invTranPlot: 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 \((X^{\lambda}-1)/\lambda\). invTranEstimate finds the nonlinear least squares estimate of \(\lambda\) and its standard error.

Usage

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)

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.

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()[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

Author

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.

Examples

Run this code

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

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