Type: Package
Title: Obtain Alpha-Outlier Regions for Well-Known Probability Distributions
Version: 1.2.0
Date: 2016-09-09
Author: Andre Rehage, Sonja Kuhnt
Maintainer: Andre Rehage <rehage@statistik.tu-dortmund.de>
Description: Given the parameters of a distribution, the package uses the concept of alpha-outliers by Davies and Gather (1993) to flag outliers in a data set. See Davies, L.; Gather, U. (1993): The identification of multiple outliers, JASA, 88 423, 782-792, <doi:10.1080/01621459.1993.10476339> for details.
License: GPL-3
Depends: Rsolnp, nleqslv, quantreg, graphics
Imports: stats
NeedsCompilation: no
Packaged: 2016-09-09 12:55:15 UTC; rehage
Repository: CRAN
Date/Publication: 2016-09-09 18:05:11

Obtain \alpha-outlier regions for well-known probability distributions

Description

Given the parameters of a distribution, the package uses the concept of \alpha-outliers by Davies and Gather (1993) to flag outliers in a data set.

Details

The structure of the package is as follows: aout.[Distribution] is the name of the function which returns the \alpha-outlier region of a random variable following [Distribution]. The names of the distributions are abbreviated as in the d, p, q, r functions. Use pre-specified or robustly estimated parameters from your data to obtain reasonable results. The sample size should be taken into account when choosing alpha, for example Gather et al. (2003) propose \alpha_N = 1 - (1 - \alpha)^{1/N}.

Author(s)

A. Rehage, S. Kuhnt

References

Davies, L.; Gather, U. (1993) The identification of multiple outliers, Journal of the American Statistical Association, 88 423, 782-792.

Gather, U.; Kuhnt, S.; Pawlitschko, J. (2003) Concepts of outlyingness for various data structures. In J. C. Misra (Ed.): Industrial Mathematics and Statistics. New Delhi: Narosa Publishing House, 545-585.

See Also

nleqslv, solnp, rq.fit.fnc

Examples


iris.setosa <- iris[1:51, 4]
aout.norm(data = iris.setosa, param = c(mean(iris.setosa), sd(iris.setosa)), alpha = 0.01)
aout.pois(data = warpbreaks[,1], param = mean(warpbreaks[,1]), alpha = 0.01, 
          hide.outliers = TRUE)

Find \alpha-outliers in Binomial data

Description

Given the parameters of a Binomial distribution, aout.binom identifies \alpha-outliers in a given data set.

Usage

aout.binom(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

data

a vector. The data set to be examined.

param

a vector. Contains the parameters of the Binomial distribution, N and p.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

See Also

dbinom

Examples

data(uis)
medbeck <- median(uis$BECK) 
aout.binom(data = uis$BECK, param = c(54, medbeck/54), alpha = 0.001)

Find \alpha-outliers in conditional Gaussian data

Description

Given the parameters of a conditional Gaussian distribution, aout.cg identifies \alpha-outliers in a given data set.

Usage

aout.cg(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

data

a matrix. First column: Class of the value, coded with an integer between 1 and d, where d is the number of classes. Second column: The value as a realization of a univariate normal with parameters \mu and \sigma. The data set to be examined.

param

a list with three elements: p: d-dimensional vector of probabilities of the classes. mu: d-dimensional vector of univariate mean values of each class. sigma: d-dimensional vector of univariate standard errors of each class

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a data frame of the outlier-free data.

Author(s)

A. Rehage

References

Edwards, D. (2000) Introduction to Graphical Modelling. 2nd edition, Springer, New York.

Kuhnt, S.; Rehage, A. (2013) The concept of \alpha-outliers in structured data situations. In C. Becker, R. Fried, S. Kuhnt (Eds.): Robustness and Complex Data Structures. Festschrift in Honour of Ursula Gather. Berlin: Springer, 91-108.

