invTranPlot {car} R Documentation

## Choose a Predictor Transformation Visually or Numerically

### Description

`invTranPlot` draws a two-dimensional scatterplot of Y versus X, along with the OLS fit from the regression of Y on (X?^(lam)-1)/lam. `invTranEstimate` finds the nonlinear least squares estimate of lambda and its standard error.

### Usage

```
invTranPlot(x, ...)

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

## Default S3 method:
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(), 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)
```

### 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 `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(), 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

### Value

`invTranPlot` plots a graph and returns a data frame with lam in the first column, and the residual sum of squares from the regression for that lam 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.

### Author(s)

Sanford Weisberg, sandy@umn.edu

### 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.

`inverseResponsePlot`,`optimize`
```with(UN, invTranPlot(ppgdp, infantMortality))