Data Generation with Count, Binary and Ordinal Components

Description

Provides R functions for generation of multiple count, binary and ordinal variables simultaneously given the marginal characteristics and association structure.

Details

PoisBinOrd package consists of ten functions. The functions validation.bin, validation.ord, and validation.corr validate the specified quantities to prevent users from committing obvious specification errors. correlation.limits returns the lower and upper bounds of the pairwise correlation of Poisson-Poisson, Poisson-binary, Poisson-ordinal, binary-binary, binary-ordinal, and ordinal-ordinal combinations given their marginal distributions, i.e. returns the range of feasible pairwise correlations. The function correlation.bound.check checks the validity of the values of pairwise correlations. The functions intermediate.corr.PP, intermediate.corr.BO, and intermediate.corr.PBO computes intermediate correlation matrix for Poisson-Poisson combinations, binary/ordinal and binary/ordinal combinations, and Poisson and binary/ordinal combinations, respectively. The function overall.corr.mat assembles the final correlation matrix. The engine function gen.PoisBinOrd generates mixed data in accordance with the specified marginal and correlational quantities. Throughout the package, variables are supposed to be inputted in a certain order, namely, first count variables, next binary variables, and then ordinal variables should be placed.

Author(s)

Gul Inan, Hakan Demirtas, Ran Gao

Maintainer: Ran Gao <rgao8@uic.edu>

References

Amatya, A. and Demirtas, H. (2015). Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation, (85)15, 3129-3139.

Demirtas, H. and Hedeker, D. (2011). A practical way for computing approximate lower and upper correlation bounds. The American Statistician, 65(2), 104-109.

Demirtas, H., Hedeker, D., and Mermelstein, R.J. (2012). Simulation of massive public health data by power polynomials. Statistics in Medicine, 31(27), 3337-3346.

Ferrari, P.A. and Barbiero, A. (2012). Simulating ordinal data. Multivariate Behavioral Research, 47(4), 566-589.

Checks if the pairwise correlation among variables are within the feasible range

Description

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

Usage

correlation.bound.check(n.P, n.B, n.O, lambda.vec = NULL, prop.vec = NULL, 
prop.list = NULL, corr.vec = NULL, corr.mat = NULL)

Arguments

Value

The function returns TRUE if no specification problem is encountered. Otherwise, it returns an error message.

References

Demirtas, H. and Hedeker, D. (2011). A practical way for computing approximate lower and upper correlation bounds. The American Statistician, 65(2), 104-109.

Demirtas, H., Hedeker, D., and Mermelstein, R.J. (2012). Simulation of massive public health data by power polynomials. Statistics in Medicine, 31(27), 3337-3346.

See Also

validation.corr, correlation.limits

Examples

## Not run: 
n.P<-1
n.B<-1
n.O<-1
lambda.vec<-c(1)
prop.vec<-c(0.3)
prop.list<-list(c(0.3,0.6))
corr.mat=matrix(c(1,0.2,0.1,0.2,1,0.5,0.1,0.5,1),3,3)
correlation.bound.check(n.P,n.B,n.O,lambda.vec,prop.vec,prop.list,corr.vec=NULL,
corr.mat)

n.P<-2
n.B<-2
n.O<-2
lambda.vec<-c(1,2)
prop.vec<-c(0.3,0.5)
prop.list<-list(c(0.3,0.6),c(0.5,0.6))
corr.mat=matrix(0.8,6,6)
diag(corr.mat)=1
correlation.bound.check(n.P,n.B,n.O,lambda.vec,prop.vec,prop.list,corr.vec=NULL,
corr.mat)

## End(Not run)

Computes lower and upper correlation bounds for each pair of variables

Description

This function computes lower and upper limits for pairwise correlations of Poisson-Poisson, Poisson-binary, Poisson-ordinal, binary-binary, binary-ordinal, and ordinal-ordinal combinations.

Usage

correlation.limits(n.P, n.B, n.O, lambda.vec = NULL, prop.vec = NULL, 
prop.list = NULL)

Arguments

Details

While the function computes the exact lower and upper bounds for pairwise correlations among binary-binary variables as formulated in Demirtas et al. (2012), it computes approximate lower and upper bounds for pairwise correlations among Poisson-Poisson, Poisson-binary, Poisson-ordinal, binary-ordinal, and ordinal-ordinal variables through the method suggested by Demirtas and Hedeker (2011).

Value

The function returns a matrix of size (n.P + n.B + n.O)*(n.P + n.B + n.O), where the lower triangular part of the matrix contains the lower bounds and the upper triangular part of the matrix contains the upper bounds of the feasible correlations.

