predictMVUE: Bias Corrected Predictions

In USGS-R/smwrStats: R functions to support statistical methods in water resources

Bias Corrected Predictions

Description

Predicts bias-corrected expected mean response values from a log-transformed regression model, using either the minimum variance unbiased estimate(MVUE), Duan's smoothing estimate, or Ferguson's maximum likelihood estimate.

Usage

predictDuan(object, newdata, back.trans = exp)

predictFerguson(object, newdata, Log10 = FALSE)

predictMVUE(object, newdata, Log10 = FALSE)

Arguments

object	an object of class "lm" on which to base the predicted values.
newdata	an optional data.frame in which to look for variables with which to predict. If omitted, then the fitted values are used.
back.trans	the back-transformation function. For common log transforms, use function(x) 10^x.
Log10	is the transform of the response variable the common log?

Value

A vector of predictions matching newdata or the model data.

References

Bradu, D. and Mundlak, Y., 1970, Estimation in the lognormal linear models: Journal of the American Statistical Association, v. 65, no. 329, p. 198–211.

Duan, N., 1983, Smearing estimate: a nonparametric retransformation method: Journal of the American Statistical Association, v. 78, p. 159–178.

Ferguson, R.I. 1986, River loads underestimated by rating curves: Water Resources Research, v. 22, p 74–76.

Helsel, D.R. and Hirsch, R.M., 2002, Statistical methods in water resources: U.S. Geological Survey Techniques of Water-Resources Investigations, book 4, chap. A3, 522 p.

See Also

lm

Examples

## Generate random log-normal data and build the regression model
set.seed(111)
XX.df <- data.frame(x=sort(runif(32, 1, 5)), y=rlnorm(32, seq(1,2, length.out=32)))
XX.lm <- lm(log(y) ~ x, data=XX.df)
## Compare the results for x=1:5
## The simple back-transformed estimates
exp(predict(XX.lm, newdata=data.frame(x=1:5)))
## The bias corrected estimates of the mean response
predictFerguson(XX.lm, newdata=data.frame(x=1:5))
predictDuan(XX.lm, newdata=data.frame(x=1:5))
predictMVUE(XX.lm, newdata=data.frame(x=1:5))

USGS-R/smwrStats documentation built on Oct. 11, 2022, 6:15 a.m.