Version:	0.9-22
Date:	2024-12-30
Title:	Generation of Artificial Binary Data
Description:	Generation of correlated artificial binary data.
License:	GPL-2
Imports:	e1071, mvtnorm (≥ 0.7-0)
NeedsCompilation:	no
Packaged:	2024-12-30 13:37:01 UTC; hornik
Author:	Friedrich Leisch [aut] (maintainer up to 2024), Andreas Weingessel [aut], Kurt Hornik [aut, cre]
Maintainer:	Kurt Hornik <Kurt.Hornik@R-project.org>
Depends:	R (≥ 2.10)
Repository:	CRAN
Date/Publication:	2024-12-30 14:07:56 UTC

Pre-simulated Joint Binary Probabilities

Description

This variable provides a pre-fabricated result from simul.commonprob such that it is normally not necessary to use this (time consuming) function, and is used by rmvbin.

Usage

SimulVals

Author(s)

Friedrich Leisch

References

Friedrich Leisch, Andreas Weingessel and Kurt Hornik (1998). On the generation of correlated artificial binary data. Working Paper Series, SFB “Adaptive Information Systems and Modelling in Economics and Management Science”, Vienna University of Economics.

See Also

simul.commonprob, rmvbin

Convert Binary Correlation Matrix to Matrix of Joint Probabilities

Description

Compute a matrix of common probabilities for a binary random vector from given marginal probabilities and correlations.

Usage

bincorr2commonprob(margprob, bincorr)

Arguments

Value

The matrix of common probabilities. This has the probabilities that variable i equals 1 in element (i,i), and the joint probability that variables i and j both equal 1 in element (i,j) (if i \ne j).

Author(s)

Friedrich Leisch

References

Friedrich Leisch, Andreas Weingessel and Kurt Hornik (1998). On the generation of correlated artificial binary data. Working Paper Series, SFB “Adaptive Information Systems and Modelling in Economics and Management Science”, Vienna University of Economics.

See Also

commonprob2sigma, simul.commonprob.

Check Joint Binary Probabilities

Description

The main diagonal elements commonprob[i,i] are interpreted as probabilities p_{A_i} that a binary variable A_i equals 1. The off-diagonal elements commonprob[i,j] are the probabilities p_{A_iA_j} that both A_i and A_j are 1.

This programs checks some necessary conditions on these probabilities which must be fulfilled in order that a joint distribution of the A_i with the given probabilities can exist.

The conditions checked are

0 \leq p_{A_i} \leq 1

\max(0, p_{A_i} + p_{A_j} - 1) \leq p_{A_iA_j} \leq \min(p_{A_i}, p_{A_j}), i \neq j

p_{A_i} + p_{A_j} + p_{A_k} - p_{A_iA_j} -p_{A_iA_k} - p_{A_jA_k} \leq 1, i \neq j, i \neq k, j \neq k

Usage

check.commonprob(commonprob)

Arguments

Value

check.commonprob returns TRUE, if all conditions are fulfilled. The attribute "message" of the return value contains some information on the errors that were found.

Author(s)

Andreas Weingessel

References

Friedrich Leisch, Andreas Weingessel and Kurt Hornik (1998). On the generation of correlated artificial binary data. Working Paper Series, SFB “Adaptive Information Systems and Modelling in Economics and Management Science”, Vienna University of Economics.

See Also

simul.commonprob, commonprob2sigma

Examples

check.commonprob(cbind(c(0.5, 0.4), c(0.4, 0.8)))

check.commonprob(cbind(c(0.5, 0.25), c(0.25, 0.8)))

check.commonprob(cbind(c(0.5, 0, 0), c(0, 0.5, 0), c(0, 0, 0.5)))

Calculate a Covariance Matrix for the Normal Distribution from a Matrix of Joint Probabilities

Description

Computes a covariance matrix for a normal distribution which corresponds to a binary distribution with marginal probabilities given by diag(commonprob) and pairwise probabilities given by commonprob.

For the simulations the values of simulvals are used.

If a non-valid covariance matrix is the result, the program stops with an error in the case of NA arguments and yields are warning message if the matrix is not positive definite.

