Package 'bindata'

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

margprob	vector of marginal probabilities.
bincorr	matrix of binary correlations.

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

commonprob

Matrix of pairwise probabilities.

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

commonprob	matrix of pairwise probabilities.
simulvals	array received by simul.commonprob.

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

x	matrix of binary data with rows corresponding to cases and columns corresponding to variables.

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

x	array of arbitrary dimension

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

n	number of observations.
margprob	margin probabilities that the components are 1.
commonprob	matrix of probabilities that components i and j are simultaneously 1.
bincorr	matrix of binary correlations.
sigma	covariance matrix for the normal distribution.
colnames	vector of column names for the resulting observation matrix.
simulvals	result from simul.commonprob, a default data array is automatically loaded if this argument is omitted.

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

margprob	vector of marginal probabilities.
corr	vector of correlation values for normal distribution.
method	either "integrate" or "monte carlo".
n1	number of normal variates if method is "monte carlo".
n2	number of repetitions if method is "monte carlo".

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), meth="mo", n1=10^4)

data(SimulVals)

---

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

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