Package {rplam}

Multiple R-squared

Description

This function returns the multiple R-squared.

Usage

R2(object, ...)

Arguments

Value

A multiple R-squared value.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Robust multiple R-squared

Description

This function returns the multiple R-squared.

Usage

R2.rob(object, ...)

Arguments

Value

A robust multiple R-squared value.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Classical estimator for additive models

Description

This function computes the least-squares based estimator for additive models based on B-splines.

Usage

am.cl(y, X, np.point = NULL, nknots = NULL, degree.spline = 3)

Arguments

Value

A list with the following components:

Author(s)

Alejandra Mercedes Martínez, ale_m_martinez@hotmail.com

References

Boente G. and Martínez A. (2023). A robust spline approach in partially linear additive models. Computational Statistics and Data Analysis, 178, 107611.

Examples

set.seed(11)
n <- 100
x1 <- runif(n,-1,1)
x2 <- runif(n,-1,1)
err <- rnorm(n, 0, 0.1)
regre <- 2+x1^3+2*sin(pi*x2)
y <- regre + err
X <- cbind(x1,x2)
sal <- am.cl(y, X)

Robust estimator for additive models

Description

This function computes a robust estimator for additive models based on B-splines.

Usage

am.rob(y, X, np.point = NULL, nknots = NULL, degree.spline = 3, maxit = 100)

Arguments

Value

A list with the following components:

Author(s)

Alejandra Mercedes Martínez, ale_m_martinez@hotmail.com

References

Boente G. and Martínez A. (2023). A robust spline approach in partially linear additive models. Computational Statistics and Data Analysis, 178, 107611.

Examples

set.seed(11)
n <- 100
x1 <- runif(n,-1,1)
x2 <- runif(n,-1,1)
err <- rnorm(n, 0, 0.1)
regre <- 2+x1^3+2*sin(pi*x2)
y <- regre + err
X <- cbind(x1,x2)
sal <- am.rob(y, X)

Deviance for objects of class am

Description

This function returns the deviance of the fitted additive model as computed with am.cl or am.rob.

Usage

## S3 method for class 'am'
deviance(object, ...)

Arguments

Value

A real number.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Deviance for objects of class plam

Description

This function returns the deviance of the fitted partially linear additive model as computed with plam.cl or plam.rob.

Usage

## S3 method for class 'plam'
deviance(object, ...)

Arguments

Value

A real number.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Fitted values for objects of class am

Description

This function returns the fitted values given the covariates of the original sample under an additive model using a classical or robust estimator computed with am.cl or am.rob.

Usage

fitted.values.am(object, ...)

Arguments

Value

A vector of fitted values.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Fitted values for objects of class plam

Description

This function returns the fitted values given the covariates of the original sample under a partially linear additive model using a classical or robust estimator computed with plam.cl or plam.rob.

Usage

fitted.values.plam(object, ...)

Arguments

Value

A vector of fitted values.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Partially linear additive model formula

Description

Description of the partially linear additive model formula extracted from an object of class plam.

Usage

## S3 method for class 'plam'
formula(x, ...)

Arguments

Value

A model formula.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Euclidean norm of a vector

Description

This function calculates the Euclidean norm of a vector.

Usage

my.norm.2(x)

Arguments

Value

The Euclidean norm of the input vector.

Author(s)

Alejandra Mercedes Martínez, ale_m_martinez@hotmail.com

Examples

x <- seq(-2, 2, length=10)
my.norm.2(x)

Classical estimator for partially linear additive models

Description

This function computes the least-squares based estimator for partially linear additive models.

Usage

plam.cl(formula, np.point = NULL, nknots = NULL, degree.spline = 3)

Arguments

Value

A list with the following components:

Author(s)

Alejandra Mercedes Martínez, ale_m_martinez@hotmail.com

References

Boente G. and Martínez A. (2023). A robust spline approach in partially linear additive models. Computational Statistics and Data Analysis, 178, 107611.

Examples

set.seed(11)
n <- 100
z1 <- rnorm(n)
z2 <- rbinom(n, 4, 1/2)
x1 <- runif(n,-1,1)
x2 <- runif(n,-1,1)
err <- rnorm(n, 0, 0.1)
regre <- 2+3*z1-4*z2+x1^3+2*sin(pi*x2)
y <- regre + err
Z <- cbind(z1,z2)
X <- cbind(x1,x2)
sal <- plam.cl(y ~ Z + a(X))

Robust estimator for partially linear additive models

Description

This function computes a robust estimator for partially linear additive models using the Tukey's loss function.

Usage

plam.rob(
  formula,
  np.point = NULL,
  nknots = NULL,
  degree.spline = 3,
  maxit = 100
)

Arguments

Value

A list with the following components:

Author(s)

Alejandra Mercedes Martínez, ale_m_martinez@hotmail.com

References

Boente G. and Martínez A. (2023). A robust spline approach in partially linear additive models. Computational Statistics and Data Analysis, 178, 107611.

