Fit a weighted least squares model

Solves the weighted least-squares problem \(\min_\beta \sum_i w_i (y_i - x_i^T \beta)^2\) using either the normal equations or a QR decomposition of the weight-scaled design.

Usage

wls_fit(
  X,
  Y,
  weights,
  intercept = FALSE,
  include_fitted = TRUE,
  include_residuals = TRUE,
  cache = TRUE,
  method = c("normal", "qr")
)

Arguments

X

Numeric matrix or adgeMatrix of predictors, shape [n, p].

Y

Numeric matrix, vector, or adgeMatrix of responses, shape [n, q].

weights

Positive numeric vector of length n; observation weights.

intercept

Logical; when TRUE a column of ones is prepended to X before fitting.

include_fitted

Logical; include fitted values in the result.

include_residuals

Logical; include residuals in the result.

cache

Logical; cache intermediate factorizations for reuse across calls sharing the same X and weights.

method

Solver method: "normal" (weighted normal equations, default) or "qr" (QR on the weight-scaled design).

Value

An object of class "wls_fit", a named list containing:

coefficients

adgeMatrix of shape [p, q].

fitted.values

adgeMatrix of shape [n, q], or NULL when include_fitted = FALSE.

residuals

adgeMatrix of shape [n, q], or NULL when include_residuals = FALSE.

rank

Integer model rank.

df.residual

Residual degrees of freedom.

See also

lm_fit, crossprod_weighted

Examples

X <- matrix(rnorm(50), nrow = 10)
y <- rnorm(10)
w <- runif(10, 0.5, 2)
fit <- wls_fit(X, y, weights = w)
coef(fit)
#> An amatrix dense matrix [cpu|policy=auto|precision=strict]
#> 5 x 1 Matrix of class "adgeMatrix"
#>             [,1]
#> [1,]  0.27670490
#> [2,] -0.32151899
#> [3,] -0.04981365
#> [4,] -0.13500564
#> [5,] -0.74870841