Type:	Package
Title:	Savvy Parity Regression Model Estimation with 'savvyPR'
Version:	0.1.0
Description:	Implements the Savvy Parity Regression 'savvyPR' methodology for multivariate linear regression analysis. The package solves an optimization problem that balances the contribution of each predictor variable to ensure estimation stability in the presence of multicollinearity. It supports two distinct parameterization methods, a Budget-based approach that allocates a fixed loss contribution to each predictor, and a Target-based approach (t-tuning) that utilizes a relative elasticity weight for the response variable. The package provides comprehensive tools for model estimation, risk distribution analysis, and parameter tuning via cross-validation (PR1, PR2, and PR3 model types) to optimize predictive accuracy. Methods are based on Asimit, Chen, Ichim and Millossovich (2026) https://openaccess.city.ac.uk/id/eprint/35005/.
License:	GPL (≥ 3)
URL:	https://ziwei-chenchen.github.io/savvyPR/
BugReports:	https://github.com/ziwei-chenchen/savvyPR/issues
Encoding:	UTF-8
RoxygenNote:	7.3.2
Depends:	R (≥ 3.6.0)
Imports:	glmnet, Matrix, stats, nleqslv, ggplot2, gridExtra
Suggests:	MASS, knitr, rmarkdown, testthat (≥ 3.0.0), covr
VignetteBuilder:	knitr
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-03-12 17:25:43 UTC; lanceyun
Author:	Ziwei Chen [aut, cre], Vali Asimit [aut], Pietro Millossovich [aut]
Maintainer:	Ziwei Chen <Ziwei.Chen.3@citystgeorges.ac.uk>
Repository:	CRAN
Date/Publication:	2026-03-17 19:10:08 UTC

Extract Coefficients From a Cross-Validated Parity Regression Model Object

Description

Extracts the estimated coefficients corresponding to the optimal tuning parameters from a fitted cross-validated parity regression model object. It seamlessly handles models optimized using either the "budget" or "target" parameterization method.

Usage

## S3 method for class 'cv.savvyPR'
coef(object, ...)

Arguments

Details

Extract Coefficients From a Cross-Validated Parity Regression Model Object

This function is an S3 method for the generic coef function. It extracts the coefficients of the optimal model identified during the cross-validation procedure. The extraction is internally delegated to the predict.cv.savvyPR method with type = "coefficients".

Value

A named numeric vector of the estimated coefficients from the optimally tuned model. If the model was fitted with an intercept, it will be included as the first element.

Author(s)

Ziwei Chen, Vali Asimit and Pietro Millossovich
Maintainer: Ziwei Chen <ziwei.chen.3@citystgeorges.ac.uk>

See Also

cv.savvyPR, predict.cv.savvyPR

Examples

# Generate synthetic data
set.seed(123)
x <- matrix(rnorm(100 * 10), 100, 10)
y <- rnorm(100)

# Example 1: Extract coefficients from a Budget-based CV model
cv_model_budget <- cv.savvyPR(x, y, method = "budget", model_type = "PR3")
coef(cv_model_budget)

# Example 2: Extract coefficients from a Target-based CV model
cv_model_target <- cv.savvyPR(x, y, method = "target", model_type = "PR1")
coef(cv_model_target)

Extract Coefficients From a Parity Regression Model Object

Description

Extracts the estimated coefficients from a fitted parity regression model object. It seamlessly handles models fitted using either the "budget" or "target" parameterization method.

Usage

## S3 method for class 'savvyPR'
coef(object, ...)

Arguments

Details

Extract Coefficients From a Parity Regression Model Object

This function is an S3 method for the generic coef function. It extracts the estimated coefficients of the fitted model. The extraction is internally delegated to the predict.savvyPR method with type = "coefficients".

Value

A named numeric vector of the estimated coefficients from the fitted model. If the model was fitted with an intercept, it will be included as the first element.

