Hmisc (version 5.1-3)

# abs.error.pred: Indexes of Absolute Prediction Error for Linear Models

## Description

Computes the mean and median of various absolute errors related to ordinary multiple regression models. The mean and median absolute errors correspond to the mean square due to regression, error, and total. The absolute errors computed are derived from $$\hat{Y} - \mbox{median(\hat{Y})}$$, $$\hat{Y} - Y$$, and $$Y - \mbox{median(Y)}$$. The function also computes ratios that correspond to $$R^2$$ and $$1 - R^2$$ (but these ratios do not add to 1.0); the $$R^2$$ measure is the ratio of mean or median absolute $$\hat{Y} - \mbox{median(\hat{Y})}$$ to the mean or median absolute $$Y - \mbox{median(Y)}$$. The $$1 - R^2$$ or SSE/SST measure is the mean or median absolute $$\hat{Y} - Y$$ divided by the mean or median absolute $$\hat{Y} - \mbox{median(Y)}$$.

## Usage

abs.error.pred(fit, lp=NULL, y=NULL)# S3 method for abs.error.pred
print(x, ...)

## Value

a list of class abs.error.pred (used by

print.abs.error.pred) containing two matrices:

differences and ratios.

## Arguments

fit

a fit object typically from lm or ols that contains a y vector (i.e., you should have specified y=TRUE to the fitting function) unless the y argument is given to abs.error.pred. If you do not specify the lp argument, fit must contain fitted.values or linear.predictors. You must specify fit or both of lp and y.

lp

a vector of predicted values (Y hat above) if fit is not given

y

a vector of response variable values if fit (with y=TRUE in effect) is not given

x

an object created by abs.error.pred

...

unused

## Author

Frank Harrell
Department of Biostatistics
Vanderbilt University School of Medicine
fh@fharrell.com

## References

Schemper M (2003): Stat in Med 22:2299-2308.

Tian L, Cai T, Goetghebeur E, Wei LJ (2007): Biometrika 94:297-311.

lm, ols, cor, validate.ols

## Examples

Run this code
set.seed(1)         # so can regenerate results
x1 <- rnorm(100)
x2 <- rnorm(100)
y  <- exp(x1+x2+rnorm(100))
f <- lm(log(y) ~ x1 + poly(x2,3), y=TRUE)
abs.error.pred(lp=exp(fitted(f)), y=y)
rm(x1,x2,y,f)


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