# invTranPlot

##### Choose a Predictor Transformation Visually or Numerically

`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.

- Keywords
- regression, hplot

##### Usage

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

# 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=palette()[1], col.lines=palette(),
xlab=deparse(substitute(x)), ylab=deparse(substitute(y)),
family="bcPower", optimal=TRUE, key="auto",
id.method = "x",
labels,
id.n = if(id.method[1]=="identify") Inf else 0,
id.cex=1, id.col=palette()[1], id.location="lr", grid=TRUE, ...)

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

##### Arguments

- 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

`palette`

- 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.method,labels,id.n,id.cex,id.col,id.location
Arguments for the labelling of points. The default is

`id.n=0`

for labeling no points. See`showLabels`

for details of these arguments.- ...
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

##### Value

`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.

##### References

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

Pendergast, L, and Sheather, S. (in press). On sensitivity of response plot
estimation of a robust estimation approach. *Scandinavian Journal of
Statistics*.

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

##### See Also

##### Examples

```
# NOT RUN {
with(UN, invTranPlot(gdp, infant.mortality))
with(UN, invTranEstimate(gdp, infant.mortality))
# }
```

*Documentation reproduced from package car, version 2.1-6, License: GPL (>= 2)*