# invResPlot: Inverse Response Plots to Transform the Response In car: Companion to Applied Regression

## Description

For a `lm` model, draws an inverse.response plot with the response Y on the vertical axis and the fitted values Yhat on the horizontal axis. Uses `nls` to estimate lambda in the function Yhat = b0 + b1(Y)^(lambda). Adds the fitted curve to the plot. `invResPlot` is an alias for `inverseResponsePlot`.

## Usage

 ```1 2 3 4 5 6 7``` ```inverseResponsePlot(model, lambda=c(-1,0,1), robust=FALSE, xlab=NULL, ...) ## S3 method for class 'lm' inverseResponsePlot(model, lambda=c(-1, 0, 1), robust=FALSE, xlab=NULL, id=FALSE, ...) invResPlot(model, ...) ```

## Arguments

 `model` A `"lm"` regression object. `lambda` A vector of values for lambda. A plot will be produced with curves corresponding to these lambdas and to the nonlinear least squares estimate of lambda. `robust` If `TRUE`, then estimation uses Huber M-estimates with the median absolute deviation to estimate scale and k= 1.345. The default is `FALSE`. `xlab` The horizontal axis label. If `NULL`, it is constructed by the function. `id` controls point identification; if `FALSE` (the default), no points are identified; can be a list of named arguments to the `showLabels` function; `TRUE` is equivalent to `list(method=list(method="x", n=2, cex=1, col=carPalette()[1], location="lr")`, which identifies the 2 points with the most extreme horizontal (X) values. `...` Other arguments passed to `invTranPlot` and then to `plot`.

## Value

As a side effect, a plot is produced with the response on the horizontal axis and fitted values on the vertical axis. Several lines are added to be plot as the ols estimates of the regression of Yhat on Y^(lambda), interpreting lambda = 0 to be natural logarithms.

Numeric output is a list with elements

 `lambda` Estimate of transformation parameter for the response `RSS` The residual sum of squares at the minimum if robust=FALSE. If robust = TRUE, the value of Huber objective function is returned.

## Author(s)

Sanford Weisberg, `[email protected]`

## References

Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second Edition, Sage.

Prendergast, L. A., & Sheather, S. J. (2013) On sensitivity of inverse response plot estimation and the benefits of a robust estimation approach. Scandinavian Journal of Statistics, 40(2), 219-237.

Weisberg, S. (2014) Applied Linear Regression, Fourth Edition, Wiley, Chapter 7.

`invTranPlot`, `powerTransform`, `showLabels`

## Examples

 ```1 2``` ```m2 <- lm(rate ~ log(len) + log(adt) + slim + shld + log(sigs1), Highway1) invResPlot(m2) ```

### Example output

```      lambda      RSS
1  0.1350783 31.57739
2 -1.0000000 35.45785
3  0.0000000 31.63514
4  1.0000000 33.68958
```

car documentation built on Aug. 26, 2018, 3 a.m.