Package 'complmrob'

Bootstrap the regression coefficients for a robust linear regression model

Description

This function provides an easy interface and useful output to bootstrapping the regression coefficients of robust linear regression models

Usage

bootcoefs(object, R = 999, method = c("frb", "residuals", "cases"),
  ncpus = NULL, cl = NULL, ...)

## S3 method for class 'complmrob'
bootcoefs(object, R = 999, method = c("frb",
  "residuals", "cases"), ncpus = NULL, cl = NULL, ...)

## S3 method for class 'lmrob'
bootcoefs(object, R = 999, method = c("frb",
  "residuals", "cases"), ncpus = NULL, cl = NULL, ...)

Arguments

object	the model to bootstrap the coefficients from
R	the number of bootstrap replicates.
method	one of "frb" for fast and robust bootstrap, "residuals" to resample the residuals or "cases" to resample the cases.
ncpus	the number of CPUs to utilize for bootstrapping.
cl	a snow or parallel cluster to use for bootstrapping.
...	currently ignored.

Details

If 'object' is created by 'complmrob' the default method is to use fast and robust bootstrap (FRB) as described in the paper by M. Salibian-Barrera, et al (2008). The same default is used if 'object' is an MM-estimate created by ‘lmrob(..., method = ’SM')'. The other options are to bootstrap the residuals or to bootstrap cases (observations), but the sampling distribution of the estimates from these methods can be numerically unstable and take longer to compute. If the 'object' is a robust estimate created by 'lmrob', but not an MM-estimate, the default is to bootstrap the residuals.

Value

A list of type bootcoefs for which print, summary and plot methods are available

Methods (by class)

• complmrob: For robust linear regression models with compositional data

• lmrob: For standard robust linear regression models

References

M. Salibian-Barrera, S. Aelst, and G. Willems. Fast and robust bootstrap. Statistical Methods and Applications, 17(1):41-71, 2008.

Examples

data <- data.frame(lifeExp = state.x77[, "Life Exp"], USArrests[ , -3])
mUSArr <- complmrob(lifeExp ~ ., data = data)
bc <- bootcoefs(mUSArr, R = 200) # the number of bootstrap replicates should
                                 # normally be higher!
summary(bc)
plot(bc) # for the model diagnostic plots

---

Bootstrap statistics functions

Description

Functions to calculate the coefficient(s) of the robust linear regression model from a bootstrapped sample

Usage

bootStatResiduals(residData, inds, coefind, intercept = TRUE,
  maxTries = 4L, control)

bootStatCases(origData, inds, coefind, formula, maxTries = 4L, control)

bootStatFastControl(model)

bootStatFast(origData, inds, control, coefind)

Arguments

residData	the original data set with the columns fit, resid and the predictor variables instead of the response variable.
inds	the resampled indices.
coefind	the index of the coefficient to extract.
intercept	if the model includes an intercept term.
maxTries	the maximum number of tries to increase the maxit control arguments for the S estimator.
control	either the control object as returned by bootStatFastControl (for 'bootStatFast') or the control object used to fit the model(s) with 'lmrob'.
origData	the original data set.
formula	the formula to fit the model
model	The lmrob model

Details

Different approaches for bootstrapping have been implemented. The default "fast and robust bootstrap" (FRB) proposed by M. Salibian-Barrera, et al. (2002), implemented with bootStatFast is the fastest and most resistant to outliers, while the other two bootStatResiduals and bootStatCases are standard bootstrap methods, where the residuals resp. the cases are resampled and the model is fit to this data.

References

M. Salibian-Barrera, S. Aelst, and G. Willems. Fast and robust bootstrap. Statistical Methods and Applications, 17(1):41-71, 2008.

See Also

bootcoefs

---

MM-type estimators for linear regression on compositional data

Description

Uses the lmrob method for robust linear regression models to fit linear regression models to compositional data.

Usage

complmrob(formula, data)

Arguments

formula	The formula for the regression model
data	The data.frame to use

Details

The variables on the right-hand-side of the formula are transformed with the isometric log-ratio transformation (isomLR) and a robust linear regression model is fit to those transformed variables. The orthonormal basis can be constructed in p different ways, where p is the number of variables on the RHS of the formula.

To get an interpretable estimate of the regression coefficient for each part of the composition, the data is transformed separately for each part. To estimate the coefficient for the *k*-th part, the *k*-th part is used as the orthonormal basis in the transformation and a regression model is fit to this data.

