Version: 1.0.7
Date: 2024-09-26
Title: Robust Analysis using Forward Search
Maintainer: Ken Beath <ken@kjbeath.id.au>
Depends: R (≥ 3.5), MASS
Description: Robust analysis using forward search in linear and generalized linear regression models, as described in Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer.
License: GPL-2
NeedsCompilation: no
Packaged: 2024-09-27 05:06:13 UTC; kenbeath
Author: Kjell Konis [aut], Marco Riani [aut], Luca Scrucca [ctb], Ken Beath [aut, cre]
Repository: CRAN
Date/Publication: 2024-09-27 14:50:05 UTC

ar data

Description

The ar data frame has 60 rows and 4 columns.

Usage

data(ar)

Format

This data frame contains the following columns:

x1

a numeric vector

x2

a numeric vector

x3

a numeric vector

y

a numeric vector

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.2

Bliss data

Description

The bliss data frame has 8 rows and 4 columns.

Usage

data(bliss)

Format

This data frame contains the following columns:

Dose

a numeric vector

Killed

a numeric vector

Total

a numeric vector

y

a numeric vector

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.20

Calcium data

Description

Calcium uptake of cells suspended in a solution of radioactive calcium.
The calcium data frame has 27 rows and 2 columns.

Usage

data(calcium)

Format

This data frame contains the following columns:

Time

a numeric vector

y

a numeric vector

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.13

Car insurance data

Description

The carinsuk data frame has 128 rows and 5 columns.

Usage

data(carinsuk)

Format

This data frame contains the following columns:

OwnerAge

a factor with levels: 17-20, 21-24, 25-29, 30-34, 35-39, 40-49, 50-59, 60+

Model

a factor with levels: A, B, C, D

CarAge

a factor with levels: 0-3, 10+, 4-7, 8-9

NClaims

a numeric vector

AvCost

a numeric vector

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.16

n-Pentane data

Description

Reaction rate for Catalytic Isomerization of n-Pentane to Isopentane
The carr data frame has 24 rows and 4 columns.

Usage

data(carr)

Format

This data frame contains the following columns:

hydrogen

partial pressure of hydrogen

npentane

partial pressure of n-pentane

isopentane

partial pressure of iso-pentane

rate

rate of disappearance of n-pentane

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.15

Cellular differentiation data

Description

The cellular data frame has 16 rows and 3 columns.

Usage

data(cellular)

Format

This data frame contains the following columns:

TNF

Dose of TNF (U/ml)

IFN

Dose of IFN (U/ml)

y

Number of cells differentiating

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.19

Chapman data

Description

The chapman data frame has 200 rows and 7 columns.

Usage

data(chapman)

Format

This data frame contains the following columns:

age

a numeric vector

highbp

a numeric vector

lowbp

a numeric vector

chol

a numeric vector

height

a numeric vector

weight

a numeric vector

y

a numeric vector

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.24

British Train Accidents.

Description

These data are obtained from Atkinson and Riani (2000), which is a simplified version of the data in Evans (2000). The outcome is the number of deaths that occurred in a train accident with a categorical covariate describing the type of rolling stock, and an exposure variable giving the annual distance travelled by trains in that year, and was originally analysed using a Poisson model. As the data does not include observations with zero deaths, it will be analysed here as a zero-truncated Poisson with an offset of log of the train distance. The derailme data frame has 67 rows and 5 columns.

Usage

data(derailme)

Format

This data frame contains the following columns:

Month

Month of accident

Year

Year of accident

Type

Type of rolling stock 1=Mark 1 train, 2=Post-Mark 1 train, 3=Non-passenger

TrainKm

Amount of traffic on the railway system (billions of train km)

y

Number of deaths that occurred in the train accident

Source

Atkinson and Riani (2000)

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.18

Evans, A. W. (2000). Fatal train accidents on Britain's mainline railways. Journal Royal Statistical Society A, 163(1), 99-119.

Dialectric data

Description

The dialectric data frame has 128 rows and 3 columns.

Usage

data(dialectric)

Format

This data frame contains the following columns:

time

Time (weeks)

temp

Temperature (degrees Celsius)

y

dialectric breakdown strength in kilovolts

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.17

Generate all combinations of elements of x taken m at a time

Description

Generate all combinations of the elements of x taken m at a time. If x is a positive integer, returns all combinations of the elements of seq(x) taken m at a time. If argument fun is not null, applies a function given by the argument to each point. If simplify is FALSE, returns a list; else returns a vector or an array. Optional arguments ... are passed unchanged to the function given by argument fun, if any.

