R: Prediction loss

cost {cvTools} | R Documentation

## Prediction loss

### Description

Compute the prediction loss of a model.

### Usage

      mspe(y, yHat, includeSE = FALSE)

      rmspe(y, yHat, includeSE = FALSE)

      mape(y, yHat, includeSE = FALSE)

      tmspe(y, yHat, trim = 0.25, includeSE = FALSE)

      rtmspe(y, yHat, trim = 0.25, includeSE = FALSE)

### Arguments

`y` | a numeric vector or matrix giving the observed values.
`yHat` | a numeric vector or matrix of the same dimensions as `y` giving the fitted values.
`trim` | a numeric value giving the trimming proportion (the default is 0.25).
`includeSE` | a logical indicating whether standard errors should be computed as well.

### Details

`mspe` and `rmspe` compute the mean squared prediction error and the root mean squared prediction error, respectively. In addition, `mape` returns the mean absolute prediction error, which is somewhat more robust.

Robust prediction loss based on trimming is implemented in `tmspe` and `rtmspe`. To be more precise, `tmspe` computes the trimmed mean squared prediction error and `rtmspe` computes the root trimmed mean squared prediction error. A proportion of the largest squared differences of the observed and fitted values are thereby trimmed.

Standard errors can be requested via the `includeSE` argument. Note that standard errors for `tmspe` are based on a winsorized standard deviation. Furthermore, standard errors for `rmspe` and `rtmspe` are computed from the respective standard errors of `mspe` and `tmspe` via the delta method.

### Value

If standard errors are not requested, a numeric value giving the prediction loss is returned.

Otherwise a list is returned, with the first component containing the prediction loss and the second component the corresponding standard error.

### Author(s)

Andreas Alfons

### References

Tukey, J.W. and McLaughlin, D.H. (1963) Less vulnerable confidence and significance procedures for location based on a single sample: Trimming/winsorization. Sankhya: The Indian Journal of Statistics, Series A, 25(3), 331–352

Oehlert, G.W. (1992) A note on the delta method. The American Statistician, 46(1), 27–29.

### See Also

`cvFit`, `cvTuning`

### Examples

    # fit an MM-regression model
    data("coleman")
    fit <- lmrob(Y~., data=coleman)

    # compute the prediction loss from the fitted values
    # (hence the prediction loss is underestimated in this simple
    # example since all observations are used to fit the model)
    mspe(coleman$Y, predict(fit))
    rmspe(coleman$Y, predict(fit))
    mape(coleman$Y, predict(fit))
    tmspe(coleman$Y, predict(fit), trim = 0.1)
    rtmspe(coleman$Y, predict(fit), trim = 0.1)

    # include standard error
    mspe(coleman$Y, predict(fit), includeSE = TRUE)
    rmspe(coleman$Y, predict(fit), includeSE = TRUE)
    mape(coleman$Y, predict(fit), includeSE = TRUE)
    tmspe(coleman$Y, predict(fit), trim = 0.1, includeSE = TRUE)
    rtmspe(coleman$Y, predict(fit), trim = 0.1, includeSE = TRUE)

[Package cvTools version 0.3.2 Index]