Author(s)

Ziwei Chen, Vali Asimit and Pietro Millossovich
Maintainer: Ziwei Chen <ziwei.chen.3@citystgeorges.ac.uk>

See Also

savvyPR, predict.savvyPR

Examples

# Generate synthetic data
set.seed(123)
x <- matrix(rnorm(100 * 10), 100, 10)
y <- rnorm(100)

# Example 1: Extract coefficients from a Budget-based model
model_budget <- savvyPR(x, y, method = "budget", val = 0.05)
coef(model_budget)

# Example 2: Extract coefficients from a Target-based model
model_target <- savvyPR(x, y, method = "target", val = 1)
coef(model_target)

Cross-Validation for Parity Regression Model Estimation

Description

Performs k-fold cross-validation for Parity Regression (PR) models to select optimal tuning parameters. The underlying PR methodology distributes the total prediction error evenly across all parameters, ensuring stability in the presence of high multicollinearity and substantial noise (such as time series data with structural changes and evolving trends). This function supports both Budget-based and Target-based parameterizations and evaluates models across a variety of loss metrics.

Usage

cv.savvyPR(
  x,
  y,
  method = c("budget", "target"),
  vals = NULL,
  nval = 100,
  lambda_vals = NULL,
  nlambda = 100,
  folds = 10,
  model_type = c("PR3", "PR1", "PR2"),
  measure_type = c("mse", "mae", "rmse", "mape"),
  foldid = FALSE,
  use_feature_selection = FALSE,
  standardize = FALSE,
  intercept = TRUE,
  exclude = NULL
)

Arguments

Details

Cross-Validation for Parity Regression Model Estimation

This function facilitates cross-validation for parity regression models across a range of tuning values (val) and regularization values (\lambda), depending on the model type specified. Each model type handles the parameters differently:

PR1

Performs cross-validation only over the val sequence while fixing \lambda=0. This model type is primarily used when the focus is on understanding how different levels of risk parity constraints impact the model performance purely based on the parity mechanism without the influence of ridge \lambda shrinkage.

PR2

Uses a fixed \lambda value determined by performing a ridge regression (lambda optimization) using cv.glmnet on the dataset. It then performs cross-validation over the val sequence while using this optimized \lambda value. This approach is useful when one wishes to maintain a stable amount of standard shrinkage while exploring the impact of varying levels of the proportional contribution constraint.

PR3

First, determines an optimal val using the same method as PR1. Then, keeping this val fixed, it conducts a cross-validation over all possible \lambda values. This dual-stage optimization can be particularly effective when the initial parity regularization needs further refinement via \lambda adjustment.

The function supports several types of loss metrics for assessing model performance:

mse

Mean Squared Error: Measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value.

mae

Mean Absolute Error: Measures the average magnitude of the errors in a set of predictions, without considering their direction. It’s the average over the test sample of the absolute differences between prediction and actual observation where all individual differences have equal weight.

rmse

Root Mean Squared Error: It is the square root of the mean of the squared errors. RMSE is a good measure of how accurately the model predicts the response, and it is the most important criterion for fit if the main purpose of the model is prediction.

mape

Mean Absolute Percentage Error: Measures the size of the error in percentage terms. It is calculated as the average of the unsigned percentage error, as shown above. Because it is based on relative errors, it is less sensitive to large deviations in small true values.

The choice of measure impacts how the model's performance is assessed during cross-validation. Users should select the measure that best reflects the requirements of their specific analytical context.

Value

A list of class "cv.savvyPR" containing the following components based on the specified model_type:

Author(s)

Ziwei Chen, Vali Asimit and Pietro Millossovich
Maintainer: Ziwei Chen <ziwei.chen.3@citystgeorges.ac.uk>

References

Asimit, V., Chen, Z., Ichim, B., & Millossovich, P. (2026). Prity Regression Estimation. Retrieved from https://openaccess.city.ac.uk/id/eprint/37017/

The optimization technique employed follows the algorithm described by: F. Spinu (2013). An Algorithm for Computing Risk Parity Weights. SSRN Preprint. doi:10.2139/ssrn.2297383

See Also

savvyPR, glmnet, cv.glmnet, calcLoss, getMeasureName, optimizeRiskParityBudget, optimizeRiskParityTarget

Examples

# Generate synthetic data
set.seed(123)
n <- 100 # Number of observations
p <- 12  # Number of variables
x <- matrix(rnorm(n * p), n, p)
beta <- matrix(rnorm(p), p, 1)
y <- x %*% beta + rnorm(n, sd = 0.5)

# Example 1: PR1 with "budget" method (focusing on c values with MSE)
result_pr1_budget <- cv.savvyPR(x, y, method = "budget", model_type = "PR1")
print(result_pr1_budget)

# Example 2: PR1 with "target" method
result_pr1_target <- cv.savvyPR(x, y, method = "target", model_type = "PR1")
print(result_pr1_target)

# Example 3: PR3 (default model_type) exploring budget parameter
result_pr3 <- cv.savvyPR(x, y, method = "budget", folds = 5)
print(result_pr3)

Plot for a Cross-Validated Parity Regression Model

Description

Generates various visualizations for a fitted cross-validated parity regression model object. It supports plotting estimated coefficients, risk contributions, coefficient paths, and cross-validation error curves based on the specified plot_type.