Usage

fwd.combn(x, m, fun = NULL, simplify = TRUE, ...)
fwd.nCm(n, m, tol = 1e-08)

Arguments

x

a vector or a single value.

n

a positive integer.

m

a positive integer.

fun

a function to be applied to each combination.

simplify

logical, if TRUE returns a vector or an array, otherwise a list.

tol

optional, tolerance value.

...

optional arguments passed to fun.

Value

Returns a vector or an array if simplify = TRUE, otherwise a list.

Note

Renamed by Kjell Konis for inclusion in the Forward Library 11/2002

Author(s)

Scott Chasalow

References

Nijenhuis, A. and Wilf, H.S. (1978) Combinatorial Computers and Calculators. NY: Academic Press.

Examples

fwd.combn(letters[1:4], 2)
fwd.combn(10, 5, min)      # minimum value in each combination
# Different way of encoding points:
fwd.combn(c(1,1,1,1,2,2,2,3,3,4), 3, tabulate, nbins = 4)
# Compute support points and (scaled) probabilities for a
# Multivariate-Hypergeometric(n = 3, N = c(4,3,2,1)) p.f.:
table(t(fwd.combn(c(1,1,1,1,2,2,2,3,3,4), 3, tabulate, nbins=4)))

Forward Search in Generalized Linear Models

Description

This function applies the forward search approach to robust analysis in generalized linear models.

Usage

fwdglm(formula, family, data, weights, na.action, contrasts = NULL, bsb = NULL, 
       balanced = TRUE, maxit = 50, epsilon = 1e-06, nsamp = 100, trace = TRUE)

Arguments

formula

a symbolic description of the model to be fit. The details of the model are the same as for glm.

family

a description of the error distribution and link function to be used in the model. See family for details.

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment from which the function is called.

weights

an optional vector of weights to be used in the fitting process.

na.action

a function which indicates what should happen when the data contain NA's. The default is set by the na.action setting of options, and is na.fail if that is unset. The default is na.omit.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

bsb

an optional vector specifying a starting subset of observations to be used in the forward search. By default the "best" starting subset is chosen using the function lmsglm with control arguments provided by nsamp.

balanced

logical, for a binary response if TRUE the proportion of successes on the full dataset is approximately balanced during the forward search algorithm.

maxit

integer giving the maximal number of IWLS iterations. See glm.control for details.

epsilon

positive convergence tolerance epsilon. See glm.control for details.

nsamp

the initial subset for the forward search in generalized linear models is found by the function lmsglm. This argument allows to control how many subsets are used in the robust fitting procedure. The choices are: the number of samples (100 by the default) or "all". Note that the algorithm tries to find nsamp good subsets or a maximum of 2*nsamp subsets.

trace

logical, if TRUE a message is printed for every ten iterations completed during the forward search.

Value

The function returns an object of class "fwdglm" with the following components:

call

the matched call.

Residuals

a (n x (n-p+1)) matrix of residuals.

Unit

a matrix of units added (to a maximum of 5 units) at each step.

included

a list with each element containing a vector of units included at each step of the forward search.

Coefficients

a ((n-p+1) x p) matrix of coefficients.

tStatistics

a ((n-p+1) x p) matrix of t statistics for the coefficients, i.e. coef.est/SE(coef.est).

Leverage

a (n x (n-p+1)) matrix of leverage values.

MaxRes

a ((n-p) x 2) matrix of max deviance residuals in the best subsets and m-th deviance residuals.

MinDelRes

a ((n-p-1) x 2) matrix of minimum deviance residuals out of best subsets and (m+1)-th deviance residuals.

ScoreTest

a ((n-p) x 1) matrix of score test statistics for a goodness of link test.

Likelihood

a ((n-p) x 4) matrix with columns containing: deviance, residual deviance, psuedo R^2 (computed as 1-deviance/null.deviance), dispersion parameter (computed as \sum(pearson.residuals^2)/(m - p)).

CookDist

a ((n-p) x 1) matrix of forward Cook's distances.

