| Title: | Data Generation with Binary and Continuous Non-Normal Components |
|---|---|
| Description: | Generation of multiple binary and continuous non-normal variables simultaneously given the marginal characteristics and association structure based on the methodology proposed by Demirtas et al. (2012) <DOI:10.1002/sim.5362>. |
| Authors: | Gul Inan, Hakan Demirtas, Ran Gao |
| Maintainer: | Ran Gao <[email protected]> |
| License: | GPL-2 | GPL-3 |
| Version: | 1.5.3 |
| Built: | 2024-11-08 06:29:53 UTC |
| Source: | CRAN |
Provides R functions for generation of multiple binary and continuous non-normal variables simultaneously given the marginal characteristics and association structure based on the methodology proposed by Demirtas et al. (2012).
| Package: | BinNonNor |
| Type: | Package |
| Version: | 1.5.3 |
| Date: | 2021-03-21 |
| License: | GPL-2 | GPL-3 |
This package consists of eleven functions. The functions validation.bin,
validation.corr, and validation.skewness.kurtosis validate the specified quantities to avoid obvious specification errors. The function
fleishman.coef computes the coefficients of the third order Fleishman polynomials that are used to simulate the continuous non-normal variables.
correlation.limits returns the lower and upper bounds of the pairwise correlation of binary and binary
and binary and continuous non-normal, and continuous non-normal and continuous non-normal pairs 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 Int.Corr.NN, Tetra.Corr.BB, and Biserial.Corr.BN
computes intermediate correlation matrix for continuous non-normal and continuous non-normal combinations,
tetrachoric correlations for binary and binary combinations, and biserial correlations for binary and continuous non-normal combinations, respectively.
The function overall.corr.mat assembles the final correlation matrix. The engine function gen.Bin.NonNor
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 binary variables, and then continuous variables should be placed.
Gul Inan, Hakan Demirtas, Ran Gao
Maintainer: Ran Gao <[email protected]>
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.
This function computes the biserial correlation matrix for binary-continuous non-normal combinations as formulated in Demirtas et al. (2012).
Biserial.Corr.BN(n.BB, n.NN, prop.vec, corr.vec = NULL, corr.mat = NULL, coef.mat)Biserial.Corr.BN(n.BB, n.NN, prop.vec, corr.vec = NULL, corr.mat = NULL, coef.mat)
n.BB |
Number of binary variables. |
n.NN |
Number of continuous non-normal variables. |
prop.vec |
Probability vector for binary variables. |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered columnwise. |
corr.mat |
Specified correlation matrix. |
coef.mat |
Matrix of coefficients produced from |
A matrix of size n.BB*n.NN.
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.
fleishman.coef, Tetra.Corr.BB, Int.Corr.NN, overall.corr.mat
n.BB=2 n.NN=4 prop.vec=c(0.4,0.7) corr.vec=NULL 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=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) bicor.mat=Biserial.Corr.BN(n.BB,n.NN,prop.vec,corr.vec=NULL,corr.mat,coef.mat) n.BB=1 n.NN=1 prop.vec=0.6 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) bicor.mat=Biserial.Corr.BN(n.BB,n.NN,prop.vec,corr.vec=NULL,corr.mat,coef.mat)n.BB=2 n.NN=4 prop.vec=c(0.4,0.7) corr.vec=NULL 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=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) bicor.mat=Biserial.Corr.BN(n.BB,n.NN,prop.vec,corr.vec=NULL,corr.mat,coef.mat) n.BB=1 n.NN=1 prop.vec=0.6 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) bicor.mat=Biserial.Corr.BN(n.BB,n.NN,prop.vec,corr.vec=NULL,corr.mat,coef.mat)
This function checks if there are range violations among correlation of binary-binary, binary-continuous, and continuous-continuous combinations.
correlation.bound.check(n.BB, n.NN, prop.vec = NULL, corr.vec = NULL, corr.mat = NULL, coef.mat = NULL)correlation.bound.check(n.BB, n.NN, prop.vec = NULL, corr.vec = NULL, corr.mat = NULL, coef.mat = NULL)
n.BB |
Number of binary variables. |
n.NN |
Number of continuous non-normal variables. |
prop.vec |
Probability vector for binary variables. |
corr.vec |
Specified correlation vector. |
corr.mat |
Specified correlation matrix. |
coef.mat |
Matrix of coefficients produced from |
The function returns TRUE if no specification problem is encountered. Otherwise, it returns an error message.