Usage

## S3 method for class 'cv.savvyPR'
plot(
  x,
  plot_type = c("estimated_coefficients", "risk_contributions", "cv_coefficients",
    "cv_errors"),
  label = TRUE,
  xvar = c("norm", "lambda", "dev", "val"),
  max_vars_per_plot = 10,
  ...
)

Arguments

Details

Plot for a Cross-Validated Parity Regression Model

This function offers four types of plots, depending on the value of plot_type:

Estimated Coefficients

Generates a line plot with points for the estimated coefficients of the optimally tuned cross-validated regression model. If an intercept term is included, it will be labeled as beta_0; otherwise, coefficients are labeled sequentially based on the covariates. If label = TRUE, numeric values are displayed on the plot. This plot helps visualize the contribution of each predictor variable to the model.

Risk Contributions

Generates two bar plots, one for the optimization variables (weights or target values) and one for risk contributions, from the risk parity model. If label = TRUE, numeric labels are added above the bars for clarity.

Coefficient Paths

Generates a plot showing the coefficient paths against the selected x-axis variable (val, lambda, norm, or dev) depending on the model type:

• PR1/PR2: Plots coefficient paths against log(val) values.

• PR3: Plots coefficient paths against log(lambda) values.

Invalid combinations of model_type and xvar will result in an error:

• PR1/PR2: Cannot use "lambda" as xvar.

• PR3: Cannot use "val" as xvar.

If max_vars_per_plot exceeds 10, it is reset to 10. The plot provides insight into how coefficients evolve across different regularization parameters.

Cross-Validation Errors

Generates a plot that shows the cross-validation error metric against the logarithm of the tuning parameter (val or lambda), depending on the model type. It adds a vertical dashed line to indicate the optimal parameter value.

• PR1/PR2: Plots cross-validation errors against log(val) values.

• PR3: Plots cross-validation errors against log(lambda) values.

Value

A ggplot object representing the requested plot.

Author(s)

Ziwei Chen, Vali Asimit and Pietro Millossovich
Maintainer: Ziwei Chen <ziwei.chen.3@citystgeorges.ac.uk>

See Also

cv.savvyPR

Examples

# Example usage for `cv.savvyPR` with Correlated Data:
set.seed(123)
n <- 100
p <- 10
# Create highly correlated predictors to demonstrate parity regression
base_var <- rnorm(n)
x <- matrix(rnorm(n * p, sd = 0.1), n, p) + base_var
beta <- matrix(rnorm(p), p, 1)
y <- x %*% beta + rnorm(n, sd = 0.5)

# Fit CV model using Budget method
cv_result1 <- cv.savvyPR(x, y, method = "budget", model_type = "PR1",
                         measure_type = "mse", intercept = FALSE)
plot(cv_result1, plot_type = "estimated_coefficients")
plot(cv_result1, plot_type = "risk_contributions", label = FALSE)
plot(cv_result1, plot_type = "cv_coefficients", xvar = "val", max_vars_per_plot = 10)
plot(cv_result1, plot_type = "cv_errors")

# Fit CV model using Target method
cv_result2 <- cv.savvyPR(x, y, method = "target", model_type = "PR2")
cv_result3 <- cv.savvyPR(x, y, method = "budget", model_type = "PR3")

plot(cv_result2, plot_type = "cv_coefficients", xvar = "val",
     max_vars_per_plot = 5, label = FALSE)
plot(cv_result3, plot_type = "cv_coefficients", xvar = "lambda",
     max_vars_per_plot = 10, label = TRUE)
plot(cv_result2, plot_type = "cv_errors", label = FALSE)
plot(cv_result3, plot_type = "cv_errors", label = TRUE)

Plot for a Parity Regression Model

Description

Generates various visualizations for a fitted parity regression model object. It supports plotting estimated coefficients and risk contributions based on the specified plot_type.