Examples

# Rats' weights data example taken from Edwards (2000)
ratweight <- cbind(Drug = c(1, 1, 2, 3, 1, 1, 2, 3, 1, 2, 3, 3, 1, 2, 2, 3, 1, 
                            2, 2, 3, 1, 2, 3, 3), 
                   Week1 = c(5, 7, 9, 14, 7, 8, 7, 14, 9, 7, 21, 12, 5, 7, 6, 
                             17, 6, 10, 6, 14, 9, 8, 16, 10))
aout.cg(ratweight, 
        list(p = c(1/3, 1/3, 1/3), mu = c(7, 7, 14), sigma = c(1.6, 1.4, 3.3)))

Find \alpha-outliers in \chi^2 data

Description

Given the parameters of a \chi^2 distribution, aout.chisq identifies \alpha-outliers in a given data set.

Usage

aout.chisq(data, param, alpha = 0.1, hide.outliers = FALSE, ncp = 0, lower = auto.l,
           upper = auto.u, method.in = "Newton", global.in = "gline", 
           control.in = list(sigma = 0.1, maxit = 1000, xtol = 1e-12, 
                             ftol = 1e-12, btol = 1e-04))

Arguments

data

a vector. The data set to be examined.

param

an atomic vector. Contains the degrees of freedom of the \chi^2 distribution.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

ncp

an atomic vector. Determines the non-centrality parameter of the \chi^2 distribution. Defaults to 0.

lower

an atomic vector. First element of x from nleqslv.

upper

an atomic vector. Second element of x from nleqslv.

method.in

See method in nleqslv.

global.in

See global in nleqslv.

control.in

See control in nleqslv.

Details

The \alpha-outlier region of a \chi^2 distribution is generally not available in closed form or via the tails, such that a non-linear equation system has to be solved.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

See Also

dchisq

Examples

aout.chisq(chisq.test(occupationalStatus)$statistic, 49)

Find \alpha-outliers in two-way contingency tables

Description

This is a wrapper function for aout.pois. We assume that each entry of a contingency table can be seen as a realization of a Poisson random variable. The parameter \lambda of each cell can either be set by the user or estimated. Given the parameters, aout.conttab identifies \alpha-outliers in a given contingency table.

Usage

aout.conttab(data, param, alpha = 0.1, hide.outliers = FALSE, show.estimates = FALSE)

Arguments

data

a matrix or data.frame. The contingency table to be examined.

param

a character string from c("ML", "L1", "MP") or a vector containing the parameters of each cell of the Poisson distribution: \lambda. "ML" yields the maximum likelihood estimate from the log-linear Poisson model using a suitable design matrix. "L1" yields the L1-estimate from rq.fit.fnc. "MP" yields the Median Polish estimate. If the parameter vector is given by the user, it is necessary that the contingency table was filled byrow = FALSE.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

show.estimates

boolean. Returns \hat{\lambda} for each cell if set to TRUE. Defaults to FALSE.

Value

Data frame of the vectorized input data and, if desired, an index named is.outlier that flags the outliers with TRUE and a vector named param containing the estimated lambdas.

Author(s)

A. Rehage

References

Kuhnt, S. (2000) Ausreisseridentifikation im Loglinearen Poissonmodell fuer Kontingenztafeln unter Einbeziehung robuster Schaetzer. Ph.D. Thesis. Universitaet Dortmund, Dortmund. Fachbereich Statistik.

Kuhnt, S.; Rapallo, F.; Rehage, A. (2014) Outlier detection in contingency tables based on minimal patterns. Statistics and Computing 24 (3), 481-491.

See Also

rq.fit.fnc, aout.pois

Examples

aout.conttab(data = HairEyeColor[,,1], param = "L1", alpha = 0.01, show.estimates = TRUE)
aout.conttab(data = HairEyeColor[,,1], param = "ML", alpha = 0.01, show.estimates = TRUE)

Find \alpha-outliers in exponentially distributed data

Description

Given the parameters of an exponential distribution, aout.exp identifies \alpha-outliers in a given data set.

Usage

aout.exp(data, param, alpha = 0.1, hide.outliers = FALSE, theta = 0)

Arguments

data

a vector. The data set to be examined.

param

an atomic vector. Contains the parameter of the exponential distribution.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

theta

an atomic vector. Determines the lower bound of the support of the exponential distribution. Defaults to 0.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

References

Gather, U.; Kuhnt, S.; Pawlitschko, J. (2003) Concepts of outlyingness for various data structures. In J. C. Misra (Ed.): Industrial Mathematics and Statistics. New Delhi: Narosa Publishing House, 545-585.