ModCookDist

a ((n-p) x 5) matrix of forward modified Cook's distances for the units (to a maximum of 5 units) included at each step.

Weights

a (n x (n-p)) matrix of weights used at each step of the forward search.

inibsb

a vector giving the best starting subset chosen by lmsglm.

binary.response

logical, equal to TRUE if binary response.

Author(s)

Originally written for S-Plus by: Kjell Konis kkonis@insightful.com and Marco Riani mriani@unipr.it
Ported to R by Luca Scrucca luca@stat.unipg.it

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Chapter 6.

See Also

summary.fwdglm, plot.fwdglm, fwdlm, fwdsco.

Examples

 
data(cellular)
cellular$TNF <- as.factor(cellular$TNF)
cellular$IFN <- as.factor(cellular$IFN)
mod <- fwdglm(y ~ TNF + IFN, data=cellular, family=poisson(log), nsamp=200)
summary(mod)
## Not run: plot(mod)
plot(mod, 1)
plot(mod, 5)
plot(mod, 6, ylim=c(-3, 20))
plot(mod, 7)
plot(mod, 8)

Forward Search in Linear Regression

Description

This function applies the forward search approach to robust analysis in linear regression models.

Usage

fwdlm(formula, data, nsamp = "best", x = NULL, y = NULL, intercept = TRUE, 
      na.action, trace = TRUE)

Arguments

formula

a symbolic description of the model to be fit. The details of the model are the same as for lm.

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment from which the function is called.

nsamp

the initial subset for the forward search in linear regression is found by fitting the regression model with the R function lmsreg. This argument allows to control how many subsets are used in the Least Median of Squares regression. The choices are: the number of samples or "best" (the default) or "exact" or "sample". For details see lmsreg.

x

A matrix of predictors values (if no formula is provided).

y

A vector of response values (if no formula is provided).

intercept

Logical for the inclusion of the intercept (if no formula is provided).

na.action

a function which indicates what should happen when the data contain NA's. The default is set by the na.action setting of options, and is na.fail if that is unset. The default is na.omit.

trace

logical, if TRUE a message is printed for every ten iterations completed during the forward search.

Value

The function returns an object of class "fwdlm" with the following components:

call

the matched call.

Residuals

a (n \times (n-p+1)) matrix of residuals.

Unit

a matrix of units added (to a maximum of 5 units) at each step.

included

a list with each element containing a vector of units included at each step of the forward search.

Coefficients

a ((n-p+1) \times p) matrix of coefficients.

tStatistics

a ((n-p+1) \times p) matrix of t statistics for the coefficients.

CookDist

a ((n-p) \times 1) matrix of forward Cook's distances.

ModCookDist

a ((n-p) \times 5) matrix of forward modified Cook's distances for the units (to a maximum of 5 units) included at each step.

Leverage

a (n \times (n-p+1)) matrix of leverage values.

S2

a ((n-p+1) \times 2) matrix with 1st column containing S^2 and the 2nd column R^2.

MaxRes

a ((n-p) \times 1) matrix of max studentized residuals.

MinDelRes

a ((n-p-1) \times 1) matrix of minimum deletion residuals.

StartingModel

a "lqs" object providing the the Least Median of Squares regression fit used to select the starting subset.

Author(s)

Originally written for S-Plus by: Kjell Konis kkonis@insightful.com and Marco Riani mriani@unipr.it
Ported to R by Luca Scrucca luca@stat.unipg.it

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Chapters 2-3.

See Also

summary.fwdlm, plot.fwdlm, fwdsco, fwdglm, lmsreg.

Examples

library(MASS)
data(forbes)
plot(forbes, xlab="Boiling point", ylab="Pressure)")
mod <- fwdlm(100*log10(pres) ~ bp, data=forbes)
summary(mod)
## Not run: plot(mod)
plot(mod, 1)
plot(mod, 6, ylim=c(-3, 1000))

Forward Search Transformation in Linear Regression

Description

This function applies the forward search approach to the Box-Cox transformation of response in linear regression models.

Usage

fwdsco(formula, data, nsamp = "best", lambda = c(-1, -0.5, 0, 0.5, 1), 
       x = NULL, y = NULL, intercept = TRUE, na.action, trace = TRUE)

Arguments

formula

a symbolic description of the model to be fit. The details of the model are the same as for lm.