Examples

set.seed(11)
n <- 100
z1 <- rnorm(n)
z2 <- rbinom(n, 4, 1/2)
x1 <- runif(n,-1,1)
x2 <- runif(n,-1,1)
err <- rnorm(n, 0, 0.1)
regre <- 2+3*z1-4*z2+x1^3+2*sin(pi*x2)
y <- regre + err
Z <- cbind(z1,z2)
X <- cbind(x1,x2)
sal <- plam.rob(y ~ Z + a(X))

Diagnostic plots for objects of class am

Description

Plot method for class am.

Usage

## S3 method for class 'am'
plot(x, which = 1:p, ask = FALSE, ...)

Arguments

Value

No return value. This function is called for its side effect of producing partial residual plots for the selected explanatory variables.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Examples

set.seed(11)
n <- 100
x1 <- runif(n,-1,1)
x2 <- runif(n,-1,1)
err <- rnorm(n, 0, 0.1)
regre <- 2+x1^3+2*sin(pi*x2)
y <- regre + err
X <- cbind(x1,x2)
fit.rob <- am.rob(y, X)
plot(fit.rob)

Diagnostic plots for objects of class plam

Description

Plot method for class plam.

Usage

## S3 method for class 'plam'
plot(x, which = 1:(q + p), ask = FALSE, ...)

Arguments

Value

No return value. This function is called for its side effect of producing partial residual plots for the selected explanatory variables.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Examples

set.seed(11)
n <- 100
z1 <- rnorm(n)
z2 <- rbinom(n, 4, 1/2)
x1 <- runif(n,-1,1)
x2 <- runif(n,-1,1)
err <- rnorm(n, 0, 0.1)
regre <- 2+3*z1-4*z2+x1^3+2*sin(pi*x2)
y <- regre + err
Z <- cbind(z1,z2)
X <- cbind(x1,x2)
fit.rob <- plam.rob(y ~ Z + a(X))
plot(fit.rob, which=3)

Fitted values for objects of class am

Description

This function returns the fitted values given the covariates of the original sample under an additive model using a classical or robust estimator computed with am.cl or am.rob.

Usage

## S3 method for class 'am'
predict(object, ...)

Arguments

Value

A vector of fitted values.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Fitted values for objects of class plam

Description

This function returns the fitted values given the covariates of the original sample under a partially linear additive model using a classical or robust estimator computed with plam.cl or plam.rob.

Usage

## S3 method for class 'plam'
predict(object, ...)

Arguments

Value

A vector of fitted values.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Print a Partially Linear Additive Model

Description

The default print method for a plam object.

Usage

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

Arguments

Value

The function prints the model formula and returns x invisibly.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Derivative of Tukey's bi-square loss function.

Description

This function evaluates the first derivative of Tukey's bi-square loss function.

Usage

psi.tukey(r, k = 4.685)

Arguments

Details

This function evaluates the first derivative of Tukey's bi-square loss function.

Value

A vector of the same length as x.

Author(s)

Matias Salibian-Barrera, matias@stat.ubc.ca, Alejandra Martínez

Examples

x <- seq(-2, 2, length=10)
psi.tukey(r=x, k = 1.5)

Derivative of the Tukey's loss function

Description

This function calculates the derivative of the Tukey's loss function.

Usage

psi.tukey.derivative(x, k = 4.685)

Arguments

Value

A vector of the same length as x which corresponds to the derivatives of the Tukey's loss function.

Author(s)

Alejandra Mercedes Martínez, ale_m_martinez@hotmail.com

Examples

x <- seq(-2, 2, length=10)
psi.tukey.derivative(x)

Tukey's weight function

Description

This function calculates the Tukey's weight function of the form "Psi(r)/r".

Usage

psi.w(r, k = 4.685)

Arguments

Value

A vector of the same length as r which corresponds to the Tukey's weight function.

Author(s)

Alejandra Mercedes Martínez, ale_m_martinez@hotmail.com

Examples

r <- seq(-2, 2, length=10)
psi.w(r)

Residuals for objects of class am

Description

This function returns the residuals of the fitted additive model using the classical or robust estimators, as computed with am.cl or am.rob.

Usage

## S3 method for class 'am'
residuals(object, ...)

Arguments

Value

A vector of residuals.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Residuals for objects of class plam

Description

This function returns the residuals of the fitted partly linear additive model using the classical or robust estimators, as computed with plam.cl or plam.rob.

Usage

## S3 method for class 'plam'
residuals(object, ...)

Arguments

Value

A vector of residuals.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Selection of the number of internal knots for the least-squares estimator under a PLAM

Description

This function automatically selects the number of internal knots for the B-spline approximation. It uses the BIC criterion with the quadratic function.