References

Demirtas, H. and Hedeker, D. (2011). A practical way for computing approximate lower and upper correlation bounds. The American Statistician, 65(2), 104-109.

Demirtas, H., Hedeker, D., and Mermelstein, R.J. (2012). Simulation of massive public health data by power polynomials. Statistics in Medicine, 31(27), 3337-3346.

See Also

validation.corr, correlation.bound.check

Examples

## Not run: 
n.P<-3
n.B<-2
n.O<-3
lambda.vec<-c(1,2,3)
prop.vec<-c(0.3,0.5)
prop.list<-list(c(0.3,0.6),c(0.25,0.5,0.75),c(0.1,0.2,0.8,0.9))

#Correlation limits among Poisson variables
correlation.limits(n.P,n.B=0,n.O=0,lambda.vec,prop.vec=NULL,prop.list=NULL)

#See also Cor.PP.Limit in R package PoisNor 

#Correlation limits among binary variables
correlation.limits(n.P=0,n.B,n.O=0,lambda.vec=NULL,prop.vec,prop.list=NULL)

#See also correlation.limits in R package BinNonNor 

#Correlation limits among ordinal variables
correlation.limits(n.P=0,n.B=0,n.O,lambda.vec=NULL,prop.vec=NULL,prop.list)

#See also Limit_forOO in R package OrdNor 

#Correlation limits among Poisson and binary variables and within themselves.
correlation.limits(n.P,n.B,n.O=0,lambda.vec,prop.vec,prop.list=NULL)

#Correlation limits among Poisson and ordinal variables and within themselves.
correlation.limits(n.P,n.B=0,n.O,lambda.vec,prop.vec=NULL,prop.list)

#Correlation limits among binary and ordinal variables and within themselves.
correlation.limits(n.P=0,n.B,n.O,lambda.vec=NULL,prop.vec,prop.list)

#Correlation limits among Poisson, binary, and ordinal variables and within themselves.
correlation.limits(n.P,n.B,n.O,lambda.vec,prop.vec,prop.list)

n.P<-2
lambda.vec=c(-1,1)
correlation.limits(n.P,n.B=0,n.O=0,lambda.vec,prop.vec=NULL,prop.list=NULL)

## End(Not run)

Simulates a sample of size n from a set of multivariate Poisson, binary, and ordinal variables

Description

This function simulates a sample of size n from a set of multivariate Poisson, binary, and ordinal data with pre-specified marginals and a correlation matrix.

Usage

gen.PoisBinOrd(n, n.P, n.B, n.O, lambda.vec = NULL, prop.vec = NULL, 
prop.list = NULL, final.corr.mat)

Arguments

Value

A matrix of size n*(n.P + n.B + n.O), of which the first n.P columns are Poisson variables, the next n.B columns are binary variables, and the last n.O columns are ordinal variables.

Examples

## Not run: 
n=10000
n.P<-2
n.B<-2
n.O<-2
lambda.vec<-sample(10,2)
prop.vec<-runif(2)
prop.list<-list(c(0.3,0.6,0.7),c(0.2,0.3,0.5))
M=c(-0.05, 0.26, 0.14, 0.09, 0.14, 0.12, 0.13, -0.02, 0.17, 0.11,
-0.04, 0.19, 0.10, 0.35, 0.39)
N=diag(6)
N[lower.tri(N)]=M
corr.mat=N+t(N)
diag(corr.mat)<-1
final.corr.mat=overall.corr.mat(n.P,n.B,n.O,lambda.vec,prop.vec,
prop.list,corr.vec=NULL,corr.mat)
mymixdata=gen.PoisBinOrd(n,n.P,n.B,n.O,lambda.vec,prop.vec,prop.list, 
final.corr.mat)

## End(Not run)

Computes an intermediate normal correlation matrix for any combination of binary and ordinal variables given the specified correlation matrix

Description

Computes an intermediate normal correlation matrix for any combination of binary and ordinal variables before dichotomization/ordinalization given the specified correlation matrix as formulated in Ferrari and Barbiero (2012).

Usage

intermediate.corr.BO(n.B, n.O, prop.vec = NULL, prop.list = NULL, corr.vec = NULL, 
corr.mat = NULL)

Arguments

Value

A correlation matrix of size (n.B+n.O)*(n.B+n.O).

References

Ferrari, P.A. and Barbiero, A. (2012). Simulating ordinal data. Multivariate Behavioral Research, 47(4), 566-589.