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment from which the function is called.

nsamp

the initial subset for the forward search in linear regression is found by fitting the regression model with the R function lmsreg. This argument allows to control how many subsets areused in the Least Median of Squares regression. The choices are: the number of samples or "best" (the default) or "exact" or "sample". For details see lmsreg.

lambda

a vector (or a single numerical value) of lambda values for the response transformation.

x

A matrix of predictors values (if no formula is provided).

y

A vector of response values (if no formula is provided).

intercept

Logical for the inclusion of the intercept (if no formula is provided).

na.action

a function which indicates what should happen when the data contain NA's. The default is set by the na.action setting of options, and is na.fail if that is unset. The default is na.omit.

trace

logical, if TRUE a message is printed for every ten iterations completed during the forward search.

Value

The function returns an object of class"fwdsco" with the following components:

call

the matched call.

Likelihood

a ((n-p+1) x n.lambda) matrix of likelihood values.

ScoreTest

a ((n-p+1) x n.lambda) matrix of score test statistic values.

Unit

a list with an element for each lambda values. Each element provides a matrix of units added (to a maximum of 5 units) at each step of the forward search.

Input

a list with n, p and the vector of lambda values used.

x

The design matrix.

y

The vector for the response.

Author(s)

Originally written for S-Plus by: Kjell Konis kkonis@insightful.com and Marco Riani mriani@unipr.it
Ported to R by Luca Scrucca luca@stat.unipg.it

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Chapter 4.

See Also

summary.fwdsco, plot.fwdsco, fwdlm, fwdglm.

Examples

data(wool)
mod <- fwdsco(y ~ x1 + x2 + x3, data = wool)
summary(mod)
plot(mod, plot.mle=FALSE)
plot(mod, plot.Sco=FALSE, plot.Lik=TRUE)

Hawkins' data

Description

The hawkins data frame has 128 rows and 9 columns.

Usage

data(hawkins)

Format

This data frame contains the following columns:

x1

a numeric vector

x2

a numeric vector

x3

a numeric vector

x4

a numeric vector

x5

a numeric vector

x6

a numeric vector

x7

a numeric vector

x8

a numeric vector

y

a numeric vector

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.4

Kinetics data

Description

Kinetics data (from Becton-Dickenson)
The kinetics data frame has 19 rows and 5 columns.

Usage

data(kinetics)

Format

This data frame contains the following columns:

Substrate

substrate indicator

I0

Inhibitor concentration

I3

Inhibitor concentration

I10

Inhibitor concentration

I30

Inhibitor concentration

y

initial velocity

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.12

Lakes data

Description

The lakes data frame has 29 rows and 3 columns.

Usage

data(lakes)

Format

This data frame contains the following columns:

NIN

average influent nitrogenon concentration

TW

water retention time

TN

mean annual nitrogen concentration

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.14

Pine data

Description

The leafpine data frame has 70 rows and 3 columns.

Usage

data(leafpine)

Format

This data frame contains the following columns:

girth

girth

height

height

volume

volume

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.10

Forward Search in Generalized Linear Models

Description

This function computes the Least Median Square robust fit for generalized linear models using deviance residuals.

Usage

lmsglm(x, y, family, weights, offset, n.samples = 100, max.samples = 200,
    epsilon = 1e-04, maxit = 50, trace = FALSE)

Arguments

x

a matrix or data frame containing the explanatory variables.

y

the response: a vector of length the number of rows of x.

family

a description of the error distribution and link function to be used in the model. See family for details.

weights

an optional vector of weights to be used in the fitting process.

offset

optional, a priori known component to be included in the linear predictor during fitting.

n.samples

number of good subsets to fit. It can be a numeric value or "all".

max.samples

maximal number of subsets to fit. By default is set to twice n.samples.

epsilon

positive convergence tolerance epsilon. See glm.control for details.

maxit

integer giving the maximal number of IWLS iterations. See glm.control for details.

trace

logical, if TRUE a message is printed for every ten iterations completed during the search.

Details

This function is used by fwdglm to select the starting subset for the forward search. For this reason, users do not generally need to use it.

Value

The function returns a list with the following components:

bsb

a vector giving the best subset found

dev.res

a vector giving the deviance residuals for all the observations

message

a short message about the status of the algorithm

model

the model provided by glm.fit using the units in the best subset found

Author(s)

Originally written for S-Plus by: Kjell Konis kkonis@insightful.com and Marco Riani mriani@unipr.it
Ported to R by Luca Scrucca luca@stat.unipg.it

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Chapter 6.

