Generate a Summary Table for ANOVA Results

Description

This function creates a summary table for ANOVA results, including degrees of freedom, sum of squares, mean squares, F-values, and p-values. The table can be output as either LaTeX (for PDF reports) or plain text (for console viewing).

Usage

ANOVA.summary.table(model, caption, latex = TRUE)

Arguments

Value

If 'latex = TRUE', a LaTeX-formatted table object. If 'latex = FALSE', prints the summary table and returns it (invisibly).

Examples

# Fit a linear model
model <- lm(mpg ~ wt + hp, data = mtcars)

# Generate a plain-text ANOVA summary table
ANOVA.summary.table(model, caption = "ANOVA Summary", latex = FALSE)

Partial Least Squares Regression via NIPALS (Internal)

Description

This function is called internally by pls.regression and is not intended to be used directly. Use pls.regression(..., calc.method = "NIPALS") instead.

Performs Partial Least Squares (PLS) regression using the NIPALS (Nonlinear Iterative Partial Least Squares) algorithm. This method estimates the latent components (scores, loadings, weights) by iteratively updating the X and Y score directions until convergence. It is suitable for cases where the number of predictors is large or predictors are highly collinear.

Usage

NIPALS.pls(x, y, n.components = NULL)

Arguments

Details

The algorithm standardizes both x and y using z-score normalization. It then performs the following for each of the n.components latent variables:

1. Initializes a random response score vector u.

2. Iteratively:

   • Updates the X weight vector w = E^\top u, normalized.

   • Computes the X score t = E w, normalized.

   • Updates the Y loading q = F^\top t, normalized.

   • Updates the response score u = F q.

   • Repeats until t converges below a tolerance threshold.

3. Computes scalar regression coefficient b = t^\top u.

4. Deflates residual matrices E and F to remove current component contribution.

After component extraction, the final regression coefficient matrix B_{original} is computed and rescaled to the original data units. Explained variance is also computed component-wise and cumulatively.

Value

A list with the following elements:

model.type

Character string indicating the model type ("PLS Regression").

T

Matrix of X scores (n × H).

U

Matrix of Y scores (n × H).

W

Matrix of X weights (p × H).

C

Matrix of normalized Y weights (q × H).

P_loadings

Matrix of X loadings (p × H).

Q_loadings

Matrix of Y loadings (q × H).

B_vector

Vector of regression scalars (length H), one for each component.

coefficients

Matrix of regression coefficients in original data scale (p × q).

intercept

Vector of intercepts (length q). Always zero here due to centering.

X_explained

Percent of total X variance explained by each component.

Y_explained

Percent of total Y variance explained by each component.

X_cum_explained

Cumulative X variance explained.

Y_cum_explained

Cumulative Y variance explained.

References

Wold, H., & Lyttkens, E. (1969). Nonlinear iterative partial least squares (NIPALS) estimation procedures. Bulletin of the International Statistical Institute, 43, 29–51.

Examples

## Not run: 
X <- matrix(rnorm(100 * 10), 100, 10)
Y <- matrix(rnorm(100 * 2), 100, 2)
model <- pls.regression(X, Y, n.components = 3, calc.method = "NIPALS")
model$coefficients

## End(Not run)

Partial Least Squares Regression via SVD (Internal)

Description

This function is called internally by pls.regression and is not intended to be used directly. Use pls.regression(..., calc.method = "SVD") instead.

Performs Partial Least Squares (PLS) regression using the Singular Value Decomposition (SVD) of the cross-covariance matrix. This method estimates the latent components by identifying directions in the predictor and response spaces that maximize their covariance, using the leading singular vectors of the matrix R = X^\top Y.

Usage

SVD.pls(x, y, n.components = NULL)

Arguments

Details

The algorithm begins by z-scoring both x and y (centering and scaling to unit variance). The initial residual matrices are set to the scaled values: E = X_scaled, F = Y_scaled.

