`invTranPlot`

draws a two-dimensional scatterplot of \(Y\) versus
\(X\), along with the OLS
fit from the regression of \(Y\) on
\((X^{\lambda}-1)/\lambda\). `invTranEstimate`

finds the nonlinear least squares estimate of \(\lambda\) and its
standard error.

`invTranPlot(x, ...)`# S3 method for formula
invTranPlot(x, data, subset, na.action, id=FALSE, ...)

# S3 method for default
invTranPlot(x, y, lambda=c(-1, 0, 1), robust=FALSE,
lty.lines=rep(c("solid", "dashed", "dotdash", "longdash", "twodash"),
length=1 + length(lambda)), lwd.lines=2,
col=carPalette()[1], col.lines=carPalette(),
xlab=deparse(substitute(x)), ylab=deparse(substitute(y)),
family="bcPower", optimal=TRUE, key="auto", id=FALSE,
grid=TRUE, ...)

invTranEstimate(x, y, family="bcPower", confidence=0.95, robust=FALSE)

`invTranPlot`

plots a graph and returns a data frame with \(\lambda\) in the first column, and the residual sum of squares from the regression for that \(\lambda\) in the second column.

`invTranEstimate`

returns a list with elements `lambda`

for the
estimate, `se`

for its standard error, and `RSS`

, the minimum
value of the residual sum of squares.

- x
The predictor variable, or a formula with a single response and a single predictor

- y
The response variable

- data
An optional data frame to get the data for the formula

- subset
Optional, as in

`lm`

, select a subset of the cases- na.action
Optional, as in

`lm`

, the action for missing data- lambda
The powers used in the plot. The optimal power than minimizes the residual sum of squares is always added unless optimal is

`FALSE`

.- robust
If

`TRUE`

, then the estimated transformation is computed using Huber M-estimation with the MAD used to estimate scale and k=1.345. The default is`FALSE`

.- family
The transformation family to use,

`"bcPower"`

,`"yjPower"`

, or a user-defined family.- confidence
returns a profile likelihood confidence interval for the optimal transformation with this confidence level. If

`FALSE`

, or if`robust=TRUE`

, no interval is returned.- optimal
Include the optimal value of lambda?

- lty.lines
line types corresponding to the powers

- lwd.lines
the width of the plotted lines, defaults to 2 times the standard

- col
color(s) of the points in the plot. If you wish to distinguish points according to the levels of a factor, we recommend using symbols, specified with the

`pch`

argument, rather than colors.- col.lines
color of the fitted lines corresponding to the powers. The default is to use the colors returned by

`carPalette`

- key
The default is

`"auto"`

, in which case a legend is added to the plot, either above the top marign or in the bottom right or top right corner. Set to NULL to suppress the legend.- xlab
Label for the horizontal axis.

- ylab
Label for the vertical axis.

- 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 values --- i.e., the response variable in the model.- ...
Additional arguments passed to the plot method, such as

`pch`

.- grid
If TRUE, the default, a light-gray background grid is put on the graph

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.

`inverseResponsePlot`

,`optimize`

```
with(UN, invTranPlot(ppgdp, infantMortality))
with(UN, invTranEstimate(ppgdp, infantMortality))
```

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