See Also

fwdglm, fwdlm, lmsreg, fwdsco.

Mice data

Description

The mice data frame has 14 rows and 4 columns.

Usage

data(mice)

Format

This data frame contains the following columns:

dose

dose level

prep

factor preparation: 0= Standard preparation, 1= Test preparation

conv

number with convultion

total

Total

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.21

Molar data

Description

Radioactivity versus molar concentration of nifedipene
The molar data frame has 15 rows and 2 columns.

Usage

data(molar)

Format

This data frame contains the following columns:

x

log10(NIF concentration)

y

Total counts for 5 \times 10^-10 Molar NTD additive

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.1

Mussels data

Description

The mussels data frame has 82 rows and 5 columns.

Usage

data(mussels)

Format

This data frame contains the following columns:

W

width

H

height

L

length

S

shell mass

M

mass

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.9

Ozone data

Description

Ozone concentration at Upland, CA.
The ozone data frame has 80 rows and 9 columns.

Usage

data(ozone)

Format

This data frame contains the following columns:

x1

a numeric vector

x2

a numeric vector

x3

a numeric vector

x4

a numeric vector

x5

a numeric vector

x6

a numeric vector

x7

a numeric vector

x8

a numeric vector

y

Ozone concentration (ppm)

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.7

Forward Search in Generalized Linear Models

Description

This function plots the results of a forward search analysis in generalized linear models.

Usage

## S3 method for class 'fwdglm'
plot(x, which.plots = 1:11, squared = FALSE, scaled =FALSE, 
     ylim = NULL, xlim = NULL, th.Res = 4, th.Lev = 0.25, sig.Tst =2.58, 
     sig.score = 1.96, plot.pf = FALSE, labels.in.plot = TRUE, ...)

Arguments

x

a "fwdglm" object.

which.plots

select which plots to draw, by default all. Each graph is addressed by an integer:

  1. deviance residuals

  2. leverages

  3. maximum deviance residuals

  4. minimum deviance residuals

  5. coefficients

  6. t statistics, i.e. coef.est/SE(coef.est)

  7. likelihood matrix: deviance, deviance explained, pseudo R-squared, dispersion parameter

  8. score statistic for the goodness of link test

  9. forward Cook's distances

  10. modified forward Cook's distances

  11. weights used at each step of the forward search for the units included

squared

logical, if TRUE plots squared deviance residuals.

scaled

logical, if TRUE plots scaled coefficient estimates.

ylim

a two component vector for the min and max of the y axis.

xlim

a two component vector for the min and max of the x axis.

th.Res

numerical, a threshold for labelling the residuals.

th.Lev

numerical, a threshold for labelling the leverages.

sig.Tst

numerical, a value used to draw the confidence interval on the plot of the t statistics.

sig.score

numerical, a value used to draw the confidence interval on the plot of the score test statistic.

plot.pf

logical, in case of binary response if TRUE graphs contain all the step of the forward search, otherwise only those in which there is no perfect fit.

labels.in.plot

logical, if TRUE units are labelled in the plots when required.

...

further arguments passed to or from other methods.

Author(s)

Originally written for S-Plus by: Kjell Konis kkonis@insightful.com and Marco Riani mriani@unipr.it
Ported to R by Luca Scrucca luca@stat.unipg.it

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Chapter 6.

See Also

fwdglm, fwdlm, fwdsco.

Examples

 
## Not run: 
data(cellular)
mod <- fwdglm(y ~ as.factor(TNF) + as.factor(IFN), data=cellular, 
              family=poisson(log), nsamp=200)
summary(mod)
plot(mod)

## End(Not run)

Forward Search in Linear Regression

Description

This function plots the results of a forward search analysis in linear regression models.

Usage

## S3 method for class 'fwdlm'
plot(x, which.plots = 1:10, squared = FALSE, scaled = TRUE, 
     ylim = NULL, xlim = NULL, th.Res = 2, th.Lev = 0.25, sig.Tst = 2.58, 
     labels.in.plot = TRUE, ...)