Usage

## S3 method for class 'savvyPR'
plot(
  x,
  plot_type = c("estimated_coefficients", "risk_contributions"),
  label = TRUE,
  ...
)

Arguments

Details

Plot for a Parity Regression Model

This function offers two types of plots, depending on the value of plot_type:

Estimated Coefficients

Generates a line plot with points for the estimated coefficients of the regression model. If an intercept term is included in the model, it will be labeled as beta_0. Otherwise, the coefficients are labeled sequentially as beta_1, beta_2, etc., based on the covariates. This plot helps to visualize the contribution of each predictor variable to the model. If label = TRUE, numeric values are displayed.

Risk Contributions

If the model includes a risk parity component, the function will check if the optimization results (e.g., orp_fit$weights for the budget method, or orp_fit$x for the target method, along with orp_fit$relativeRiskContrib) are available. If available, two bar plots are created:

• Optimization Variables: A bar plot that visualizes the optimal variables assigned to each covariate and the response variable (weights for budget, target parameters for target).

• Risk Contributions: A bar plot that visualizes the relative risk contributions of each covariate and the response variable.

If label = TRUE, numeric labels are added above the bars for clarity. If they are not found, a warning is issued.

Value

A ggplot object representing the requested plot.

Author(s)

Ziwei Chen, Vali Asimit and Pietro Millossovich
Maintainer: Ziwei Chen <ziwei.chen.3@citystgeorges.ac.uk>

See Also

savvyPR

Examples

# Example usage for `savvyPR` with Correlated Data:
set.seed(123)
n <- 100
p <- 12
# Create highly correlated predictors to demonstrate parity regression
base_var <- rnorm(n)
x <- matrix(rnorm(n * p, sd = 0.1), n, p) + base_var
beta <- matrix(rnorm(p), p, 1)
y <- x %*% beta + rnorm(n, sd = 0.5)

# Fit a Budget-based parity regression model
result_budget <- savvyPR(x, y, method = "budget", val = 0.05, intercept = TRUE)
plot(result_budget, plot_type = "estimated_coefficients", label = FALSE)
plot(result_budget, plot_type = "risk_contributions", label = TRUE)

# Fit a Target-based parity regression model
result_target <- savvyPR(x, y, method = "target", val = 1, intercept = TRUE)
plot(result_target, plot_type = "risk_contributions", label = TRUE)

Predict for Cross-Validated Parity Regression Models

Description

Predicts fitted values or extracts estimated coefficients from a fitted cross-validated parity regression model object. It handles models optimized using either the "budget" or "target" parameterization method seamlessly.

Usage

## S3 method for class 'cv.savvyPR'
predict(object, newx = NULL, type = c("response", "coefficients"), ...)

Arguments

Details

Predict for Cross-Validated Parity Regression Models

This function is an S3 method for the generic predict function. It utilizes the optimal model identified during the cross-validation procedure. For type = "response", it computes predictions based on the provided newx matrix. For type = "coefficients", it extracts the optimal coefficients. The underlying computation is delegated to an internal helper function to ensure consistency across the package.

Value

Depending on the type argument, this function returns:

• "response": A numeric vector of predicted values corresponding to the rows of newx.

• "coefficients": A named numeric vector of the estimated optimal coefficients. If the model was fitted with an intercept, it will be included as the first element.

Author(s)

Ziwei Chen, Vali Asimit and Pietro Millossovich
Maintainer: Ziwei Chen <ziwei.chen.3@citystgeorges.ac.uk>

See Also

cv.savvyPR

Examples

# Generate synthetic data
set.seed(123)
x <- matrix(rnorm(100 * 20), 100, 20)
y <- rnorm(100)

# Example 1: Predict using a cross-validated Budget-based model
cv_fit_budget <- cv.savvyPR(x, y, method = "budget", model_type = "PR3")
predict(cv_fit_budget, newx = x[1:5, ], type = "response")

# Example 2: Predict using a cross-validated Target-based model
cv_fit_target <- cv.savvyPR(x, y, method = "target", model_type = "PR1")
predict(cv_fit_target, newx = x[1:5, ], type = "response")

# Extract optimal coefficients
predict(cv_fit_budget, type = "coefficients")

Predict for Parity Regression Models

Description

Predicts fitted values or extracts estimated coefficients from a fitted parity regression model object. It handles models optimized using either the "budget" or "target" parameterization method seamlessly.