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.
fleishman.coef, correlation.limits, validation.corr
prop.vec=c(0.4,0.7) n.BB=2 n.NN=4 corr.vec=NULL 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=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) correlation.bound.check(n.BB,n.NN,prop.vec,corr.vec=NULL,corr.mat,coef.mat) cor.mat.BB=corr.mat[1:2,1:2] correlation.bound.check(n.BB,n.NN=0,prop.vec,corr.vec=NULL,corr.mat=cor.mat.BB, coef.mat=NULL) cor.mat.NN=corr.mat[3:6,3:6] correlation.bound.check(n.BB=0,n.NN,prop.vec=NULL,corr.vec=NULL,corr.mat=cor.mat.NN, coef.mat) n.BB=1 prop.vec=0.5 corr.mat=diag(n.BB) correlation.bound.check(n.BB,n.NN=0,prop.vec,corr.vec=NULL,corr.mat=corr.mat, coef.mat=NULL) ## Not run: cor.mat.NNnew=cor.mat.NN cor.mat.NNnew[1,2]=0.92 cor.mat.NNnew[2,1]=0.92 correlation.bound.check(n.BB=0,n.NN,prop.vec=NULL,corr.vec=NULL,corr.mat=cor.mat.NNnew, coef.mat) ## End(Not run)prop.vec=c(0.4,0.7) n.BB=2 n.NN=4 corr.vec=NULL 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=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) correlation.bound.check(n.BB,n.NN,prop.vec,corr.vec=NULL,corr.mat,coef.mat) cor.mat.BB=corr.mat[1:2,1:2] correlation.bound.check(n.BB,n.NN=0,prop.vec,corr.vec=NULL,corr.mat=cor.mat.BB, coef.mat=NULL) cor.mat.NN=corr.mat[3:6,3:6] correlation.bound.check(n.BB=0,n.NN,prop.vec=NULL,corr.vec=NULL,corr.mat=cor.mat.NN, coef.mat) n.BB=1 prop.vec=0.5 corr.mat=diag(n.BB) correlation.bound.check(n.BB,n.NN=0,prop.vec,corr.vec=NULL,corr.mat=corr.mat, coef.mat=NULL) ## Not run: cor.mat.NNnew=cor.mat.NN cor.mat.NNnew[1,2]=0.92 cor.mat.NNnew[2,1]=0.92 correlation.bound.check(n.BB=0,n.NN,prop.vec=NULL,corr.vec=NULL,corr.mat=cor.mat.NNnew, coef.mat) ## End(Not run)
This function computes lower and upper limits for pairwise correlation of binary-binary, binary-continuous non-normal, and continuous non-normal-continuous non-normal combinations.
correlation.limits(n.BB, n.NN, prop.vec = NULL, coef.mat = NULL)correlation.limits(n.BB, n.NN, prop.vec = NULL, coef.mat = NULL)
n.BB |
Number of binar variables. |
n.NN |
Number of continuous non-normal variables. |
prop.vec |
Probability vector for binary variables. |
coef.mat |
Matrix of coefficients produced from |
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 binary-continuous non-normal and continuous non-normal-continuous non-normal variables through the method suggested by Demirtas and Hedeker (2011).
The function returns a matrix of size (n.BB + n.NN)*(n.BB + n.NN), 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.
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.
fleishman.coef, correlation.bound.check
n.BB=2 n.NN=4 prop.vec=c(0.4,0.7) 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) limits=correlation.limits(n.BB,n.NN,prop.vec,coef.mat) limits.bin=correlation.limits(n.BB,n.NN=0,prop.vec,coef.mat=NULL) limits.nonnor=correlation.limits(n.BB=0,n.NN,prop.vec=NULL,coef.mat) ## Not run: n.BB=1 prop.vec=0.5 limits=correlation.limits(n.BB,n.NN,prop.vec,coef.mat=NULL) ## End(Not run)n.BB=2 n.NN=4 prop.vec=c(0.4,0.7) 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) limits=correlation.limits(n.BB,n.NN,prop.vec,coef.mat) limits.bin=correlation.limits(n.BB,n.NN=0,prop.vec,coef.mat=NULL) limits.nonnor=correlation.limits(n.BB=0,n.NN,prop.vec=NULL,coef.mat) ## Not run: n.BB=1 prop.vec=0.5 limits=correlation.limits(n.BB,n.NN,prop.vec,coef.mat=NULL) ## End(Not run)
Computes the coefficients of Fleishman third order polynomials given the marginal skewness and kurtosis parameters of continuous variables.
fleishman.coef(n.NN, skewness.vec = NULL, kurtosis.vec = NULL)fleishman.coef(n.NN, skewness.vec = NULL, kurtosis.vec = NULL)
n.NN |
Number of continuous non-normal variables. |
skewness.vec |
Skewness vector for continuous non-normal variables. |
kurtosis.vec |
Kurtosis vector for continuous non-normal variables. |
The execution of the function may take some time since it uses multiple starting points to solve the system of nonlinear equations based on the third order Fleishman polynomials. However, since users need to run it only once for a given set of specifications, it does not constitute a problem.