See Also

dexp

Examples

aout.exp(attenu[,5], median(attenu[,5]), alpha = 0.05)

Find \alpha-outliers in data from the family of g-and-h distributions

Description

Given the parameters of a g-and-h distribution, aout.gandh identifies \alpha-outliers in a given data set.

Usage

aout.gandh(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

data

a vector. The data set to be examined.

param

a vector. Contains the parameters of the g-and-h distribution: median, scale, g, h.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

Details

The concept of \alpha-outliers is based on the p.d.f. of the random variable. Since for g-and-h distributions this does not exist in closed form, the computation of the outlier region is based on an optimization of the quantile function with side conditions.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Note

Makes use of solnp.

Author(s)

A. Rehage

References

Xu, Y.; Iglewicz, B.; Chervoneva, I. (2014) Robust estimation of the parameters of g-and-h distributions, with applications to outlier detection. Computational Statistics and Data Analysis 75, 66-80.

Examples

durations <- faithful$eruptions
aout.gandh(durations, c(4.25, 1.14, 0.05, 0.05), alpha = 0.1)

Find \alpha-outliers in hypergeometric data

Description

Given the parameters of a hypergeometric distribution, aout.hyper identifies \alpha-outliers in a given data set.

Usage

aout.hyper(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

data

a vector. The data set to be examined.

param

a vector. Contains the parameters of the hypergeometric distribution: m, n, k.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

See Also

Hypergeometric

Examples

set.seed(1)
lotto6aus49 <- rhyper(100, 6, 43, 6) 
aout.hyper(lotto6aus49, c(6, 43, 6), 0.1)

Find \alpha-outliers in arbitrary univariate data using kernel density estimation

Description

Given the arguments of the density, aout.kernel identifies \alpha-outliers in a given data set.

Usage

aout.kernel(data, alpha, plot = TRUE, plottitle = "", kernel = "gaussian", 
nkernel = 1024, kern.bw = "SJ", kern.adj = 1, 
xlim = NA, ylim = NA, outints = FALSE, w = NA, ...)

Arguments

data

a vector. The data set to be examined.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain.

plot

boolean. If TRUE, a plot of the data and estimated density with shaded outlier region is printed.

plottitle

character string. Title of the plot.

kernel

See kernel in density.

nkernel

See n in density.

kern.bw

See bw in density.

kern.adj

See adjust in density.

xlim

a vector. Specify if you want to change the x-limits of the plot.

ylim

a vector. Specify if you want to change the y-limits of the plot.

outints

boolean. If TRUE, then the bounds of the inlier-regions and the chosen bandwidth are shown.

w

a vector. See weights in density.

...

Further arguments for density and plot.

Value

If outints = TRUE, a list of

Results

A data frame containing one row for each observation. The observations are labelled whether they are outlying, the value of the estimated density at the observation is shown and the bound of the outlier identifier.

Bounds.of.Inlier.Regions

The bounds of the inlier region(s).

KDE.Chosen.Bandwidth

The bandwidth that was chosen by density.

Author(s)

A. Rehage

Examples

set.seed(23)
tempx <- rnorm(1000, 0, 1)
tempx[1] <- -2.5
aout.kernel(tempx[1:10], alpha = 0.1, kern.adj = 1, xlim = c(-3,3), outints = TRUE)
# not run:
# aout.kernel(tempx[1:200], alpha = 0.1, kern.adj = 1, xlim = c(-3,3))

Find \alpha-outliers in Laplace / double exponential data

Description

Given the parameters of a Laplace distribution, aout.laplace identifies \alpha-outliers in a given data set.

Usage

aout.laplace(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

data

a vector. The data set to be examined.

param

a vector. Contains the parameters of the Laplace distribution: \mu, \sigma.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

References

Dumonceaux, R.; Antle, C. E. (1973) Discrimination between the log-normal and the Weibull distributions. Technometrics, 15 (4), 923-926.

