices to make inversion easier.
point_size	size of points in scatter plot.

Value

three-dimensional plot. If type = "pca" returns three principal components scores - defaulted to the first three - against each other. If type = "cva" returns three-dimensional plot of residuals. If type = "lda" returns three-dimensional plot of three linear discriminant scores plotted against each other.

Examples

## Not run: 
data(pendigits)
digits_features <- pendigits[, -35:-36]
threewise_plot(digits_features, digits_class, type = "pca", k = 0.0001)

library(dplyr)
data(COMBO17)
galaxy <- as_data_frame(COMBO17)
galaxy <- select(galaxy, -starts_with("e."), -Nr, -UFS:-IFD)
galaxy <- na.omit(galaxy)
galaxy_x <- select(galaxy, -Rmag:-chi2red)
galaxy_y <- select(galaxy, Rmag:chi2red)
threewise_plot(galaxy_x, galaxy_y, type = "cva")

data(iris)
iris_x <- iris[,1:4]
iris_y <- iris[5]
threewise_plot(iris_x, iris_y, type = "lda")

## End(Not run)

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MMST TOBACCO DATA

Description

chemical composition of tobacco, 183, 187

Usage

tobacco

Format

a data frame with 25 observations on the following 9 variables.

• ‘Y1.BurnRate’ a numeric vector

• ‘Y2.PercentSugar’ a numeric vector

• ‘Y3.PercentNicotine’ a numeric vector

• ‘X1.PercentNitrogen’ a numeric vector

• ‘X2.PercentChlorine’ a numeric vector

• ‘X3.PercentPotassium’ a numeric vector

• ‘X4.PercentPhosphorus’ a numeric vector

• ‘X5.PercentCalcium’ a numeric vector

• ‘X6.PercentMagnesium’ a numeric vector

References

A. Izenman (2008). Modern Multivariate Statistical Techniques. Springer.

Anderson, R.L. and Bancroft, T.A. (1952). Statistical Theory in Research. New York: Mcgraw-Hill.

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