Arguments

x

a "fwdlm" object.

which.plots

select which plots to draw, by default all. Each graph is addressed by an integer:

  1. scaled residuals

  2. leverages

  3. maximum studentized residuals

  4. minimum deletion residuals

  5. coefficients

  6. statistics

  7. forward Cook's distances

  8. modified forward Cook's distances

  9. S^2 values

  10. R^2 values

squared

logical, if TRUE plots squared residuals.

scaled

logical, if TRUE plots scaled coefficient estimates.

ylim

a two component vector for the min and max of the y axis.

xlim

a two component vector for the min and max of the x axis.

th.Res

numerical, a threshold for labelling the residuals.

th.Lev

numerical, a threshold for labelling the leverages.

sig.Tst

numerical, a value (on the scale of the t statistics) used to draw the confidence interval on the plot of the t statistics.

labels.in.plot

logical, if TRUE units are labelled in the plots when required.

...

further arguments passed to or from other methods.

Author(s)

Originally written for S-Plus by: Kjell Konis kkonis@insightful.com and Marco Riani mriani@unipr.it
Ported to R by Luca Scrucca luca@stat.unipg.it

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Chapters 2-3.

See Also

fwdlm, fwdsco, fwdglm.

Examples

library(MASS)
data(forbes)
plot(forbes)
mod <- fwdlm(100*log10(pres) ~ bp, data=forbes)
summary(mod)
## Not run: plot(mod)

Forward Search Transformation in Linear Regression

Description

This function plots the results of a forward search analysis for Box-Cox transformation of response in linear regression models.

Usage

## S3 method for class 'fwdsco'
plot(x, plot.Sco = TRUE, plot.Lik = FALSE, th.Sco = 2.58, 
      plot.mle = TRUE, ylim = NULL, xlim = NULL, ...)

Arguments

x

a "fwdsco" object.

plot.Sco

logical, if TRUE plots the score test statistic at each step of the forward search for each lambda value.

plot.Lik

logical, if TRUE plots the likelihood value at each step of the forward search for each lambda value.

th.Sco

numerical, a value used to draw the confidence interval on the plot of the score test statistic.

plot.mle

logical, if TRUE adds a point at the maximum likelihood value for the transformation computed in the final step, i.e. on the full dataset.

ylim

a two component vector for the min and max of the y axis.

xlim

a two component vector for the min and max of the x axis.

...

further arguments passed to or from other methods.

Author(s)

Originally written for S-Plus by: Kjell Konis kkonis@insightful.com and Marco Riani mriani@unipr.it
Ported to R by Luca Scrucca luca@stat.unipg.it

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Chapters 2-3.

See Also

fwdsco, fwdlm, fwdglm.

Examples

## Not run: 
data(wool)
mod <- fwdsco(y ~ x1 + x2 + x3, data = wool)
plot(mod, plot.mle=FALSE)
plot(mod, plot.Sco=FALSE, plot.Lik=TRUE)

## End(Not run)

Poison data

Description

Box and Cox poison data. Survival times in 10 hour units of animals in a 3 \times 4 factorial experiment.
The poison data frame has 48 rows and 3 columns.

Usage

data(poison)

Format

This data frame contains the following columns:

time

a numeric vector

poison

a factor

treat

a factor with levels: A, B, C, D

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.8

Rainfall data

Description

Toxoplasmosis data.
The rainfall data frame has 34 rows and 3 columns.

Usage

data(rainfall)

Format

This data frame contains the following columns:

Rain

mm of rain

Cases

cases of toxoplasmosis

Total

total

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.22

Salinity data

Description

The salinity data frame has 28 rows and 4 columns.

Usage

data(salinity)

Format

This data frame contains the following columns:

lagsalinity

Lagged salinity

trend

Trend

waterflow

Water flow

salinity

Salinity

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.6

Goodness of Link Test in GLM

Description

Computes the score test statistic for the goodness of link test in generalized linear models.

Usage

scglm(x, y, family, weights, beta, phi = 1, offset)

Arguments

x

a matrix or data frame containing the explanatory variables.

y

the response: a vector of length the number of rows of x.

family

a description of the error distribution and link function to be used in the model. See family for details.

weights

an optional vector of weights to be used in the fitting process.

beta

a vector of coefficients estimates

phi

the dispersion parameter

offset

optional, a priori known component to be included in the linear predictor during fitting.

Details

See pag. 200–201 of Atkinson and Riani (2000).