Usage

## S3 method for class 'savvyPR'
predict(object, newx = NULL, type = c("response", "coefficients"), ...)

Arguments

Details

Predict for Parity Regression Models

This function is an S3 method for the generic predict function. It utilizes the parameters estimated during the fitting procedure. For type = "response", it computes predictions based on the provided newx matrix. For type = "coefficients", it extracts the estimated coefficients. The underlying computation is delegated to an internal helper function to ensure consistency across the package.

Value

Depending on the type argument, this function returns:

• "response": A numeric vector of predicted values corresponding to the rows of newx.

• "coefficients": A named numeric vector of the estimated coefficients. If the model was fitted with an intercept, it will be included as the first element.

Author(s)

Ziwei Chen, Vali Asimit and Pietro Millossovich
Maintainer: Ziwei Chen <ziwei.chen.3@citystgeorges.ac.uk>

See Also

savvyPR

Examples

# Generate synthetic data
set.seed(123)
x <- matrix(rnorm(100 * 20), 100, 20)
y <- rnorm(100)

# Example 1: Predict using a Budget-based model
fit_budget <- savvyPR(x, y, method = "budget", val = 0.05)
predict(fit_budget, newx = x[1:5, ], type = "response")

# Example 2: Predict using a Target-based model
fit_target <- savvyPR(x, y, method = "target", val = 1)
predict(fit_target, newx = x[1:5, ], type = "response")

# Extract coefficients
predict(fit_budget, type = "coefficients")

Print a Cross-Validated Parity Regression Model Object

Description

Prints a summarized output of a fitted cross-validated parity regression model object. It clearly displays the optimal tuning parameters and the resulting estimated coefficients.

Usage

## S3 method for class 'cv.savvyPR'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Details

Print a Cross-Validated Parity Regression Model Object

This function is an S3 method for the generic print function. It formats and prints the matched call that produced the cv.savvyPR object, followed by a summary data frame. This summary includes:

• The parameterization method used ("budget" or "target").

• The number of non-zero coefficients.

• Whether an intercept was included.

• The optimal tuning value (val) and/or lambda parameter, depending on the model_type (PR1, PR2, or PR3).

Finally, it prints a data frame of the optimally tuned estimated coefficients.

Value

Invisibly returns a data frame summarizing the cross-validation results, including the parameterization method, number of non-zero coefficients, and optimal tuning parameters.

Author(s)

Ziwei Chen, Vali Asimit and Pietro Millossovich
Maintainer: Ziwei Chen <ziwei.chen.3@citystgeorges.ac.uk>

See Also

cv.savvyPR

Examples

# Generate synthetic data
set.seed(123)
n <- 100
p <- 10
x <- matrix(rnorm(n * p), n, p)
beta <- matrix(rnorm(p), p, 1)
y <- x %*% beta + rnorm(n, sd = 0.5)

# Fit and print a cross-validated budget-based parity regression model
cv_fit_budget <- cv.savvyPR(x, y, method = "budget", model_type = "PR3")
print(cv_fit_budget)

# Fit and print a cross-validated target-based parity regression model
cv_fit_target <- cv.savvyPR(x, y, method = "target", model_type = "PR1")
print(cv_fit_target)

Print a Parity Regression Model Object

Description

Prints a summarized output of a fitted parity regression model object. It clearly displays the model's configuration and the resulting estimated coefficients.

Usage

## S3 method for class 'savvyPR'
print(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

Details

Print a Parity Regression Model Object

This function is an S3 method for the generic print function. It formats and prints the matched call that produced the savvyPR object, followed by a summary data frame. This summary includes:

• The parameterization method used ("budget" or "target").

• The number of non-zero coefficients.

• Whether an intercept was included.

• The penalty value (lambda), if any was applied.

Finally, it prints a data frame of the estimated coefficients.

Value

Invisibly returns a data frame summarizing the model, including the parameterization method, number of non-zero coefficients, intercept status, and lambda value.