For each component h = 1, ..., H:

1. Compute the cross-covariance matrix R = E^\top F.

2. Perform SVD on R = U D V^\top.

3. Extract the first singular vectors: w = U[,1], q = V[,1].

4. Compute scores: t = E w (normalized), u = F q.

5. Compute loadings: p = E^\top t, regression scalar b = t^\top u.

6. Deflate residuals: E \gets E - t p^\top, F \gets F - b t q^\top.

After all components are extracted, a post-processing step removes components with zero regression weight. The scaled regression coefficients are computed using the Moore–Penrose pseudoinverse of the loading matrix P, and then rescaled to the original variable units.

Value

A list containing:

model.type

Character string indicating the model type ("PLS Regression").

T

Matrix of predictor scores (n × H).

U

Matrix of response scores (n × H).

W

Matrix of predictor weights (p × H).

C

Matrix of normalized response weights (q × H).

P_loadings

Matrix of predictor loadings (p × H).

Q_loadings

Matrix of response loadings (q × H).

B_vector

Vector of scalar regression weights (length H).

coefficients

Matrix of final regression coefficients in the original scale (p × q).

intercept

Vector of intercepts (length q). All zeros due to centering.

X_explained

Percent of total X variance explained by each component.

Y_explained

Percent of total Y variance explained by each component.

X_cum_explained

Cumulative X variance explained.

Y_cum_explained

Cumulative Y variance explained.

References

Abdi, H., & Williams, L. J. (2013). Partial least squares methods: Partial least squares correlation and partial least square regression. Methods in Molecular Biology (Clifton, N.J.), 930, 549–579. doi:10.1007/978-1-62703-059-5_23

de Jong, S. (1993). SIMPLS: An alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18(3), 251–263. doi:10.1016/0169-7439(93)85002-X

Examples

## Not run: 
X <- matrix(rnorm(100 * 10), 100, 10)
Y <- matrix(rnorm(100 * 2), 100, 2)
model <- pls.regression(X, Y, n.components = 3, calc.method = "SVD")
model$coefficients

## End(Not run)

Display a Color Reference Palette

Description

This function generates a plot displaying a predefined color palette with color codes for easy reference. The palette includes shades of Red, Orange, Yellow, Green, Blue, Purple, and Grey.

Usage

color.ref()

Details

Value

A plot displaying the color palette.

Examples

color.ref()

SnazzieR Color Palette

Description

A collection of named hex colors grouped by hue and tone. Each color is available as an exported object (e.g., Red, Dark.Red).

Usage

color.list

Format

Each color is a character string representing a hex code.

An object of class character of length 1.

An object of class list of length 35.

Details

Name	Hex	Swatch		Name	Hex	Swatch
Deep.Red	#590D21			Deep.Green	#304011
Dark.Red	#9F193D			Dark.Green	#54711E
Red	#C31E4A			Green	#83B02F
Light.Red	#E66084			Light.Green	#ABD45E
Pale.Red	#F1A7BB			Pale.Green	#C4E18E
Deep.Orange	#6F4B0B			Deep.Blue	#002429
Dark.Orange	#A77011			Dark.Blue	#004852
Orange	#E99F1F			Blue	#008C9E
Light.Orange	#F0BF6A			Light.Blue	#1FE5FF
Pale.Orange	#F4CF90			Pale.Blue	#85F1FF
Deep.Yellow	#9D7F06			Deep.Purple	#271041
Dark.Yellow	#CEA708			Dark.Purple	#4E2183
Yellow	#E8D206			Purple	#743496
Light.Yellow	#FFE373			Light.Purple	#A06CDA
Pale.Yellow	#FFF8DC			Pale.Purple	#CAADEB
Deep.Grey	#151315
Dark.Grey	#403A3F
Grey	#6F646C
Light.Grey	#9E949B
Pale.Grey	#CFC9CD

See Also

color.ref, snazzieR.theme

Create K-Fold Cross Validation Splits

Description

Create K-Fold Cross Validation Splits

Usage

create_kfold_splits(data, k = 5, seed = NULL)

Arguments

Value

A list containing fold assignments for each observation

Compute Cross-Validated Mean Squared Error

Description

Computes mean squared error via k-fold cross-validation for a fixed lambda value.