Value

A list of type complmrob with fields

coefficients

the estimated coefficients

models

the single regression models (one for each orthonormal basis)

npred

the number of predictor variables

predictors

the names of the predictor variables

coefind

the index of the relevant coefficient in the single regression models

call

how the function was called

intercept

if an intercept is included

References

K. Hron, P. Filzmoser & K. Thompson (2012): Linear regression with compositional explanatory variables, Journal of Applied Statistics, DOI:10.1080/02664763.2011.644268

Examples

crimes <- data.frame(lifeExp = state.x77[, "Life Exp"],
                     USArrests[ , c("Murder", "Assault", "Rape")])
mUSArr <- complmrob(lifeExp ~ ., data = crimes)
summary(mUSArr)

---

Calculate confidence intervals

Description

Calculate confidence intervals for bootstrapped robust linear regression estimates with or without compositional data

Usage

## S3 method for class 'bccomplmrob'
confint(object, parm, level = 0.95,
  type = c("bca", "perc", "norm", "basic", "stud"), ...)

## S3 method for class 'bclmrob'
confint(object, parm, level = 0.95, type = c("bca",
  "perc", "norm", "basic", "stud"), ...)

Arguments

object	an object returned from bootcoefs.
parm	a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered.
level	the confidence level required.
type	the type of interval required (see the type argument of boot.ci).
...	currently ignored.

Methods (by class)

• bccomplmrob: for bootstrapped estimates of robust linear regression models for compositional data

• bclmrob: for bootstrapped estimates of robust linear regression models

Examples

data <- data.frame(lifeExp = state.x77[, "Life Exp"], USArrests[ , -3])
mUSArr <- complmrob(lifeExp ~ ., data = data)
bc <- bootcoefs(mUSArr, R = 200) # the number of bootstrap replicates should
                                 # normally be higher!
confint(bc, level = 0.95, type = "perc")

### For normal robust linear regression models ###
require(robustbase)
data(aircraft)

mod <- lmrob(Y ~ ., data = aircraft)
bootEst <- bootcoefs(mod, R = 200)
confint(bootEst, level = 0.95, type = "perc")

---

Simple function (just copied from the stats package) to format percentages

Description

Simple function (just copied from the stats package) to format percentages

Usage

## S3 method for class 'perc'
format(probs, digits)

Arguments

probs	the percentages
digits	the number of digits

---

(Inverse) Isometric log-ratio transformation for compositional data

Description

Projects the D-dimensional compositional data on the (D-1)-dimensional simplex isometrically back and forth by transforming the values according to

$z_i = \sqrt{\frac{D - i}{D -i + 1}} \log{ \frac{x_i}{ \left( \prod_{j=i+1}^{D} x_j \right)^{1/(D - i)} }}$

Usage

isomLR(x, comp = 1)

isomLRinv(z, perc = TRUE)

Arguments

x	a numeric vector of length D or a numeric matrix with D columns
comp	the component to use as the first compositional part
z	a numeric vector of length D-1 or a numeric matrix with D-1 columns.
perc	should the result be a matrix with percentage shares (default TRUE).

Value

isomLR: a numeric matrix with (D-1) columns with the transformed values. The name of the first column is the name of the first part (the other names are according to the order of the columns in the given matrix x)

isomLRinv: a numeric matrix with D columns with the transformed values. The values in the matrix are not on the original scale, but the percentage shares are equal.

Functions

• isomLRinv: Inverse transformation

Examples

X <- as.matrix(USArrests[ , -3])
# Get the ilr with relative information of the 1st column to the other cols
ilrZ1 <- isomLR(X)
# Get the ilr with relative information of the 2nd column to the other cols
ilrZ2 <- isomLR(X, 2)
isomLRinv(ilrZ1)

---

Plot the distribution of the bootstrap estimates

Description

Plot the distribution of the bootstrap estimates and the confidence intervals for the estimates

Usage

## S3 method for class 'bootcoefs'
plot(x, y = NULL, conf.level = 0.95,
  conf.type = "perc", kernel = "gaussian", adjust = 1,
  which = "all", theme = theme_bw(), confStyle = list(color =
  "#56B4E9", alpha = 0.4), estLineStyle = list(color = "black", width =
  rel(1), alpha = 1, linetype = "dashed"), densityStyle = list(color =
  "black", width = rel(0.5), alpha = 1, linetype = "solid"), ...)

