Simulates a sample of size n from a set of multivariate binary and continuous non-normal variables

Description

This function simulates a multivariate data set with binary and continuous components with pre-specified marginals and a correlation matrix. Setting n.NN=0 and quantities that are pertinent to the continuous part to NULL results in simulation of a sample of size n from a set of multivariate binary variables. Similarly, setting n.BB=0 and prop.vec=NULL results in simulation of a sample of size n from a set of multivariate continuous non-normal variables.

Usage

gen.Bin.NonNor(n, n.BB, n.NN, prop.vec = NULL, mean.vec = NULL, variance.vec = NULL, 
skewness.vec = NULL, kurtosis.vec = NULL, final.corr.mat, coef.mat = NULL)

Arguments

Value

A matrix of size n*(n.BB + n.NN) of which the first n.BB columns are binary variables and the last n.NN columns are continuous variables.

References

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.

Vale, C.D. and Maurelli, V.A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48(3), 465-471.

See Also

validation.bin, validation.skewness.kurtosis,overall.corr.mat, fleishman.coef

Examples

## Not run: 
n=1
n.BB=2
n.NN=4
prop.vec=c(0.4,0.7)
mean.vec=c(1,0.5,4/6,100)
variance.vec=c(1,0.02777778,0.03174603,1000)
skewness.vec=c(2,0,-0.4677,0.6325)
kurtosis.vec=c(6,-0.5455,-0.3750,0.6)
corr.mat=matrix(c(1.0,-0.3,-0.3,-0.3,-0.3,-0.3,
-0.3,1.0,-0.3,-0.3,-0.3,-0.3,
-0.3,-0.3,1.0,0.4,0.5,0.6,
-0.3,-0.3,0.4,1.0,0.7,0.8,
-0.3,-0.3,0.5,0.7,1.0,0.9,
-0.3,-0.3,0.6,0.8,0.9,1.0),6,byrow=TRUE)

coef.mat=fleishman.coef(n.NN,skewness.vec,kurtosis.vec)

coef.mat=matrix(c(
 -0.31375,  0.00000,  0.10045, -0.10448,
  0.82632,  1.08574,  1.10502,  0.98085,
  0.31375,  0.00000, -0.10045,  0.10448,
  0.02271, -0.02945, -0.04001,  0.00272),4,byrow=TRUE)

intcor.mat=Int.Corr.NN(n.NN,corr.vec=NULL,corr.mat,coef.mat) 

intcor.mat=matrix(c(
1.0000000, 0.4487800, 0.5940672, 0.6471184,
0.4487800, 1.0000000, 0.7099443, 0.8112701,
0.5940672, 0.7099443, 1.0000000, 0.9436195,
0.6471184, 0.8112701, 0.9436195, 1.0000000),4,byrow=TRUE)

tetcor.mat=Tetra.Corr.BB(n.BB,prop.vec,corr.vec=NULL,corr.mat)
tetcor.mat=matrix(c(
 1.0000000, -0.4713861,
-0.4713861,  1.0000000),2,byrow=TRUE)

bicor.mat=Biserial.Corr.BN(n.BB,n.NN,prop.vec,corr.vec=NULL,corr.mat,coef.mat)
bicor.mat=matrix(c(
-0.4253059, -0.3814058, -0.3862068, -0.3846430,
-0.4420613, -0.3964317, -0.4014219, -0.3997964),2,byrow=TRUE)

final.corr.mat=overall.corr.mat(n.BB,n.NN,prop.vec,corr.vec=NULL,corr.mat,coef.mat)

final.corr.mat=matrix(c(
  1.0000000, -0.4713861, -0.4253059, -0.3814058, -0.3862068, -0.3846430,
 -0.4713861,  1.0000000, -0.4420613, -0.3964317, -0.4014219, -0.3997964,
 -0.4253059, -0.4420613,  1.0000000,  0.4487800,  0.5940672,  0.6471184,
 -0.3814058, -0.3964317,  0.4487800,  1.0000000,  0.7099443,  0.8112701,
 -0.3862068, -0.4014219,  0.5940672,  0.7099443,  1.0000000,  0.9436195,
 -0.3846430, -0.3997964,  0.6471184,  0.8112701,  0.9436195,  1.0000000),6, byrow=TRUE)

data=gen.Bin.NonNor(n,n.BB,n.NN,prop.vec,mean.vec,variance.vec,skewness.vec, 
kurtosis.vec,final.corr.mat,coef.mat)

amat=final.corr.mat[1:2,1:2]
multibin=gen.Bin.NonNor(n=1000,n.BB,n.NN=0,prop.vec,mean.vec=NULL,variance.vec=NULL, 
skewness.vec=NULL,kurtosis.vec=NULL,final.corr.mat=amat,coef.mat=NULL)

apply(multibin,2,mean)

bmat=final.corr.mat[3:6,3:6]
multinonnor=gen.Bin.NonNor(n=100,n.BB=0,n.NN,prop.vec=NULL,mean.vec,variance.vec, 
skewness.vec,kurtosis.vec,final.corr.mat=bmat,coef.mat)
apply(multinonnor,2,mean)
apply(multinonnor,2,var)


n=1000
n.BB=1
n.NN=1
prop.vec=0.6
mean.vec=1
variance.vec=1
skewness.vec=2
kurtosis.vec=6
corr.vec=NULL
corr.mat=matrix(c(1,-0.3,-0.3,1),2,2)
coef.mat=matrix(c(-0.31375,0.82632,0.31375,0.02271),4,1)
final.corr.mat=overall.corr.mat(n.BB,n.NN,prop.vec,corr.vec=NULL,corr.mat,coef.mat)
data=gen.Bin.NonNor(n,n.BB,n.NN,prop.vec,mean.vec,variance.vec,skewness.vec,
kurtosis.vec,final.corr.mat,coef.mat)


n=1000
n.BB=1
n.NN=0
prop.vec=0.6
mean.vec=1
variance.vec=NULL
skewness.vec=NULL
kurtosis.vec=NULL
corr.vec=NULL
corr.mat=diag(1)
coef.mat=NULL

final.corr.mat=overall.corr.mat(n.BB,n.NN,prop.vec,corr.vec=NULL,corr.mat,coef.mat)

data=gen.Bin.NonNor(n,n.BB,n.NN,prop.vec,mean.vec,variance.vec,skewness.vec, 
kurtosis.vec,final.corr.mat,coef.mat)

## End(Not run)