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

predict.lmrob {robustbase} | R Documentation

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

### Description

Predicted values based on robust linear model object.

### Usage

    ## 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

    ## 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)))

[Package robustbase version 0.95-0 Index]