A matrix of coefficients. The columns represent the variables and rows represent the corresponding a,b,c, and d coefficients.
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.
Fleishman, A.I. (1978). A method for simulating non-normal distributions. Psychometrika, 43(4), 521-532.
## Not run: #Consider four nonnormal continuous variables, which come from #Exp(1),Beta(4,4),Beta(4,2) and Gamma(10,10), respectively. #Skewness and kurtosis values of these variables are as follows: n.NN=4 skewness.vec=c(2,0,-0.4677,0.6325) kurtosis.vec=c(6,-0.5455,-0.3750,0.6) coef.mat=fleishman.coef(n.NN,skewness.vec,kurtosis.vec) n.NN=1 skewness.vec=c(0) kurtosis.vec=c(-1.2) coef.mat=fleishman.coef(n.NN,skewness.vec,kurtosis.vec) n.NN=1 skewness.vec1=c(3) kurtosis.vec1=c(5) coef.mat=fleishman.coef(n.NN,skewness.vec1,kurtosis.vec1) ## End(Not run)## Not run: #Consider four nonnormal continuous variables, which come from #Exp(1),Beta(4,4),Beta(4,2) and Gamma(10,10), respectively. #Skewness and kurtosis values of these variables are as follows: n.NN=4 skewness.vec=c(2,0,-0.4677,0.6325) kurtosis.vec=c(6,-0.5455,-0.3750,0.6) coef.mat=fleishman.coef(n.NN,skewness.vec,kurtosis.vec) n.NN=1 skewness.vec=c(0) kurtosis.vec=c(-1.2) coef.mat=fleishman.coef(n.NN,skewness.vec,kurtosis.vec) n.NN=1 skewness.vec1=c(3) kurtosis.vec1=c(5) coef.mat=fleishman.coef(n.NN,skewness.vec1,kurtosis.vec1) ## End(Not run)
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.
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)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)
n |
Number of variates. |
n.BB |
Number of binary variables. |
n.NN |
Number of continuous non-normal variables. |
prop.vec |
Probability vector for binary variables. |
mean.vec |
Mean vector for continuous non-normal variables. |
variance.vec |
Variance vector for continuous non-normal variables. |
skewness.vec |
Skewness vector for continuous non-normal variables. |
kurtosis.vec |
Kurtosis vector for continuous non-normal variables. |
final.corr.mat |
Final correlation matrix produced from |
coef.mat |
Matrix of coefficients produced from |
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.
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.
validation.bin, validation.skewness.kurtosis,overall.corr.mat, fleishman.coef
## 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)## 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)
This function computes the intermediate correlation matrix for continuous non-normal-continuous non-normal combinations as formulated in Demirtas et al. (2012).
Int.Corr.NN(n.NN, corr.vec = NULL, corr.mat = NULL, coef.mat)Int.Corr.NN(n.NN, corr.vec = NULL, corr.mat = NULL, coef.mat)
n.NN |
Number of continuous non-normal variables. |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered columnwise. |
corr.mat |
Specified correlation matrix. |
coef.mat |
Matrix of coefficients produced from |
A correlation matrix of size n.NN*n.NN.
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.
fleishman.coef, Tetra.Corr.BB, Biserial.Corr.BN, overall.corr.mat
n.NN=4 corr.vec=NULL 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=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)n.NN=4 corr.vec=NULL 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=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)
This function computes the final correlation matrix by combining tetrachoric correlation for binary-binary combinations, biserial correlations for binary-continuous combinations, and intermediate correlation matrix for continuous-continuous combinations.
overall.corr.mat(n.BB, n.NN, prop.vec = NULL, corr.vec = NULL, corr.mat = NULL, coef.mat = NULL)overall.corr.mat(n.BB, n.NN, prop.vec = NULL, corr.vec = NULL, corr.mat = NULL, coef.mat = NULL)
n.BB |
Number of binary variables. |
n.NN |
Number of continuous non-normal variables. |
prop.vec |
Probability vector for binary variables. |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered columnwise. |
corr.mat |
Specified correlation matrix. |
coef.mat |
Matrix of coefficients produced from |
A matrix of size (n.BB+n.NN)*(n.BB+n.NN).