Usage

commonprob2sigma(commonprob, simulvals)

Arguments

Value

A covariance matrix is returned with the same dimensions as commonprob.

Author(s)

Friedrich Leisch

References

Friedrich Leisch, Andreas Weingessel and Kurt Hornik (1998). On the generation of correlated artificial binary data. Working Paper Series, SFB “Adaptive Information Systems and Modelling in Economics and Management Science”, Vienna University of Economics.

See Also

simul.commonprob

Examples

m <- cbind(c(1/2,1/5,1/6),c(1/5,1/2,1/6),c(1/6,1/6,1/2))
sigma <- commonprob2sigma(m)

Conditional Probabilities of Binary Data

Description

Returns a matrix containing the conditional probabilities P(x_i=1|x_j=1) where x_i corresponds to the i-th column of x.

Usage

condprob(x)

Arguments

Author(s)

Friedrich Leisch

Convert Real Valued Array to Binary Array

Description

Converts all values of the real valued array x to binary values by thresholding at 0.

Usage

ra2ba(x)

Arguments

Author(s)

Friedrich Leisch

Examples

x <- array(rnorm(10), dim=c(2,5))
ra2ba(x)

Multivariate Binary Random Variates

Description

Creates correlated multivariate binary random variables by thresholding a normal distribution. The correlations of the components can be specified either as common probabilities, correlation matrix of the binary distribution, or covariance matrix of the normal distribution.

Usage

rmvbin(n, margprob, commonprob=diag(margprob),
       bincorr=diag(length(margprob)),
       sigma=diag(length(margprob)),
       colnames=NULL, simulvals=NULL)

Arguments

Details

Only one of the arguments commonprob, bincorr and sigma may be specified. Default are uncorrelated components.

n samples from a multivariate normal distribution with mean and variance chosen in order to get the desired margin and common probabilities are sampled. Negative values are converted to 0, positive values to 1.

Author(s)

Friedrich Leisch

References

Friedrich Leisch, Andreas Weingessel and Kurt Hornik (1998). On the generation of correlated artificial binary data. Working Paper Series, SFB “Adaptive Information Systems and Modelling in Economics and Management Science”, Vienna University of Economics.

See Also

commonprob2sigma, check.commonprob, simul.commonprob

Examples

## uncorrelated columns:
rmvbin(10, margprob=c(0.3,0.9))

## correlated columns
m <- cbind(c(1/2,1/5,1/6),c(1/5,1/2,1/6),c(1/6,1/6,1/2))
rmvbin(10,commonprob=m)

## same as the second example, but faster if the same probabilities are
## used repeatedly (commonprob2sigma rather slow)
sigma <- commonprob2sigma(m)
rmvbin(10,margprob=diag(m),sigma=sigma)

Simulate Joint Binary Probabilities

Description

Compute common probabilities of binary random variates generated by thresholding normal variates at 0.

Usage

simul.commonprob(margprob, corr=0, method="integrate", n1=10^5, n2=10)

Arguments

Details

The output of this function is used by rmvbin. For all combinations of marginprob[i], marginprob[j] and corr[k], the probability that both components of a normal random variable with mean qnorm(marginprob[c(i,j)]) and correlation corr[k] are larger than zero is computed.

The probabilities are either computed by numerical integration of the multivariate normal density, or by Monte Carlo simulation.

For normal usage of rmvbin it is not necessary to use this function, one simulation result is provided as variable SimulVals in this package and loaded by default.

Value

simul.commonprob returns an array of dimension c(length(margprob), length(margprob), length(corr)).

Author(s)

Friedrich Leisch

References

Friedrich Leisch, Andreas Weingessel and Kurt Hornik (1998). On the generation of correlated artificial binary data. Working Paper Series, SFB “Adaptive Information Systems and Modelling in Economics and Management Science”, Vienna University of Economics.

See Also

rmvbin

Examples

simul.commonprob(seq(0,1,0.5), seq(-1,1,0.5), method="mo", n1=10^4)

data(SimulVals)