Predict method for Robust Linear Model ("lmrob") Fits

Description

Predicted values based on robust linear model object.

Usage

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## S3 method for class 'lmrob'
predict(object, newdata, se.fit = FALSE,
       scale = NULL, df = NULL,
       interval = c("none", "confidence", "prediction"), level = 0.95,
       type = c("response", "terms"), terms = NULL,
       na.action = na.pass, pred.var = res.var/weights, weights = 1, ...)

Arguments

object

object of class inheriting from "lmrob"

newdata

an optional data frame in which to look for variables with which to predict. If omitted, the fitted values are used.

se.fit

a switch indicating if standard errors are required.

scale

scale parameter for std.err. calculation

df

degrees of freedom for scale

interval

type of interval calculation.

level

tolerance/confidence level

type

Type of prediction (response or model term).

terms

if type="terms", which terms (default is all terms)

na.action

function determining what should be done with missing values in newdata. The default is to predict NA.

pred.var

the variance(s) for future observations to be assumed for prediction intervals. See ‘Details’.

weights

variance weights for prediction. This can be a numeric vector or a one-sided model formula. In the latter case, it is interpreted as an expression evaluated in newdata

...

further arguments passed to or from other methods.

Details

Note that this lmrob method for predict is closely modeled after the method for lm(), predict.lm, maybe see there for caveats with missing value treatment. The prediction intervals are for a single observation at each case in newdata (or by default, the data used for the fit) with error variance(s) pred.var. This can be a multiple of res.var, the estimated value of σ^2: the default is to assume that future observations have the same error variance as those used for fitting. If weights is supplied, the inverse of this is used as a scale factor. For a weighted fit, if the prediction is for the original data frame, weights defaults to the weights used for the model fit, with a warning since it might not be the intended result. If the fit was weighted and newdata is given, the default is to assume constant prediction variance, with a warning.

Value

predict.lmrob produces a vector of predictions or a matrix of predictions and bounds with column names fit, lwr, and upr if interval is set. If se.fit is TRUE, a list with the following components is returned:

fit

vector or matrix as above

se.fit

standard error of predicted means

residual.scale

residual standard deviations

df

degrees of freedom for residual

Author(s)

Andreas Ruckstuhl

See Also

lmrob and the (non-robust) traditional predict.lm method.

Examples

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## Predictions --- artificial example -- closely following  example(predict.lm)

set.seed(5)
n <- length(x <- sort(c(round(rnorm(25), 1), 20)))
y <- x + rnorm(n)
iO <- c(sample(n-1, 3), n)
y[iO] <- y[iO] + 10*rcauchy(iO)

p.ex <- function(...) {
  plot(y ~ x, ...); abline(0,1, col="sky blue")
  points(y ~ x, subset=iO, col="red", pch=2)
  abline(lm   (y ~ x), col = "gray40")
  abline(lmrob(y ~ x), col = "forest green")
  legend("topleft", c("true", "Least Squares", "robust"),
         col = c("sky blue", "gray40", "forest green"), lwd=1.5, bty="n")
}
p.ex()

fm <- lmrob(y ~ x)
predict(fm)
new <- data.frame(x = seq(-3, 10, 0.25))
str(predict(fm, new, se.fit = TRUE))
pred.w.plim <- predict(fm, new, interval = "prediction")
pred.w.clim <- predict(fm, new, interval = "confidence")
pmat <- cbind(pred.w.clim, pred.w.plim[,-1])

matlines(new$x, pmat, lty = c(1,2,2,3,3))# add to first plot
## show zoom-in region :
rect(xleft = -3, ybottom = -20, xright = 10, ytop = 40,
     lty = 3, border="orange4")

## now zoom in :
p.ex(xlim = c(-3,10), ylim = c(-20, 40))
matlines(new$x, pmat, lty = c(1,2,2,3,3))
box(lty = 3, col="orange4", lwd=3)
legend("bottom", c("fit", "lwr CI", "upr CI", "lwr Pred.I", "upr Pred.I"),
       col = 1:5, lty=c(1,2,2,3,3), bty="n")

## Prediction intervals, special cases
##  The first three of these throw warnings
w <- 1 + x^2
fit <- lmrob(y ~ x)
wfit <- lmrob(y ~ x, weights = w)
predict(fit,       interval = "prediction")
predict(wfit,      interval = "prediction")
predict(wfit, new, interval = "prediction")
predict(wfit, new, interval = "prediction", weights = (new$x)^2) -> p.w2
p.w2
stopifnot(identical(p.w2, ## the same as using formula:
     predict(wfit, new, interval = "prediction", weights = ~x^2)))

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