Barbiero, A. and Ferrari, P.A. (2015). GenOrd: Simulation of ordinal and discrete variables with given correlation matrix and marginal distributions. http://www.cran.r-project.org/web/packages/GenOrd.

See Also

intermediate.corr.PBO

Examples

## Not run: 
n.B=1
n.O=2
prop.vec=0.7
prop.list=list(cumsum(c(0.30, 0.40)), cumsum(c(0.4, 0.2, 0.3)))
corr.mat=matrix ( c(
1.0000000, 0.1767231, 0.3006186,
0.1767231, 1.0000000, -0.139923,
0.3006186, -0.1399230, 1.0000000),3,3)
intmatBO=intermediate.corr.BO(n.B,n.O,prop.vec,prop.list,corr.vec=NULL, 
corr.mat)

n.B=1
n.O=1
prop.vec<-c(0.3)
prop.list<-list(c(0.3,0.6))
corr.mat=matrix(c(1,0.2,0.1,0.2,1,0.5,0.1,0.5,1),3,3)
intmatBO=intermediate.corr.BO(n.B,n.O,prop.vec,prop.list,corr.vec=NULL, 
corr.mat)

n.B=2
prop.vec=c(0.4,0.7)
corr.mat=matrix(c(1,-0.3,-0.3,1),2,2)
intmatBB=intermediate.corr.BO(n.B,n.O=0,prop.vec,prop.list=NULL,corr.vec=NULL, 
corr.mat)

#See Tetra.Corr.BB in R package BinNonNor 
#Tetra.Corr.BB(n.BB=2,prop.vec=c(0.4,0.7),corr.vec=NULL,corr.mat=corr.mat)

n.B=0
n.O=2
prop.list=list(cumsum(c(0.30, 0.40)), cumsum(c(0.4,0.2,0.3)))
corr.mat=matrix(c(1.0000000, -0.139923,-0.139923,1.0000000),2,2)
intmatOO=intermediate.corr.BO(n.B,n.O,prop.vec=NULL,prop.list,corr.vec=NULL, 
corr.mat)

#See IntermediateOO(plist, OOCorrMat) in R package OrdNor
#IntermediateOO(plist=list(cumsum(c(0.30,0.40)),cumsum(c(0.4,0.2,0.3))), 
OOCorrMat=corr.mat)

## End(Not run)

Computes the pairwise entries of the intermediate normal correlation matrix for all Poisson-binary and Poisson-ordinal variable combinations given the specified correlation matrix.

Description

This function computes the pairwise entries of the intermediate normal correlation matrix for all Poisson-binary and Poisson-ordinal variable combinations given the specified correlation matrix as formulated in Amatya and Demirtas (2015).

Usage

intermediate.corr.PBO(n.P, n.B, n.O, lambda.vec = NULL, prop.vec = NULL, 
prop.list = NULL, corr.vec = NULL, corr.mat = NULL)

Arguments

Value

A matrix of n.P*(n.B+n.O)

References

Amatya, A. and Demirtas, H. (2015). Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation, 85(15), 3129-3139.

See Also

intermediate.corr.PP, intermediate.corr.BO

Examples

## Not run: 
n.P<-1
n.B<-1
n.O<-1
lambda.vec<-c(1)
prop.vec<-c(0.3)
prop.list<-list(c(0.3,0.6))
corr.mat=matrix(c(1,0.2,0.1,0.2,1,0.5,0.1,0.5,1),3,3)

intmatPBO=intermediate.corr.PBO(n.P,n.B,n.O,lambda.vec,prop.vec,prop.list, 
corr.vec=NULL,corr.mat)

## End(Not run)

Computes an intermediate normal correlation matrix for Poisson variables given the specified correlation matrix

Description

This function computes the intermediate normal correlation matrix for Poisson-Poisson combinations before inverse cdf matching as formulated in Amatya and Demirtas (2015).

Usage

intermediate.corr.PP(n.P, lambda.vec, corr.vec = NULL, corr.mat = NULL)

Arguments

Value

A correlation matrix of size n.P*n.P

References

Amatya, A. and Demirtas, H. (2015). Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation, 85(15), 3129-3139.

See Also

intermediate.corr.PBO

Examples

n.P<-3
lambda.vec<-c(1,2,3)
corr.mat<-matrix(c(1,0.352,0.265,0.352,1,0.121,0.265,0.121,1),n.P,n.P)
intmatPP=intermediate.corr.PP(n.P,lambda.vec,corr.vec=NULL,corr.mat)

## Not run: 
#See also cmat.star in  R package PoisNor 
#cmat.star(no.pois=3,no.norm=0,corMat=corr.mat,lamvec=lambda.vec)

## End(Not run)

Computes the final intermediate correlation matrix

Description

This function computes the final correlation matrix by combining pairwise intermediate correlation matrix entries for Poisson-Poisson, Poisson-binary, Poisson-ordinal, binary-binary, binary-ordinal, and ordinal-ordinal combinations. If the resulting correlation matrix is not positive definite, a nearest positive matrix will be used.

