Package 'dwmmlRidge'

DWMML3 Ridge Regression Estimator

Description

Full regression results using the DWMML3 Ridge Regression Estimator

Usage

dwmmlR.reg(x, y)

Arguments

x	A numeric vector or matrix of predictor variables.
y	A numeric vector or matrix of response values.

Value

A list containing 'esttabledataframe', 'stdtabledataframe', and additional model diagnostics.

See Also

Weightedridge.reg for the underlying weighted ridge regression implementation, ridgereg_k for the ridge parameter selection method used internally by Styperidge.reg.

Examples

if (requireNamespace("mctest", quietly = TRUE)) {
  data(Hald, package = "mctest")
  x <- Hald[, -1]
  y <- Hald[, 1]
  fit <- dwmmlR.reg(x, y)
  fit$esttabledataframe
}

if (requireNamespace("isdals", quietly = TRUE)) {
  data(bodyfat, package = "isdals")
  x <- bodyfat[, -1]
  y <- bodyfat[, 1]
  fit <- dwmmlR.reg(x, y)
  fit$esttabledataframe
}

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Weighted least squares regression

Description

Fits a weighted least squares (WLS) regression model with an intercept term. Weights can be supplied as a vector, a single-column data frame, or a square weight matrix. If a vector or data frame is supplied, it is internally converted to a diagonal weight matrix. In the example below, the weight vector W is generated from a Uniform(0, 1) distribution purely to illustrate how to call the function. In practice, users should provide weights that reflect the structure of their data (e.g., from variance estimates or a robust weighting scheme).

Usage

Weightedls.reg(x, y, W)

Arguments

x	Explanatory variables. A data.frame or matrix with observations in rows and predictors in columns.
y	Dependent variable. A numeric vector, data.frame, or matrix. For a univariate response, this should be a length-n vector or an n x 1 matrix.
W	Observation weights. Can be a numeric vector of length n, or a single-column data.frame of length n, or an n x n weight matrix. If W is a vector or data.frame, the function converts it to diag(W) internally.

Value

A list with the following components:

beta

Numeric matrix ((p+1) x 1). Estimated regression coefficients, including the intercept in the first row.

e

Numeric matrix (n x 1). Residuals (y - yhat).

ew

Numeric matrix (n x 1). Weighted residuals (W^(1/2) %*% e).

yhat

Numeric matrix (n x 1). Fitted values (X %*% beta).

yhatw

Numeric matrix (n x 1). Fitted values in the weighted space (Xw %*% beta).

MSE

Numeric scalar. Mean squared error computed from weighted residuals.

F

Numeric scalar. Overall model F statistic based on the weighted ANOVA decomposition.

sig

Numeric scalar. P-value associated with F.

varbeta

Numeric matrix ((p+1) x (p+1)). Estimated covariance matrix of beta.

stdbeta

Numeric vector (length p+1). Standard errors of beta.

R2

Numeric scalar. Weighted coefficient of determination (R-squared).

R2adj

Numeric scalar. Adjusted weighted R-squared.

anovatable

A data.frame. ANOVA-style table with sums of squares, degrees of freedom, mean squares, F, and p-value.

confint

Numeric matrix (2 x (p+1)). Confidence intervals for beta; first row is lower, second row is upper.

Examples

if (requireNamespace("isdals", quietly = TRUE)) {
  data(bodyfat, package = "isdals")
  x <- bodyfat[, -1]
  y <- bodyfat[, 1]

  n <- nrow(x)
  W <- runif(n, min = 0, max = 1)

  fit <- Weightedls.reg(x, y, W)
  fit$beta
  fit$R2
  fit$anovatable
}

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