cost {cvTools}

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.

includeSE

a logical indicating whether standard errors should be computed as well.

trim

a numeric value giving the trimming proportion (the default is 0.25).

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)