Usage

overall.corr.mat(n.P, n.B, n.O, lambda.vec = NULL, prop.vec = NULL, prop.list = NULL, 
corr.vec = NULL, corr.mat = NULL)

Arguments

Value

A matrix of size (n.P+n.B+n.O)*(n.P+n.B+n.O)

See Also

intermediate.corr.PP, intermediate.corr.BO,intermediate.corr.PBO

Examples

## Not run: 
n.P<-1
n.B<-1
n.O<-1
lambda.vec<-c(1)
prop.vec<-c(0.3)
prop.list<-list(c(0.3,0.6))
corr.vec=NULL
corr.mat=matrix(c(1,0.2,0.1,0.2,1,0.5,0.1,0.5,1),3,3)
finalmat=overall.corr.mat(n.P,n.B,n.O,lambda.vec,prop.vec,prop.list,corr.vec=NULL, 
corr.mat)

## End(Not run)

Validates the marginal specification of the binary variables

Description

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

Usage

validation.bin(n.B, prop.vec = NULL)

Arguments

Value

The function returns TRUE if no specification problem is encountered. Otherwise, it returns an error message.

Examples

n.B<-3
prop.vec<-c(0.25,0.5,0.75)
validation.bin(n.B,prop.vec)

## Not run: 
n.B<-3
validation.bin(n.B)

n.B<--3
prop.vec<-c(0.25,0.5,0.75)
validation.bin(n.B,prop.vec)

n.B<-0
prop.vec<-c(0.25,0.5,0.75)
validation.bin(n.B,prop.vec)

n.B<-5
prop.vec<-c(0.25,0.5,0.75)
validation.bin(n.B,prop.vec)

n.B<-3
prop.vec<-c(0.25,0.5,-0.75)
validation.bin(n.B,prop.vec)

## End(Not run)

Validates the specified correlation matrix

Description

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

Usage

validation.corr(n.P, n.B, n.O, corr.vec = NULL, corr.mat = NULL)

Arguments

Value

The function returns TRUE if no specification problem is encountered. Otherwise, it returns an error message.

See Also

correlation.limits, correlation.bound.check

Examples

n.P<-1
n.B<-1
n.O<-1
corr.vec=c(0.2,0.1,0.5)
validation.corr(n.P,n.B,n.O,corr.vec,corr.mat=NULL)

n.P<-2
n.B<-2
n.O<-2
corr.mat=matrix(0.5,6,6)
diag(corr.mat)=1
validation.corr(n.P,n.B,n.O,corr.vec=NULL,corr.mat)

Validates the marginal specification of the ordinal variables

Description

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

Usage

validation.ord(n.O, prop.list = NULL)

Arguments

Value

The function returns TRUE if no specification problem is encountered. Otherwise, it returns an error message.

Examples

n.O<-3
prop.list<-list(c(0.3,0.6),c(0.25,0.5,0.75),c(0.1,0.2,0.8,0.9))
validation.ord(n.O,prop.list)

## Not run: 
n.O<-3
validation.ord(n.O)

n.O<-NULL
prop.list<-list(c(0.3,0.6),c(0.25,0.5,0.75),c(0.1,0.2,0.8,0.9))
validation.ord(prop.list=prop.list)

n.O<--3
prop.list<-list(c(0.3,0.6),c(0.25,0.5,0.75),c(0.1,0.2,0.8,0.9))
validation.ord(-3,prop.list)

n.O<--0
prop.list<-list(c(0.3,0.6),c(0.25,0.5,0.75),c(0.1,0.2,0.8,0.9))
validation.ord(n.O,prop.list)

n.O<-5
prop.list<-list(c(0.3,0.6),c(0.25,0.5,0.75),c(0.1,0.2,0.8,0.9))
validation.ord(n.O,prop.list)

n.O<-3
prop.list<-list(c(0.3,0.6),c(0.25,0.5,-0.75),c(0.1,0.2,0.8,1.5))
validation.ord(n.O,prop.list)

n.O<-3
prop.list<-list(0.3,c(0.3,0.4),c(0.4,0.2,0.3))
validation.ord(n.O,prop.list)

## End(Not run)