Author(s)

Ziwei Chen, Vali Asimit and Pietro Millossovich
Maintainer: Ziwei Chen <ziwei.chen.3@citystgeorges.ac.uk>

See Also

savvyPR

Examples

# Generate synthetic data
set.seed(123)
n <- 100
p <- 10
x <- matrix(rnorm(n * p), n, p)
beta <- matrix(rnorm(p), p, 1)
y <- x %*% beta + rnorm(n, sd = 0.5)

# Fit and print a Budget-based model
fit_budget <- savvyPR(x, y, method = "budget", val = 0.05)
print(fit_budget)

# Fit and print a Target-based model
fit_target <- savvyPR(x, y, method = "target", val = 1)
print(fit_target)

Parity Regression Model Estimation

Description

Implements the Parity Regression (PR) methodology for multiple linear regression. Instead of minimizing the aggregate prediction error in the dependent variable, PR distributes the total prediction error evenly across all parameters. This approach ensures stability in the presence of high multicollinearity and is particularly suitable for data affected by substantial noise, such as time series data experiencing structural changes and evolving trends.

Usage

savvyPR(
  x,
  y,
  method = c("budget", "target"),
  val = NULL,
  lambda_val = NULL,
  use_feature_selection = FALSE,
  standardize = FALSE,
  intercept = TRUE,
  exclude = NULL
)

Arguments

Details

Parity Regression Model Estimation

The PR methodology assigns an equal risk contribution constraint on each predictor variable within a specific search cone, leading to a robust solution. This solution is defined in the context of a penalized regression, wherein the penalty term is a function of both the regularization parameter (lambda_val) and the proportional contribution parameter (val). The function uses the nleqslv package to solve non-linear systems of equations.

The function supports two parameterization methods:

• Budget: Uses val (acting as c) to set a strict budget constraint on the risk contributions.

• Target: Uses val (acting as t) to set a risk target for the response variable relative to the predictors.

The function can handle different practical scenarios:

• While the PR theorem is not specifically designed for variable selection, the package makes this available as an optional preprocessing step. If use_feature_selection is TRUE, Lasso regression is performed to select features by zeroing out non-contributive predictors before applying the PR model.

• It checks the matrix rank of predictors and applies Ridge regression as a fallback to ordinary least squares if the matrix is not full rank, ensuring computational stability.

For the budget method, the PR methodology optimizes an objective function that includes a variance term and a penalization term:

1/2 * RRSS(x, x_{p+1}; \lambda) - \widetilde{\mu} ( c \sum_{k=0}^p \log(\delta_k x_k) + (1 - (p+1)c) \log(x_{p+1}) )

For the target method, the methodology optimizes a related objective function defined by the target parameter t:

1/2 * RRSS(x, x_{p+1}; \lambda) - \widetilde{\mu} ( \sum_{k=0}^p \log(\delta_k x_k) + t \log(x_{p+1}) )

In both formulas, x represents the parameters (with x_{p+1} as an auxiliary parameter set to 1), \lambda is the regularization parameter, p is the number of predictors, and \widetilde{\mu} is a constant with respect to \lambda. The resulting model provides estimates of the regression coefficients that are equitable across all predictors in terms of contribution to the model's predictive power.

Value

Returns an S3 object of class "savvyPR" containing the following components:

Author(s)

Ziwei Chen, Vali Asimit and Pietro Millossovich
Maintainer: Ziwei Chen <ziwei.chen.3@citystgeorges.ac.uk>

References

Asimit, V., Chen, Z., Ichim, B., & Millossovich, P. (2026). Prity Regression Estimation. Retrieved from https://openaccess.city.ac.uk/id/eprint/37017/

The optimization technique employed follows the algorithm described by: F. Spinu (2013). An Algorithm for Computing Risk Parity Weights. SSRN Preprint. doi:10.2139/ssrn.2297383

See Also

cv.savvyPR, glmnet, cv.glmnet

Examples

library(glmnet)
library(nleqslv)

# Generate synthetic data
set.seed(123)
n <- 100 # Number of observations
p <- 10  # Number of variables
x <- matrix(rnorm(n * p), n, p)
beta <- matrix(rnorm(p), p, 1)
y <- x %*% beta + rnorm(n, sd = 0.5) # Linear combination with noise

# Example 1: Run PR estimation using the "budget" method (acting as c)
result_budget <- savvyPR(x, y, method = "budget", val = 0.05, intercept = TRUE)
print(result_budget$coefficients)

# Example 2: Run PR estimation using the "target" method (acting as t)
result_target <- savvyPR(x, y, method = "target", val = 1, intercept = TRUE)
print(result_target$coefficients)

