get_residuals {api2lm}

Extract residuals from a model

Description

Extracts different types of residuals from a fitted model. The types of residuals are discussed in Details.

Usage

get_residuals(
  x,
  rtype = c("ordinary", "standardized", "studentized", "jackknife", "loo", "deleted",
    "internally studentized", "externally studentized")
)

Arguments

x

An lm object

rtype

The desired residual type. The options are "ordinary", "standardized", "studentized", "jackknife", "loo", "deleted", "internally studentized", and "externally studentized".

Details

For observations 1, 2, \ldots, n, let:

1. Y_i denote the response value for the ith observation.

2. \hat{Y}_i denote the fitted value for the ith observation.

3. h_i denote the leverage value for the ith observation.

We assume that \mathrm{sd}(Y_i) = \sigma for i \in \{1, 2, \ldots, n\} and that \hat{\sigma} is the estimate produced by sigma(x), where x is the fitted model object.

The ordinary residual for the ith observation is computed as

\hat{\epsilon}_i = Y_i - \hat{Y}_i.

The variance of the ith ordinary residual under standard assumptions is \sigma^2(1-h_i).

The standardized residual for the ith observation is computed as

r_i = \frac{\hat{\epsilon}_i}{\hat{\sigma}\sqrt{1-h_i}}.

The standardized residual is also known as the internally studentized residual.

Let \hat{Y}_{i(i)} denote the predicted value of Y_i for the model fit with all n observations except observation i. The leave-one-out (LOO) residual for observation i is computed as

l_i = Y_i - \hat{Y}_{i(i)} = \frac{\hat{\epsilon}_i}{1-h_i}.

The LOO residual is also known as the deleted or jackknife residual.

The studentized residual for the ith observation is computed as

t_i = \frac{l_i}{\hat{\sigma}_{(i)}\sqrt{1-h_i}},

where \hat{\sigma}_{(i)} is the leave-one-out estimate of \sigma.

The studentized residual is also known as the externally studentized residual.

Value

A vector of residals.

Examples

lmod <- lm(Girth ~ Height, data = trees)
# ordinary residuals
rord <- get_residuals(lmod)
all.equal(rord, residuals(lmod))
# standardized residuals
rstand <- get_residuals(lmod, "standardized")
all.equal(rstand, rstandard(lmod))
# studentized residuals
rstud <- get_residuals(lmod, "studentized")
all.equal(rstud, rstudent(lmod))
# loo residuals
rl <- get_residuals(lmod, "loo")
all.equal(rl, rloo(lmod))