Usage

cv.mse(x, y, lambda, folds = 5, fold_indices = NULL)

Arguments

Value

A numeric scalar representing the CV-MSE

Summarize Eigenvalues and Eigenvectors of a Covariance Matrix

Description

This function computes the eigenvalues and eigenvectors of a given covariance matrix, ensures sign consistency in the eigenvectors, and outputs either a LaTeX table or plaintext summary displaying the results.

Usage

eigen.summary(
  cov.matrix,
  caption = "Eigenvectors of Covariance Matrix",
  latex = TRUE
)

Arguments

Value

A LaTeX formatted table (if latex = TRUE) or plaintext console output (if latex = FALSE).

Examples

cov_matrix <- matrix(c(4, 2, 2, 3), nrow = 2)
eigen.summary(cov_matrix, caption = "Eigenvalues and Eigenvectors", latex = FALSE)

Fit Ridge Regression with Closed-Form Solution

Description

Computes ridge regression coefficients and standard errors using the closed-form solution: \hat{\beta} = (X^T X + \lambda I)^{-1} X^T y

Usage

fit.ridge(x, y, lambda)

Arguments

Value

A list containing:

coefficients

Ridge regression coefficients (length p)

std_errors

Standard errors of the coefficients (length p)

Format PLS Model Output as LaTeX or Console Tables

Description

Formats and displays Partial Least Squares (PLS) model output from pls.regression() as either LaTeX tables (for PDF rendering) or console-friendly output.

Usage

## S3 method for class 'pls'
format(x, ..., include.scores = TRUE, latex = FALSE)

Arguments

Value

When latex = TRUE, returns a knitr::asis_output object (LaTeX code). When FALSE, prints formatted tables to console.

Perform K-Fold Cross Validation

Description

Perform K-Fold Cross Validation

Usage

kfold_cross_validation(
  data,
  formula,
  model_function,
  predict_function = predict,
  metric_function = NULL,
  k = 5,
  seed = NULL,
  ...
)

Arguments

Value

A list containing fold results and summary statistics

Generate a Model Equation from a Linear Model

Description

This function extracts and formats the equation from a linear model object. It includes an option to return the equation as a LaTeX-formatted string or print it to the console.

Usage

model.equation(model, latex = TRUE)

Arguments

Value

If 'latex' is TRUE, the equation is returned as LaTeX code using 'knitr::asis_output()'. If FALSE, the equation is printed to the console.

Examples

# Fit a linear model
model <- lm(mpg ~ wt + hp, data = mtcars)

# Get LaTeX equation
model.equation(model)

# Print equation to console
model.equation(model, latex = FALSE)

Generate a Summary Table for a Linear Model

Description

This function creates a summary table for a linear model, including estimated coefficients, standard errors, p-values with significance codes, and model statistics such as MSE and R-squared. The table can be output as either LaTeX (for PDF reports) or plain text (for console viewing).

Usage

model.summary.table(model, caption, latex = TRUE)

Arguments

Value

If 'latex = TRUE', returns a LaTeX-formatted 'kableExtra' table object. If 'latex = FALSE', prints formatted summary tables to the console and returns the underlying data frame.

Examples

# Fit a linear model
model <- lm(mpg ~ wt + hp, data = mtcars)

# Print a plain-text version to the console
model.summary.table(model, caption = "Linear Model Summary", latex = FALSE)

Optimize Lambda Using Cross-Validation

Description

Searches the lambda range to minimize CV-MSE using Brent's method via 'optimize()'.

Usage

optimize.cv.lambda(x, y, lambda.range, folds)

Arguments

Value

A list containing:

minimum

Optimal lambda value

objective

Minimum CV-MSE achieved

trace

Data frame with lambda and CV-MSE pairs

Partial Least Squares (PLS) Regression Interface

Description

Performs Partial Least Squares (PLS) regression using either the NIPALS or SVD algorithm for component extraction. This is the main user-facing function for computing PLS models. Internally, it delegates to either NIPALS.pls() or SVD.pls().