Gather, U.; Kuhnt, S.; Pawlitschko, J. (2003) Concepts of outlyingness for various data structures. In J. C. Misra (Ed.): Industrial Mathematics and Statistics. New Delhi: Narosa Publishing House, 545-585.

Examples

# Using the flood data from Dumonceaux and Antle (1973):
temp <- c(0.265, 0.269, 0.297, 0.315, 0.3225, 0.338, 0.379, 0.380, 0.392, 0.402,
         0.412, 0.416, 0.418, 0.423, 0.449, 0.484, 0.494, 0.613, 0.654, 0.74)
aout.laplace(temp, c(median(temp), median(abs(temp - median(temp)))), 0.05)

Find \alpha-outliers in logistic data

Description

Given the parameters of a logistic distribution, aout.logis identifies \alpha-outliers in a given data set.

Usage

aout.logis(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

data

a vector. The data set to be examined.

param

a vector. Contains the parameters of the logistic distribution: \mu, \sigma.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

References

Balakrishnan, N. (1992) Maximum likelihood estimation based on complete and type II censored samples. In N. Balakrishnan (Ed.): Handbook of the Logistic Distribution. Dekker, New York, 49-78.

Gather, U.; Kuhnt, S.; Pawlitschko, J. (2003) Concepts of outlyingness for various data structures. In J. C. Misra (Ed.): Industrial Mathematics and Statistics. New Delhi: Narosa Publishing House, 545-585.

See Also

dlogis

Examples

# Data example from Balakrishnan (1967)
lifetime <- c(785, 855, 905, 918, 919, 920, 929, 936, 948, 950)
aout.logis(lifetime, c(949.9, 63.44))

Find \alpha-outliers in multivariate normal data

Description

Given the parameters of a multivariate normal distribution, aout.mvnorm identifies \alpha-outliers in a given data set.

Usage

aout.mvnorm(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

data

a data.frame or matrix. The data set to be examined.

param

a list. Contains the parameters of the normal distribution: the mean vector \mu and the covariance matrix \sigma.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a data frame of the outlier-free data.

Author(s)

A. Rehage

References

Kuhnt, S.; Rehage, A. (2013) The concept of \alpha-outliers in structured data situations. In C. Becker, R. Fried, S. Kuhnt (Eds.): Robustness and Complex Data Structures. Festschrift in Honour of Ursula Gather. Berlin: Springer, 91-108.

See Also

dnorm

Examples

temp <- iris[1:51,-5]
temp.xq <- apply(FUN = median, MARGIN = 2, temp)
aout.mvnorm(as.matrix(temp), param = list(temp.xq, cov(temp)), alpha = 0.001)

Find \alpha-outliers in negative Binomial data

Description

Given the parameters of a negative Binomial distribution, aout.nbinom identifies \alpha-outliers in a given data set.

Usage

aout.nbinom(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

data

a vector. The data set to be examined.

param

a vector. Contains the parameters of the negative Binomial distribution: N, p.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

See Also

dnbinom, daysabs

Examples

data(daysabs)
aout.nbinom(daysabs, c(8, 0.6), 0.05)

Find \alpha-outliers in normal data

Description

Given the parameters of a normal distribution, aout.norm identifies \alpha-outliers in a given data set.

Usage

aout.norm(data, param = c(0, 1), alpha = 0.1, hide.outliers = FALSE)

Arguments

data

a vector. The data set to be examined.

param

a vector. Contains the parameters of the normal distribution: \mu, \sigma.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

References

Gather, U.; Kuhnt, S.; Pawlitschko, J. (2003) Concepts of outlyingness for various data structures. In J. C. Misra (Ed.): Industrial Mathematics and Statistics. New Delhi: Narosa Publishing House, 545-585.

See Also

dnorm

Examples

iris.setosa <- iris[1:51, 4]
# implosion breakdown point:
aout.norm(data = iris.setosa, param = c(median(iris.setosa), mad(iris.setosa)), 
          alpha = 0.01) 
# better:
aout.norm(data = iris.setosa, param = c(median(iris.setosa), sd(iris.setosa)), 
          alpha = 0.01)

Find \alpha-outliers in Pareto data

Description

Given the parameters of a Pareto distribution, aout.pareto identifies \alpha-outliers in a given data set.