Usage

select.nknots.cl(y, Z, X, degree.spline = 3)

Arguments

Value

A list with the following components:

Author(s)

Alejandra Mercedes Martínez, ale_m_martinez@hotmail.com

References

Boente G. and Martínez A. (2023). A robust spline approach in partially linear additive models. Computational Statistics and Data Analysis, 178, 107611.

Examples

set.seed(11)
n <- 100
z1 <- rnorm(n)
z2 <- rbinom(n, 4, 1/2)
x1 <- runif(n,-1,1)
x2 <- runif(n,-1,1)
err <- rnorm(n, 0, 0.1)
regre <- 2+3*z1-4*z2+x1^3+2*sin(pi*x2)
y <- regre + err
Z <- cbind(z1,z2)
X <- cbind(x1,x2)
sal <- select.nknots.cl(y, Z, X)

Selection of the number of internal knots for the least-squares estimator for additive models

Description

This function automatically selects the number of internal knots for the B-spline approximation. It uses the BIC criterion with the quadratic function.

Usage

select.nknots.cl.am(y, X, degree.spline = 3)

Arguments

Value

A list with the following components:

Author(s)

Alejandra Mercedes Martínez, ale_m_martinez@hotmail.com

References

Boente G. and Martínez A. (2023). A robust spline approach in partially linear additive models. Computational Statistics and Data Analysis, 178, 107611.

Examples

set.seed(11)
n <- 100
x1 <- runif(n,-1,1)
x2 <- runif(n,-1,1)
err <- rnorm(n, 0, 0.1)
regre <- 2+x1^3+2*sin(pi*x2)
y <- regre + err
X <- cbind(x1,x2)
sal <- select.nknots.cl.am(y, X)

Selection of the number of knots for the robust estimator under a PLAM

Description

This function automatically selects the number of internal knots for the B-spline approximation. It uses the BIC criterion with the Tukey's loss function.

Usage

select.nknots.rob(y, Z, X, degree.spline = 3, maxit = 100)

Arguments

Value

A list with the following components:

Author(s)

Alejandra Mercedes Martínez, ale_m_martinez@hotmail.com

References

Boente G. and Martínez A. (2023). A robust spline approach in partially linear additive models. Computational Statistics and Data Analysis, 178, 107611.

Examples

set.seed(11)
n <- 100
z1 <- rnorm(n)
z2 <- rbinom(n, 4, 1/2)
x1 <- runif(n,-1,1)
x2 <- runif(n,-1,1)
err <- rnorm(n, 0, 0.1)
regre <- 2+3*z1-4*z2+x1^3+2*sin(pi*x2)
y <- regre + err
Z <- cbind(z1,z2)
X <- cbind(x1,x2)
sal <- select.nknots.rob(y, Z, X)

Selection of the number of knots for the robust estimator for additive models

Description

This function automatically selects the number of internal knots for the B-spline approximation. It uses the BIC criterion with the Tukey's loss function.

Usage

select.nknots.rob.am(y, X, degree.spline = 3, maxit = 100)

Arguments

Value

A list with the following components:

Author(s)

Alejandra Mercedes Martínez, ale_m_martinez@hotmail.com

References

Boente G. and Martínez A. (2023). A robust spline approach in partially linear additive models. Computational Statistics and Data Analysis, 178, 107611.

Examples

set.seed(11)
n <- 100
x1 <- runif(n,-1,1)
x2 <- runif(n,-1,1)
err <- rnorm(n, 0, 0.1)
regre <- 2+x1^3+2*sin(pi*x2)
y <- regre + err
X <- cbind(x1,x2)
sal <- select.nknots.rob.am(y, X)

Summary for additive models fits

Description

Summary method for class am.

Usage

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

Arguments

Details

This function returns the estimation of the intercept and also the five-number summary and the mean of the residuals for both classical and robust estimators. For the robust estimator it also returns the estimate of the residual standard error.

Value

An object containing the summary of the residuals, as returned by summary. The function also displays the estimated intercept and the coefficient of determination. For robust estimation, it additionally displays the estimated residual standard error.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Summary for partially linear additive models fits

Description

Summary method for class plam.

Usage

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

Arguments

Details

This function returns the estimation of the intercept, the linear regression coefficients and also the five-number summary and the mean of the residuals for both classical and robust estimators. For the robust estimator it also returns the estimate of the residual standard error.

Value

An object containing the summary of the residuals, as returned by summary. The function also displays the estimated intercept, the linear regression coefficients, and the coefficient of determination. For robust estimation, it additionally displays the estimated residual standard error.

Author(s)

Alejandra Mercedes Martínez ale_m_martinez@hotmail.com

Tukey's loss function

Description

This function computes the Tukey's loss function.

Usage

tukey.loss(x, k = 4.685)

Arguments

Value

A vector of the same length as x which corresponds to values obtained by the Tukey's loss function.

Author(s)

Alejandra Mercedes Martínez, ale_m_martinez@hotmail.com

Examples

x <- seq(-2, 2, length=10)
tukey.loss(x)