`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)

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

`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.

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.

# NOT RUN { with(UN, invTranPlot(ppgdp, infantMortality)) with(UN, invTranEstimate(ppgdp, infantMortality)) # }