Usage

pls.regression(x, y, n.components = NULL, calc.method = c("SVD", "NIPALS"))

Arguments

Details

This function provides a unified interface for Partial Least Squares regression. Based on the value of calc.method, it computes latent variables using either:

• "SVD" — A direct method using the singular value decomposition of the cross-covariance matrix (X^\top Y).

• "NIPALS" — An iterative method that alternately estimates predictor and response scores until convergence.

The outputs from both methods include scores, weights, loadings, regression coefficients, and explained variance.

Value

A list (from either SVD.pls() or NIPALS.pls()) containing:

model.type

Character string ("PLS Regression").

T, U

Score matrices for X and Y.

W, C

Weight matrices for X and Y.

P_loadings, Q_loadings

Loading matrices.

B_vector

Component-wise regression weights.

coefficients

Final regression coefficient matrix (rescaled).

intercept

Intercept vector (typically zero due to centering).

X_explained, Y_explained

Variance explained by each component.

X_cum_explained, Y_cum_explained

Cumulative variance explained.

References

Abdi, H., & Williams, L. J. (2013). Partial least squares methods: Partial least squares correlation and partial least square regression. Methods in Molecular Biology (Clifton, N.J.), 930, 549–579. doi:10.1007/978-1-62703-059-5_23

de Jong, S. (1993). SIMPLS: An alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18(3), 251–263. doi:10.1016/0169-7439(93)85002-X

See Also

SVD.pls, NIPALS.pls

Examples

## Not run: 
X <- matrix(rnorm(100 * 10), 100, 10)
Y <- matrix(rnorm(100 * 2), 100, 2)

# Using SVD (default)
model1 <- pls.regression(X, Y, n.components = 3)

# Using NIPALS
model2 <- pls.regression(X, Y, n.components = 3, calc.method = "NIPALS")

## End(Not run)

Format PLS Model Output as LaTeX Tables

Description

Formats and displays Partial Least Squares (PLS) model output from pls.regression() as LaTeX tables for PDF rendering.

Usage

pls.summary(x, ..., include.scores = TRUE)

Arguments

Value

Returns a knitr::asis_output object (LaTeX code) for PDF rendering.

Examples

# Load example data
data(mtcars)

# Prepare data for PLS regression
X <- mtcars[, c("wt", "hp", "disp")]
Y <- mtcars[, "mpg", drop = FALSE]

# Fit PLS model with 2 components
pls.fit <- pls.regression(X, Y, n.components = 2)

# Print a LaTeX-formatted summary
pls.summary(pls.fit, include.scores = FALSE)

Predict Method for Ridge Model Objects

Description

Predicts response values for new data using a fitted ridge model.

Usage

## S3 method for class 'ridge.model'
predict(object, newdata = NULL, ...)

Arguments

Value

A numeric vector of predicted values

Print Method for Ridge Model Objects

Description

Prints a summary of the ridge model fit.

Usage

## S3 method for class 'ridge.model'
print(x, ...)

Arguments

Ridge Regression with Automatic Lambda Selection

Description

Performs ridge regression with automatic selection of the optimal regularization parameter 'lambda' by minimizing k-fold cross-validated mean squared error (CV-MSE) using Brent's method. Supports both formula and matrix interfaces.

Usage

ridge.regression(
  formula = NULL,
  data = NULL,
  x = NULL,
  y = NULL,
  lambda.range = c(1e-04, 100),
  folds = 5,
  ...
)

Arguments

Details

This function implements ridge regression with automatic hyperparameter tuning. The algorithm:

• Standardizes predictor variables (centers and scales)

• Centers the response variable

• Uses k-fold cross-validation to find the optimal lambda

• Fits the final model with the optimal lambda

• Returns a structured object for prediction and analysis

The ridge regression solution is computed using the closed-form formula: \hat{\beta} = (X^T X + \lambda I)^{-1} X^T y

Value

A 'ridge.model' object containing:

coefficients

Final ridge coefficients (no intercept)

std_errors

Standard errors of the coefficients

intercept

Intercept term (from y centering)

optimal.lambda

Best lambda minimizing CV-MSE

cv.ms

Minimum CV-MSE achieved

cv.results

Data frame with lambda and CV-MSE pairs

x.scale

Standardization info: mean and sd for each predictor

y.center

Centering constant for y

fitted.values

Final model predictions on training data

residuals

Training residuals (y - fitted)

call

Matched call (for debugging)

method

Always "ridge"

folds

Number of CV folds used

formula

Stored if formula interface used

terms

Stored if formula interface used

References

Hoerl, A. E., & Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67.