# Example 3: Run PR estimation with feature selection
result_fs <- savvyPR(x, y, method = "budget", val = 0.05, use_feature_selection = TRUE)
print(result_fs$coefficients)

# Inspect the risk parity portfolio object for more details
if(!is.null(result_fs$orp_fit)) {
  print("Risk parity portfolio details:")
  print(result_fs$orp_fit)
}

# Example 4: Run PR estimation excluding some predictors
result_exclude <- savvyPR(x, y, method = "budget", val = 0.05, exclude = c(1, 2))
print("Coefficients with first two predictors excluded:")
print(result_exclude$coefficients)

Summary of Cross-Validated Parity Regression Model

Description

Prints a comprehensive statistical summary of a fitted cross-validated parity regression model object. It displays the model's configuration, statistical summaries of the estimated coefficients, model fit statistics, and cross-validation results.

Usage

## S3 method for class 'cv.savvyPR'
summary(object, ...)

Arguments

Details

Summary of a Fitted Cross-Validated Parity Regression Model with Statistics

This function is an S3 method for the generic summary function. It formats and prints a detailed statistical overview of the optimal cross-validated model. The output includes:

• The parameterization method used ("budget" or "target").

• The matched call that produced the model.

• Residual quantiles.

• A table of estimated optimal coefficients with their corresponding standard errors, t-values, p-values, confidence intervals, and significance codes.

• Overall model fit statistics, including Residual Standard Error, Multiple and Adjusted R-squared, F-statistic, AIC, BIC, and Deviance.

• A Cross-Validation Summary displaying the minimum mean cross-validation error and the optimal tuning values (val and/or lambda).

Value

Invisibly returns NULL. This function is primarily called for its side effect of printing the summary to the console.

Author(s)

Ziwei Chen, Vali Asimit and Pietro Millossovich
Maintainer: Ziwei Chen <ziwei.chen.3@citystgeorges.ac.uk>

See Also

cv.savvyPR

Examples

# Simulate some data
set.seed(123)
n <- 100
p <- 10
x <- matrix(rnorm(n * p), n, p)
beta <- matrix(rnorm(p), p, 1)
y <- x %*% beta + rnorm(n, sd = 0.5)

# Example 1: Fit and summarize a budget-based cross-validated model
cv_fit_budget <- cv.savvyPR(x, y, method = "budget", model_type = "PR3")
summary(cv_fit_budget)

# Example 2: Fit and summarize a target-based cross-validated model
cv_fit_target <- cv.savvyPR(x, y, method = "target", model_type = "PR1")
summary(cv_fit_target)

Summary of Parity Regression Model

Description

Prints a comprehensive statistical summary of a fitted parity regression model object. It displays the model's configuration, statistical summaries of the estimated coefficients, and overall model fit statistics.

Usage

## S3 method for class 'savvyPR'
summary(object, ...)

Arguments

Details

Summary of a Fitted Parity Regression Model with Statistics

This function is an S3 method for the generic summary function. It formats and prints a detailed statistical overview of the fitted model. The output includes:

• The parameterization method used ("budget" or "target").

• The matched call that produced the model.

• Residual quantiles.

• A table of estimated coefficients with their corresponding standard errors, t-values, p-values, confidence intervals, and significance codes.

• Overall model fit statistics, including Residual Standard Error, Multiple and Adjusted R-squared, F-statistic, AIC, BIC, and Deviance.

Value

Invisibly returns NULL. This function is primarily called for its side effect of printing the summary to the console.

Author(s)

Ziwei Chen, Vali Asimit and Pietro Millossovich
Maintainer: Ziwei Chen <ziwei.chen.3@citystgeorges.ac.uk>

See Also

savvyPR

Examples

# Simulate some data
set.seed(123)
n <- 100
p <- 10
x <- matrix(rnorm(n * p), n, p)
beta <- matrix(rnorm(p), p, 1)
y <- x %*% beta + rnorm(n, sd = 0.5)

# Example 1: Fit and summarize a Budget-based parity regression model
fit_budget <- savvyPR(x, y, method = "budget", val = 0.05, intercept = FALSE)
summary(fit_budget)

# Example 2: Fit and summarize a Target-based parity regression model
fit_target <- savvyPR(x, y, method = "target", val = 1, intercept = TRUE)
summary(fit_target)