Package 'BinNor'

A package for simultaneous generation of binary and normal data.

Description

Provides R functions for generating multiple binary and normal variables simultaneously given the marginal characteristics and association structure via combining well established results from the random number generation literature, based on the methodology proposed by Demirtas and Doganay (2012).

Details

Package:	BinNor
Type:	Package
Version:	2.3.3
Date:	2021-03-05
License:	GPL-2
LazyLoad:	yes

There are eight functions in this package. The functions lower.tri.to.corr.mat,
validation.bin, validation.nor, validation.range and validation.nor are designed to prevent obvious specification errors and to validate the specified quantities. The most important functions are compute.sigma.star, jointly.generate.binary.normal and simulation. The function compute.sigma.star computes the matrix of tetrachoric correlations that will be used in the generation of multivariate normal data whose some components are dichotomized to obtain binary variables. The function jointly.generate.binary.normal generates mixed data, and the function simulation is capable of repating this process many times and produces averages of some key statistical quantities across replications.

Author(s)

Anup Amatya, Hakan Demirtas, Ran Gao

Maintainer: Ran Gao <[email protected]>

References

Demirtas, H., Doganay, B. (2012). Simultaneous generation of binary and normal data with specified marginal and association structures. Journal of Biopharmaceutical Statistics; 22(2), 223-236.

Demirtas, H., Amatya, A., and Doganay, B. (2014). BinNor: An R package for con-current generation of binary and normal data. Communications in Statistic-Simulation and Computation; 43(3), 569-579.

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Computes intermediate correlation matrix

Description

This function computes the intermediate correlation matrix by assembling tetrachoric correlations for binary-binary combinations, biserial correlations for binary-normal combinations, and specified correlation for normal-normal combinations. If the resulting correlation matrix is not positive definite, a nearest positive matrix will be used.

Usage

compute.sigma.star(no.bin, no.nor, prop.vec.bin = NULL,
		 corr.vec = NULL, corr.mat = NULL)

Arguments

no.bin	Number of binary variables
no.nor	Number of normal variables
prop.vec.bin	Probability vector for binary variables
corr.vec	Vector of elements below the diagonal of correlation matrix ordered columnwise
corr.mat	Specified correlation matrix

Value

sigma_star	A resulting intermediate correlation matrix $\Sigma^*$
nonPD	If a resulting intermediate correlation matrix is non-positive definite, it is stored in this value. Otherwise it is NULL.
PD	TRUE if $\Sigma^*$ is positive definite, FALSE otherwise. A FALSE indicates that the nearest positive definite matrix is returned.
eigenv	Eigenvalues of the $\Sigma^*$ before the conversion

See Also

validation.corr, nearPD, phi2tetra, is.positive.definite,
jointly.generate.binary.normal, simulation

Examples

cmat = lower.tri.to.corr.mat(corr.vec= c(0.16, 0.04, 0.38, 0.14, 0.47, 0.68),4)
compute.sigma.star(no.bin=2, no.nor=2, prop.vec.bin=c(0.4,0.7), 
corr.vec=NULL,corr.mat=cmat)

---

Generates a mix of binary and normal data

Description

Generates multiple binary and normal variables simultaneously given marginal characteristics and association structures.

Usage

jointly.generate.binary.normal(no.rows, no.bin, 
			no.nor, prop.vec.bin = NULL, mean.vec.nor = NULL, var.nor = NULL, 
			sigma_star = NULL, corr.vec = NULL, corr.mat = NULL, 
			continue.with.warning = TRUE)

Arguments

no.rows	Number of rows.
no.bin	Number of binary variables
no.nor	Number of normal variables
prop.vec.bin	Probability vector for binary variables
mean.vec.nor	Vector of means for normal variables
var.nor	Vector of variances for normal variables
sigma_star	Intermediate correlation matrix
corr.vec	Vector of elements below the diagonal of correlation matrix ordered columnwise
corr.mat	Specified correlation matrix
continue.with.warning	TRUE to proceed with the nearest positive definite $\Sigma^*$. FALSE to terminate program execution if $\Sigma^*$ is not positive definite

Value

data	A matrix of generated data.

See Also

compute.sigma.star, validation.corr, validation.bin, validation.nor, nearPD, simulation, rmvnorm

Examples

no.rows=100
no.bin=2; no.nor=2
mean.vec.nor=c(3,1); var.nor=c(4,2)
prop.vec.bin=c(0.4,0.7)
corr.vec=c(0.16,0.04,0.38,0.14,0.47,0.68);

cmat = lower.tri.to.corr.mat(corr.vec,4)
sigma.star=compute.sigma.star(no.bin=2, no.nor=2, prop.vec.bin=c(0.4,0.7),
								corr.mat=cmat)
mydata=jointly.generate.binary.normal(no.rows,no.bin,no.nor,prop.vec.bin,
				mean.vec.nor,var.nor, sigma_star=sigma.star$sigma_star, 
				continue.with.warning=TRUE)

---

Converts a vector of correlations to a full correlation matrix

Description

This function creates full correlation matrix from the vector containing elements below the diagonal.

