# abs.error.pred: Indexes of Absolute Prediction Error for Linear Models In Hmisc: Harrell Miscellaneous

## 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 \var{Yhat} - median(\var{Yhat}), \var{Yhat} - \var{Y}, and \var{Y} - median(\var{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 Yhat - median(Yhat) to the mean or median absolute Y - median(Y). The 1 - R^2 or SSE/SST measure is the mean or median absolute Yhat - Y divided by the mean or median absolute Y - median(Y).

## Usage

 ```1 2 3 4``` ```abs.error.pred(fit, lp=NULL, y=NULL) ## S3 method for class 'abs.error.pred' print(x, ...) ```

## 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

## Value

a list of class `abs.error.pred` (used by `print.abs.error.pred`) containing two matrices: `differences` and `ratios`.

## Author(s)

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.

## See Also

`lm`, `ols`, `cor`, `validate.ols`

## Examples

 ```1 2 3 4 5 6 7``` ```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) ```

### Example output

```Loading required package: lattice
Loading required package: survival
Loading required package: Formula
Loading required package: ggplot2

Attaching package: 'Hmisc'

The following objects are masked from 'package:base':

format.pval, round.POSIXt, trunc.POSIXt, units

Mean/Median |Differences|

Mean    Median
|Yi hat - median(Y hat)| 1.983447 0.8651185
|Yi hat - Yi|            2.184563 0.5436367
|Yi - median(Y)|         2.976277 1.0091661

Ratios of Mean/Median |Differences|

Mean    Median
|Yi hat - median(Y hat)|/|Yi - median(Y)| 0.6664189 0.8572607
|Yi hat - Yi|/|Yi - median(Y)|            0.7339920 0.5386989
```

Hmisc documentation built on Feb. 28, 2021, 9:05 a.m.