Value

Return the value of the score test statistic.

Author(s)

Originally written for S-Plus by: Kjell Konis kkonis@insightful.com and Marco Riani mriani@unipr.it
Ported to R by Luca Scrucca luca@stat.unipg.it

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Chapter 6.

See Also

fwdglm, fwdlm, score.s.

Score test for the Box-Cox transformation of the response

Description

Computes the approximate score test statistic for the Box-Cox transformation

Usage

score.s(x, y, la, tol = 1e-20)
lambda.mle(x, y, init = c(-2, 2), tol = 1e-04)

Arguments

x

a matrix or data frame containing the explanatory variables.

y

the response: a vector of length the number of rows of x.

la

the value of the lambda parameter.

tol

tolerance value used to check for full rank matrix.

init

range of values to search for MLE.

Details

See pag. 82–86 of Atkinson and Riani (2000).

Value

Return a list with two components:

Score

the value of the score test statistic

Likelihood

the value of the likelihood

Author(s)

Originally written for S-Plus by: Kjell Konis kkonis@insightful.com and Marco Riani mriani@unipr.it
Ported to R by Luca Scrucca luca@stat.unipg.it

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Chapter 4.

See Also

fwdsco, fwdlm, fwdglm.

Stackloss data

Description

Brownlee?s stack loss data.
The stackloss data frame has 21 rows and 4 columns.

Usage

data(stackloss)

Format

This data frame contains the following columns:

Air

Air flow

Temp

Cooling water inlet temperature

Conc

Acid concentration

Loss

Stack loss

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.5

Summarizing Fit of Forward Search in Generalized Linear Regression

Description

summary method for class "fwdglm".

Usage

## S3 method for class 'fwdglm'
summary(object, steps = "auto", remove.perfect.fit = TRUE, ...)

Arguments

object

an object of class "fwdglm".

steps

the number of forward steps to show.

remove.perfect.fit

logical, controlling if perfect fit steps should be removed (only apply to binary responses).

...

further arguments passed to or from other methods.

Author(s)

Originally written for S-Plus by: Kjell Konis kkonis@insightful.com and Marco Riani mriani@unipr.it
Ported to R by Luca Scrucca luca@stat.unipg.it

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Chapter 6.

See Also

fwdglm.

Summarizing Fit of Forward Search in Linear Regression

Description

summary method for class "fwdlm".

Usage

## S3 method for class 'fwdlm'
summary(object, steps = "auto", ...)

Arguments

object

an object of class "fwdlm".

steps

the number of forward steps to show.

...

further arguments passed to or from other methods.

Author(s)

Originally written for S-Plus by: Kjell Konis kkonis@insightful.com and Marco Riani mriani@unipr.it
Ported to R by Luca Scrucca luca@stat.unipg.it

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Chapters 2-3.

See Also

fwdlm.

Summarizing Fit of Forward Search Transformation in Linear Regression

Description

summary method for class "fwdsco".

Usage

## S3 method for class 'fwdsco'
summary(object, steps = "auto", lambdaMLE = FALSE, ...)

Arguments

object

an object of class "fwdsco".

steps

the number of forward steps to show.

lambdaMLE

logical, controlling if the MLE of lambda calculated on the full dataset must be be shown.

...

further arguments passed to or from other methods.

Author(s)

Originally written for S-Plus by: Kjell Konis kkonis@insightful.com and Marco Riani mriani@unipr.it
Ported to R by Luca Scrucca luca@stat.unipg.it

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Chapter 4.

See Also

fwdsco.

Vaso data

Description

Finney's data on vaso-contriction in the skin of the digits.
The vaso data frame has 39 rows and 3 columns.

Usage

data(vaso)

Format

This data frame contains the following columns:

volume

volume

rate

rate

y

response: 0= nonoccurrence, 1= occurrence

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.23

Wool data

Description

Number of cycles to failure of samples of worsted yarn in a 33 experiment.
The wool data frame has 27 rows and 4 columns.

Usage

data(wool)

Format

This data frame contains the following columns:

x1

factor levels: -1, 0, 1

x2

factor levels: -1, 0, 1

x3

factor levels: -1, 0, 1

y

cycles to failure a numeric vector

References

Atkinson, A.C. and Riani, M. (2000), Robust Diagnostic Regression Analysis, First Edition. New York: Springer, Table A.3