Usage

lower.tri.to.corr.mat(corr.vec = NULL, d)

Arguments

corr.vec	A vector of elements below diagonal of correlation matrix. The elements must be ordered starting from first element below diagonal of the first column, then second element below diagonal of the first column and so on.
d	Number of column in final correlation matrix.

Value

corr.mat

Full correlation matrix

See Also

lower.tri

Examples

corr.vec=c(0.16,0.04,0.38,0.14,0.47,0.68)
lower.tri.to.corr.mat(corr.vec,4)

---

Repeats the data generation process in a simulation scheme

Description

Simulates many versions of mixed data, and reports averaged proportion, mean, variance and correlation estimates across replications.

Usage

simulation(seed = NULL, nsim, no.rows, no.bin, no.nor, 
	mean.vec.nor = NULL, var.nor = NULL, prop.vec.bin = NULL, 
	corr.vec = NULL, corr.mat = NULL, continue.with.warning = TRUE)

Arguments

seed	A seed value for the random number generator. Seed value will be randomly generated unless specified.
nsim	Number of simulation runs.
no.rows	Number of rows.
no.bin	Number of binary variables
no.nor	Number of normal variables
prop.vec.bin	Probability vector for binary variables
mean.vec.nor	Vector of means for normal variables
var.nor	Vector of variances for normal variables
corr.vec	Vector of elements below the diagonal of correlation matrix ordered columnwise
corr.mat	Specified correlation matrix
continue.with.warning	TRUE to proceed with the nearest positive definite $\Sigma^*$. FALSE to terminate program execution if $\Sigma^*$ is not positive definite

See Also

compute.sigma.star, jointly.generate.binary.normal

Examples

simulation(nsim=10, no.rows=100, no.bin=2, no.nor=2, 
		mean.vec.nor=c(3,1), var.nor=c(4,2), prop.vec.bin=c(0.4,0.7),
		corr.vec=c(0.16,0.04,0.38,0.14,0.47,0.68), corr.mat=NULL)

---

Validates the marginal specification of the binary part

Description

Checks whether the marginal specification of the binary part is valid and consistent.

Usage

validation.bin(no.bin, prop.vec.bin = NULL)

Arguments

no.bin	Number of binary variates.
prop.vec.bin	Probability vector for binary variables

Examples

## Not run: validation.bin (3,  rep(0.6,4)) 
	validation.bin (4,  rep(0.6,4))

---

Validates the specified correlation matrix

Description

This function validates the correlation vector and/or matrix for appropriate dimension, symmetry, range, and positive definiteness. If both correlation matrix and correlation vector were supplied, it checks whether the matrix and vector are conformable.

Usage

validation.corr(no.bin, no.nor, prop.vec.bin = NULL, 
		corr.vec = NULL, corr.mat = NULL)

Arguments

no.bin	Number of binary variables
no.nor	Number of normal variables
prop.vec.bin	Probability vector for binary variables
corr.vec	Vector of elements below the diagonal of correlation matrix ordered columnwise
corr.mat	Specified correlation matrix

See Also

validation.bin, validation.range

Examples

d=4
corr.vec=c(0.21,0.61,0.78,0.10,0.12,0.65)
corr.mat=lower.tri.to.corr.mat(corr.vec,d)	


validation.corr (no.bin=2, no.nor=2,prop.vec.bin=c(0.4,0.7), 
		corr.vec,corr.mat=corr.mat)

---

Validates the marginal specification of the normal part

Description

This function checks whether mean and variance parameters for the normal part are valid and consistent.

Usage

validation.nor(no.nor, mean.vec.nor = NULL, var.nor = NULL)

Arguments

no.nor	Number of normal variables
mean.vec.nor	Vector of means for normal variables
var.nor	Vector of variances for normal variables

---

Checks if the correlation terms are within the feasible range

Description

This function checks if there are correlation range violations among binary-binary, binary-normal and normal-normal combinations.

Usage

validation.range(no.bin, no.nor, prop.vec.bin = NULL, corr.mat)

Arguments

no.bin	Number of binary variables
no.nor	Number of normal variables
prop.vec.bin	Probability vector for binary variables
corr.mat	Specified correlation matrix

Examples

cmat=lower.tri.to.corr.mat(corr.vec=c(0.16,0.04,0.38,0.4,0.47,0.68),4) 
validation.range(no.bin=2, no.nor=2, prop.vec.bin=c(0.4,0.7), corr.mat=cmat)

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