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

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

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

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)

• bootcoefs(complmrob): For robust linear regression models with compositional data

• bootcoefs(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

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

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

Methods (by class)

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

• confint(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")

(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

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

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

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

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

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