Arguments

x	the object returned by a call to the bootcoefs function.
y	ignored.
conf.level	the level of the confidence interval that is plotted as shaded region under the density estimate.
conf.type	the confidence interval type, see boot.ci for details.
kernel	the kernel used for density estimation, see density for details.
adjust	see density for details.
which	which parameters to plot
theme	the ggplot2 theme to use for the plot.
confStyle	a list with style parameters for the confidence region below the density estimate (possible entries are color, and alpha)
estLineStyle	a list with style parameters for the line at the original parameter estimate (possible entries are color, width, alpha, and linetype)
densityStyle	a list with style parameters for the line of the density estimate (possible entries are color, width, alpha, and linetype)
...	ignored

See Also

confint to get the numerical values for the confidence intervals

Examples

data <- data.frame(lifeExp = state.x77[, "Life Exp"], USArrests[ , -3])
mUSArr <- complmrob(lifeExp ~ ., data = data)
bc <- bootcoefs(mUSArr, R = 200) # this can take some time
plot(bc) # for the model diagnostic plots

---

Diagnostic plots for the robust regression model with compositional covariates

Description

Plot the response or the model diagnostic plots for robust linear regression model with compositional data

Usage

## S3 method for class 'complmrob'
plot(x, y = NULL, type = c("response", "model"),
  se = TRUE, conf.level = 0.95, scale = c("ilr", "percent"),
  theme = theme_bw(), pointStyle = list(color = "black", size = rel(1),
  alpha = 1, shape = 19), lineStyle = list(color = "grey20", width =
  rel(1), linetype = "solid"), seBandStyle = list(color = "gray80", alpha
  = 0.5), stack = c("horizontal", "vertical"), ...)

Arguments

x	the object returned by complmrob.
y	ignored.
type	one of "response" to plot the response or "model" to get the standard lmrob model diagnostic plots. Partial matching is performed, so any unique abbreviation of the two possible values is excepted (e.g., "r" for the response plot).
se	should the confidence interval be shown in the response plot.
conf.level	if the confidence interval is shown in the response plot, this parameter sets the level of the confidence interval.
scale	should the x-axis in the response plot be in percentage or in the ILR-transformed scale?
theme	the ggplot2 theme to use for the response plot.
pointStyle	a list with style parameters for the points in the response plot (possible entries are color, size, alpha, and shape). If color and/or shape is a vector of length equal to the number of observations in the model, the points will be colored/shaped according to this vector.
lineStyle	list with style parameters for the smoothing lines in the response plot (possible entries are color, width, and linetype)
seBandStyle	a list with style parameters (color and alpha) for the confidence band (if se is TRUE)
stack	how the facets are laid out in the response plot. "horizontal" for side by side and "vertical" for on top of each other.
...	further arguments to the model diagnostic plot method (see plot.lmrob for details).

Details

The response plot shows the value on the first component of the orthonormal basis versus the response and the fitted values. For the fitted values, the other components are set to the median of the values in that direction. This usually causes aberrant predictions when plotting on the *percent* scale.

For the model diagnostic plots see the details in the help file for plot.lmrob. The model diagnostic plots are the same for all sub-models fit to the data transformed with the different orthonormal basis.

Examples

data <- data.frame(lifeExp = state.x77[, "Life Exp"], USArrests[ , -3])
mUSArr <- complmrob(lifeExp ~ ., data = data)
plot(mUSArr)
plot(mUSArr, type = "model") # for the model diagnostic plots

---

Print the object

Description

Print information about the models returned by complmrob or bootcoefs. For a detailed description see the help on summary.

Usage

## S3 method for class 'complmrob'
print(x, conf.level = 0.95, ...)

## S3 method for class 'bootcoefs'
print(x, conf.level = 0.95, conf.type = "perc",
  ...)

Arguments

x	the object to be printed.
conf.level	the confidence level for the confidence interval.
...	ignored.
conf.type	the type of the printed confidence interval.

See Also

summary-methods

---

Print the summary information

Description

Print the summary information

Usage

## S3 method for class 'summary.complmrob'
print(x, digits = max(3, getOption("digits")
  - 3), signif.stars = getOption("show.signif.stars"), ...)

Arguments

x	the summary object.
digits	the number of digits for the reported figures
signif.stars	should stars be displayed to show the significance of certain figures
...	further arguments currently not used

---

Get summary information

Description

List the estimates, standard errors, p-values and confidence intervals for the coefficients of robust linear regression models with compositional data as returned by complmrob or bootcoefs

Usage

## S3 method for class 'complmrob'
summary(object, conf.level = 0.95, ...)

## S3 method for class 'bccomplmrob'
summary(object, conf.level = 0.95,
  conf.type = "perc", ...)

## S3 method for class 'bclmrob'
summary(object, conf.level = 0.95,
  conf.type = "perc", ...)

Arguments

object	the object for which the summary information should be returned.
conf.level	the level of the returned confidence intervals.
...	ignored.
conf.type	the type of the returned confidence interval (see boot.ci for the meaning of this parameter).

---