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.
fleishman.coef, Tetra.Corr.BB, Int.Corr.NN, Biserial.Corr.BN
n.BB=2 n.NN=4 prop.vec=c(0.4,0.7) corr.vec=NULL 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=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) final.corr.mat=overall.corr.mat(n.BB,n.NN,prop.vec,corr.vec=NULL,corr.mat, coef.mat) corr.mat.BB=corr.mat[1:2,1:2] final.corr.mat=overall.corr.mat(n.BB,n.NN=0,prop.vec,corr.vec=NULL, corr.mat=corr.mat.BB,coef.mat=NULL) corr.mat.NN=corr.mat[3:6,3:6] final.corr.mat=overall.corr.mat(n.BB=0,n.NN,prop.vec=NULL,corr.vec=NULL, corr.mat=corr.mat.NN,coef.mat) n.BB=1 n.NN=1 prop.vec=0.6 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)n.BB=2 n.NN=4 prop.vec=c(0.4,0.7) corr.vec=NULL 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=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) final.corr.mat=overall.corr.mat(n.BB,n.NN,prop.vec,corr.vec=NULL,corr.mat, coef.mat) corr.mat.BB=corr.mat[1:2,1:2] final.corr.mat=overall.corr.mat(n.BB,n.NN=0,prop.vec,corr.vec=NULL, corr.mat=corr.mat.BB,coef.mat=NULL) corr.mat.NN=corr.mat[3:6,3:6] final.corr.mat=overall.corr.mat(n.BB=0,n.NN,prop.vec=NULL,corr.vec=NULL, corr.mat=corr.mat.NN,coef.mat) n.BB=1 n.NN=1 prop.vec=0.6 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)
This function computes the tetrachoric correlation matrix for binary-binary combinations as formulated in Demirtas et al. (2012).
Tetra.Corr.BB(n.BB, prop.vec, corr.vec = NULL, corr.mat = NULL)Tetra.Corr.BB(n.BB, prop.vec, corr.vec = NULL, corr.mat = NULL)
n.BB |
Number of binary variables. |
prop.vec |
Probability vector for binary variables. |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered columnwise. |
corr.mat |
Specified correlation matrix. |
A correlation matrix of size n.BB*n.BB.
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.
Tetra.Corr.BB, Biserial.Corr.BN, overall.corr.mat
n.BB=2 prop.vec=c(0.4,0.7) corr.vec=NULL 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,by=TRUE) tetcor.mat=Tetra.Corr.BB(n.BB,prop.vec,corr.vec=NULL,corr.mat)n.BB=2 prop.vec=c(0.4,0.7) corr.vec=NULL 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,by=TRUE) tetcor.mat=Tetra.Corr.BB(n.BB,prop.vec,corr.vec=NULL,corr.mat)
Checks whether the marginal specification of the binary part is valid and consistent.
validation.bin(n.BB, prop.vec = NULL)validation.bin(n.BB, prop.vec = NULL)
n.BB |
Number of binary variables. |
prop.vec |
Probability vector for binary variables. |
The function returns TRUE if no specification problem is encountered. Otherwise, it returns an error message.
n.B<-2 prop.vec=c(0.5,0.6) validation.bin(n.B,prop.vec) ## Not run: n.B<-3 prop.vec=c(0.5,0.6) validation.bin(n.B,prop.vec) n.B<-3 prop.vec=c(0.5,0.6) validation.bin(n.B) n.B<-0 prop.vec=c(0.5,0.6) validation.bin(n.B,prop.vec) n.B<-3 prop.vec=c(0.5,0.6) validation.bin(n.B,prop.vec) n.B<-3 prop.vec=NULL validation.bin(n.B,prop.vec) n.B<-3 prop.vec=c(1,1.5,-1.5) validation.bin(n.B,prop.vec) ## End(Not run)n.B<-2 prop.vec=c(0.5,0.6) validation.bin(n.B,prop.vec) ## Not run: n.B<-3 prop.vec=c(0.5,0.6) validation.bin(n.B,prop.vec) n.B<-3 prop.vec=c(0.5,0.6) validation.bin(n.B) n.B<-0 prop.vec=c(0.5,0.6) validation.bin(n.B,prop.vec) n.B<-3 prop.vec=c(0.5,0.6) validation.bin(n.B,prop.vec) n.B<-3 prop.vec=NULL validation.bin(n.B,prop.vec) n.B<-3 prop.vec=c(1,1.5,-1.5) validation.bin(n.B,prop.vec) ## End(Not run)
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.
