For a `lm`

model, draws an inverse.response plot with the response \(Y\) on the
vertical axis and the fitted values \(\hat{Y}\)
on the horizontal axis. Uses `nls`

to
estimate \(\lambda\) in the function
\(\hat{Y}=b_0+b_1Y^{\lambda}\).
Adds the fitted curve to the plot.
`invResPlot`

is an alias for `inverseResponsePlot`

.

`inverseResponsePlot(model, lambda=c(-1,0,1), robust=FALSE, xlab=NULL, ...)`# S3 method for lm
inverseResponsePlot(model, lambda=c(-1, 0, 1),
robust=FALSE, xlab=NULL, id=FALSE, ...)

invResPlot(model, ...)

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 \(\hat{Y}\) 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.

- 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`

.

Sanford Weisberg, `sandy@umn.edu`

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`

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

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