# pre: Proportional and Expected Proportional Reductions in Error In DAMisc: Dave Armstrong's Miscellaneous Functions

## Description

Calculates proportional reduction in error (PRE) and expected proportional reduction in error (epre) from Herron (1999).

## Usage

 `1` ```pre(mod1, mod2=NULL, sim=FALSE, R=2500) ```

## Arguments

 `mod1` A model of class `glm` (with family `binomial`), `polr` or `multinom` for which (e)PRE will be calculated. `mod2` A model of the same class as `mod1` against which proportional reduction in error will be measured. If `NULL`, the null model will be used. `sim` A logical argument indicating whether a parametric bootstrap should be used to calculate confidence bounds for (e)PRE. See `Details` for more information. `R` Number of bootstrap samples to be drawn if `sim=TRUE`.

## Details

Proportional reduction in error is calculated as a function of correct and incorrect predictions (and the probabilities of correct and incorrect predictions for ePRE). When `sim=TRUE`, a parametric bootstrap will be used that draws from the multivariate normal distribution centered at the coefficient estimates from the model and using the estimated variance-covariance matrix of the estimators as Sigma. This matrix is used to form `R` versions of XB and predictions are made for each of the `R` different versions of XB. Confidence intervals can then be created from the bootstrap sampled (e)PRE values.

## Value

An object of class `pre`, which is a list with the following elements:

 `pre` The proportional reduction in error `epre` The expected proportional reduction in error `m1form` The formula for model 1 `m2form` The formula for model 2 `pcp` The percent correctly predicted by model 1 `pmc` The percent correctly predicted by model 2 `epcp` The expected percent correctly predicted by model 1 `epmc` The expected percent correctly predicted by model 2 `pre.sim` A vector of bootstrapped PRE values if `sim=TRUE` `epre.sim` A vector of bootstrapped ePRE values if `sim=TRUE`

## Author(s)

Dave Armstrong (UW-Milwaukee, Department of Political Science)

## References

Herron, M. 1999. Postestimation Uncertainty in Limited Dependent Variable Models. Political Analysis 8(1): 83–98.

## Examples

 ```1 2 3 4``` ```data(france) left.mod <- glm(voteleft ~ male + age + retnat + poly(lrself, 2), data=france, family=binomial) pre(left.mod) ```

### Example output

```Loading required package: car
lattice theme set by effectsTheme()
See ?effectsTheme for details.
Warning message:
no DISPLAY variable so Tk is not available
mod1:  voteleft ~ male + age + retnat + poly(lrself, 2)
mod2:  voteleft ~ 1

Analytical Results
PMC =  0.607
PCP =  0.882
PRE =  0.700
ePMC =  0.523
ePCP =  0.825
ePRE =  0.634
```

DAMisc documentation built on May 2, 2019, 4:52 p.m.