See Also

predict.ridge.model

Examples

## Not run: 
# Formula interface
model1 <- ridge.regression(mpg ~ wt + hp + disp, data = mtcars)

# Matrix interface
X <- as.matrix(mtcars[, c("wt", "hp", "disp")])
y <- mtcars$mpg
model2 <- ridge.regression(x = X, y = y)

# Custom lambda range and folds
model3 <- ridge.regression(mpg ~ .,
    data = mtcars,
    lambda.range = c(0.1, 10), folds = 10
)

## End(Not run)

Format Ridge Model Output as LaTeX Tables

Description

Formats and displays ridge regression model output from ridge.regression() as LaTeX tables for PDF rendering or plain text for console viewing.

Usage

ridge.summary(x, ..., include.cv.trace = TRUE, latex = TRUE)

Arguments

Value

If latex = TRUE, returns a knitr::asis_output object (LaTeX code) for PDF rendering. If latex = FALSE, prints formatted summary tables to the console and returns the underlying data frames.

Examples

# Load example data
data(mtcars)

# Fit ridge regression model
ridge.fit <- ridge.regression(mpg ~ wt + hp + disp, data = mtcars)

# Print a LaTeX-formatted summary
ridge.summary(ridge.fit, include.cv.trace = FALSE)

# Print a plain-text summary
ridge.summary(ridge.fit, include.cv.trace = FALSE, latex = FALSE)

A Custom ggplot2 Theme for Publication-Ready Plots

Description

This theme provides a clean, polished look for ggplot2 plots, with a focus on readability and aesthetics. It includes a custom color palette and formatting for titles, axes, and legends.

Usage

snazzieR.theme()

Value

A ggplot2 theme object.

See Also

color.list, color.ref

Examples

library(ggplot2)
set.seed(123)
chains.df <- data.frame(
  Iteration = 1:500,
  alpha.1 = cumsum(rnorm(500, mean = 0.01, sd = 0.2)) + rnorm(1, 5, 0.2),
  alpha.2 = cumsum(rnorm(500, mean = 0.005, sd = 0.2)) + rnorm(1, 5, 0.2),
  alpha.3 = cumsum(rnorm(500, mean = 0.000, sd = 0.2)) + rnorm(1, 5, 0.2),
  alpha.4 = cumsum(rnorm(500, mean = -0.005, sd = 0.2)) + rnorm(1, 5, 0.2),
  alpha.5 = cumsum(rnorm(500, mean = -0.01, sd = 0.2)) + rnorm(1, 5, 0.2)
)
chain.colors <- c("Chain 1" = Red, "Chain 2" = Orange, "Chain 3" = Yellow,
                  "Chain 4" = Green, "Chain 5" = Blue)
ggplot(chains.df, aes(x = Iteration)) +
  geom_line(aes(y = alpha.1, color = "Chain 1"), linewidth = 1.2) +
  geom_line(aes(y = alpha.2, color = "Chain 2"), linewidth = 1.2) +
  geom_line(aes(y = alpha.3, color = "Chain 3"), linewidth = 1.2) +
  geom_line(aes(y = alpha.4, color = "Chain 4"), linewidth = 1.2) +
  geom_line(aes(y = alpha.5, color = "Chain 5"), linewidth = 1.2) +
  labs(x = "Iteration", y = expression(alpha),
       title = expression("Traceplot for " ~ alpha)) +
  scale_color_manual(values = chain.colors, name = "Chains") +
  snazzieR.theme()