Usage

aout.pareto(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

data

a vector. The data set to be examined.

param

a vector. Contains the parameters of the Pareto distribution: \lambda, \theta.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

Details

We use the Pareto distribution with Lebesgue-density f(x) = \frac{\lambda \theta^{\lambda}}{x^{\lambda + 1}}.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

References

Gather, U.; Kuhnt, S.; Pawlitschko, J. (2003) Concepts of outlyingness for various data structures. In J. C. Misra (Ed.): Industrial Mathematics and Statistics. New Delhi: Narosa Publishing House, 545-585.

See Also

citiesData

Examples

data(citiesData)
aout.pareto(citiesData[[1]], c(1.31, 14815), alpha = 0.01)

Find \alpha-outliers in Poisson count data

Description

Given the parameters of a Poisson distribution, aout.pois identifies \alpha-outliers in a given data set.

Usage

aout.pois(data, param, alpha = 0.1, hide.outliers = FALSE)

Arguments

data

a vector. The data set to be examined.

param

a vector. Contains the parameter of the Poisson distribution: \lambda.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

See Also

dpois

Examples

aout.pois(data = c(discoveries), param = median(discoveries), alpha = 0.01)

Find \alpha-outliers in Weibull data

Description

Given the parameters of a Weibull distribution, aout.weibull identifies \alpha-outliers in a given data set.

Usage

aout.weibull(data, param, alpha = 0.1, hide.outliers = FALSE, lower = auto.l, 
             upper = auto.u, method.in = "Broyden", global.in = "qline", 
             control.in = list(sigma = 0.1, maxit = 1000, xtol = 1e-12, 
                               ftol = 1e-12, btol = 1e-04))

Arguments

data

a vector. The data set to be examined.

param

a vector. Contains the parameters of the Weibull distribution: \beta, \lambda.

alpha

an atomic vector. Determines the maximum amount of probability mass the outlier region may contain. Defaults to 0.1.

hide.outliers

boolean. Returns the outlier-free data if set to TRUE. Defaults to FALSE.

lower

an atomic vector. First element of x from nleqslv.

upper

an atomic vector. Second element of x from nleqslv.

method.in

See method in nleqslv

global.in

See global in nleqslv

control.in

See control in nleqslv

Details

The \alpha-outlier region of a Weibull distribution is generally not available in closed form or via the tails, such that a non-linear equation system has to be solved.

Value

Data frame of the input data and an index named is.outlier that flags the outliers with TRUE. If hide.outliers is set to TRUE, a simple vector of the outlier-free data.

Author(s)

A. Rehage

References

Dodson, B. (2006) The Weibull Analysis Handbook. American Society for Quality, 2nd edition.

See Also

dweibull, nleqslv

Examples

# lifetime data example taken from Table 2.2, Dodson (2006)
temp <- c(12.5, 24.4, 58.2, 68.0, 69.1, 95.5, 96.6, 97.0, 
          114.2, 123.2, 125.6, 152.7)
aout.weibull(temp, c(2.25, 97), 0.1)

Population of the 999 largest German cities

Description

Population of the 999 largest German cities as a real life example for Pareto distributed data

Usage

data(citiesData)

Format

List with one element

References

http://bevoelkerungsstatistik.de

Create design matrix for log-linear models of contingency tables

Description

This function creates a design matrix for contingency tables and is particularly useful for log-linear Poisson models. It uses effect coding of the variables: First the rows of the contingency table from top to bottom, then the columns from left to right.

Usage

createDesMat(n, p)

Arguments

n

Number of rows of the corresponding contingency table.

p

Number of columns of the corresponding contingency table.

Value

A (n+p-1) times (n*p) design matrix.

Author(s)

A. Rehage

References

Kuhnt, S.; Rapallo, F.; Rehage, A. (2014) Outlier detection in contingency tables based on minimal patterns. Statistics and Computing 24 (3), 481-491.

Examples

createDesMat(3, 5)

Number of absence days of students

Description

Number of absence days of students

Usage

data(daysabs)

Format

Vector with 314 elements

References

http://www.ats.ucla.edu/stat/r/dae/nbreg.htm

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