# boxCox: Graph the profile log-likelihood for Box-Cox transformations... In car: Companion to Applied Regression

## Description

Computes and optionally plots profile log-likelihoods for the parameter of the Box-Cox power family, the Yeo-Johnson power family, or for either of the parameters in a bcnPower family. This is a slight generalization of the `boxcox` function in the MASS package that allows for families of transformations other than the Box-Cox power family. the `boxCox2d` function produces a contour plot of the two-dimensional likelihood profile for the bcnPower family.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ```boxCox(object, ...) ## Default S3 method: boxCox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE, interp = plotit, eps = 1/50, xlab=NULL, ylab=NULL, family="bcPower", param=c("lambda", "gamma"), gamma=NULL, grid=TRUE, ...) ## S3 method for class 'formula' boxCox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE, family = "bcPower", param = c("lambda", "gamma"), gamma = NULL, grid = TRUE, ...) ## S3 method for class 'lm' boxCox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE, ...) boxCox2d(x, ksds = 4, levels = c(0.5, 0.95, 0.99, 0.999), main = "bcnPower Log-likelihood", grid=TRUE, ...) ```

## Arguments

 `object` a formula or fitted model object of class `lm` or `aov`. `lambda` vector of values of lambda, with default (-2, 2) in steps of 0.1, where the profile log-likelihood will be evaluated. `plotit` logical which controls whether the result should be plotted; default `TRUE`. `interp` logical which controls whether spline interpolation is used. Default to `TRUE` if plotting with lambda of length less than 100. `eps` Tolerance for lambda = 0; defaults to 0.02. `xlab` defaults to `"lambda"` or `"gamma"`. `ylab` defaults to `"log-Likelihood"` or for bcnPower family to the appropriate label. `family` Defaults to `"bcPower"` for the Box-Cox power family of transformations. If set to `"yjPower"` the Yeo-Johnson family, which permits negative responses, is used. If set to `bcnPower` the function gives the profile log-likelihood for the parameter selected via `param`. `param` Relevant only to `family="bcnPower"`, produces a profile log-likelihood for the parameter selected, maximizing over the remaining parameter. `gamma` For use when the `family="bcnPower", param="gamma"`. If this is a vector of positive values, then the profile log-likelihood for the location (or start) parameter in the `bcnPower` family is evaluated at these values of gamma. If gamma is `NULL`, then evaulation is done at 100 equally spaced points between `min(.01, gmax - 3*sd)` and `gmax + 3*sd`, where `gmax` is the maximimum likelihood estimate of gamma, and `sd` is the sd of the response. See `bcnPower` for the definition of `gamma`. `grid` If TRUE, the default, a light-gray background grid is put on the graph. `...` additional arguments passed to the `lm` method with `boxCox.formula` or passed to `contour` with `boxCox2d`. `x` An object created by a call to `powerTransform` using `family="bcnPower"`. `ksds` Contour plotting of the log-likelihood surface will cover plus of minus `ksds` standard deviations on each axis. `levels` Contours will be drawn at the values of levels. For example, `levels=c(.5, .99)` would display two contours, at the 50% level and at the 99% level. `main` Title for the contour plot

## Details

The `boxCox` function is an elaboration of the `boxcox` function in the MASS package. The first 7 arguments are the same as in `boxcox`, and if the argument `family="bcPower"` is used, the result is essentially identical to the function in MASS. Two additional families are the `yjPower` and `bcnPower` families that allow a few values of the response to be non-positive. The bcnPower family has two parameters: a power lambda and a start or location parameter gamma, and the `boxCox` function can be used to obtain a profile log-likelihood for either parameter with lambda as the default. Alternatively, the `boxCox2d` function can be used to get a contour plot of the profile log-likelihood.

## Value

Both functions ae designed for their side effects of drawing a graph. The `boxCox` function returns a list of the lambda (or possibly, gamma) vector and the computed profile log-likelihood vector, invisibly if the result is plotted. If `plotit=TRUE` plots log-likelihood vs lambda and indicates a 95% confidence interval about the maximum observed value of lambda. If `interp=TRUE`, spline interpolation is used to give a smoother plot.

## Author(s)

Sanford Weisberg, <[email protected]>

## References

Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations. Journal of the Royal Statisistical Society, Series B. 26 211-46.

Cook, R. D. and Weisberg, S. (1999) Applied Regression Including Computing and Graphics. Wiley.

Fox, J. (2016) Applied Regression Analysis and Generalized Linear Models, Third Edition. Sage.

Fox, J. and Weisberg, S. (2019) An R Companion to Applied Regression, Third Edition, Sage.

Hawkins, D. and Weisberg, S. (2017) Combining the Box-Cox Power and Generalized Log Transformations to Accomodate Nonpositive Responses In Linear and Mixed-Effects Linear Models South African Statistics Journal, 51, 317-328.

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

Yeo, I. and Johnson, R. (2000) A new family of power transformations to improve normality or symmetry. Biometrika, 87, 954-959.

`boxcox`, `yjPower`, `bcPower`, `bcnPower`, `powerTransform`, `contour`

## Examples

 ```1 2 3 4 5 6``` ``` with(trees, boxCox(Volume ~ log(Height) + log(Girth), data = trees, lambda = seq(-0.25, 0.25, length = 10))) data("quine", package = "MASS") with(quine, boxCox(Days ~ Eth*Sex*Age*Lrn, data = quine, lambda = seq(-0.05, 0.45, len = 20), family="yjPower")) ```

### Example output

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car documentation built on April 6, 2018, 3:05 p.m.