validation.corr(n.BB, n.NN, corr.vec = NULL, corr.mat = NULL)validation.corr(n.BB, n.NN, corr.vec = NULL, corr.mat = NULL)
n.BB |
Number of binary variables. |
n.NN |
Number of continuous non-normal variables. |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered columnwise. |
corr.mat |
Specified correlation matrix. |
The function returns TRUE if no specification problem is encountered. Otherwise, it returns an error message.
correlation.limits, correlation.bound.check
n.BB=2 n.NN=4 corr.vec=NULL 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) validation.corr(n.BB,n.NN,corr.vec=NULL,corr.mat) n.BB=2 n.NN=4 corr.vec=c(-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,0.4,0.5,0.6,0.7,0.8,0.9) validation.corr(n.BB,n.NN,corr.vec,corr.mat=NULL) ## Not run: n.BB=0 n.NN=4 validation.corr(n.BB,n.NN,corr.vec=NULL,corr.mat) n.BB=2 n.NN=0 validation.corr(n.BB,n.NN=0,corr.vec=NULL,corr.mat) corr.matc=corr.mat[3:6,3:6] validation.corr(n.BB=0,n.NN=4,corr.vec=NULL,corr.mat=corr.matc) corr.mat[2,1]=0.5 validation.corr(n.BB,n.NN,corr.vec=NULL,corr.mat) corr.mat[1,2]=0.5 corr.mat[3,1]=1.5 corr.mat[1,3]=1.5 validation.corr(n.BB,n.NN,corr.vec=NULL,corr.mat) npd<-matrix(c(1, 0.477, 0.644, 0.478, 0.651, 0.826, 0.477, 1, 0.516, 0.233, 0.682, 0.75, 0.644, 0.516, 1, 0.599, 0.581, 0.742, 0.478, 0.233, 0.599, 1, 0.741, 0.8, 0.651, 0.682, 0.581, 0.741, 1, 0.798, 0.826, 0.75, 0.742, 0.8, 0.798, 1), nrow = 6, ncol = 6) validation.corr(n.BB,n.NN,corr.vec=NULL,corr.mat=npd) n.BB=1 n.NN=0 corr.mat<-diag(1) validation.corr(n.BB,n.NN,corr.vec=NULL,corr.mat) ## End(Not run)n.BB=2 n.NN=4 corr.vec=NULL 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) validation.corr(n.BB,n.NN,corr.vec=NULL,corr.mat) n.BB=2 n.NN=4 corr.vec=c(-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,-0.3,0.4,0.5,0.6,0.7,0.8,0.9) validation.corr(n.BB,n.NN,corr.vec,corr.mat=NULL) ## Not run: n.BB=0 n.NN=4 validation.corr(n.BB,n.NN,corr.vec=NULL,corr.mat) n.BB=2 n.NN=0 validation.corr(n.BB,n.NN=0,corr.vec=NULL,corr.mat) corr.matc=corr.mat[3:6,3:6] validation.corr(n.BB=0,n.NN=4,corr.vec=NULL,corr.mat=corr.matc) corr.mat[2,1]=0.5 validation.corr(n.BB,n.NN,corr.vec=NULL,corr.mat) corr.mat[1,2]=0.5 corr.mat[3,1]=1.5 corr.mat[1,3]=1.5 validation.corr(n.BB,n.NN,corr.vec=NULL,corr.mat) npd<-matrix(c(1, 0.477, 0.644, 0.478, 0.651, 0.826, 0.477, 1, 0.516, 0.233, 0.682, 0.75, 0.644, 0.516, 1, 0.599, 0.581, 0.742, 0.478, 0.233, 0.599, 1, 0.741, 0.8, 0.651, 0.682, 0.581, 0.741, 1, 0.798, 0.826, 0.75, 0.742, 0.8, 0.798, 1), nrow = 6, ncol = 6) validation.corr(n.BB,n.NN,corr.vec=NULL,corr.mat=npd) n.BB=1 n.NN=0 corr.mat<-diag(1) validation.corr(n.BB,n.NN,corr.vec=NULL,corr.mat) ## End(Not run)
Checks whether the marginal specification of the continuous non-normal part is valid and consistent.
validation.skewness.kurtosis(n.NN, skewness.vec = NULL, kurtosis.vec = NULL)validation.skewness.kurtosis(n.NN, skewness.vec = NULL, kurtosis.vec = NULL)
n.NN |
Number of continuous non-normal variables. |
skewness.vec |
Skewness vector for continuous non-normal variables. |
kurtosis.vec |
Kurtosis vector for continuous non-normal variables. |
The function returns TRUE if no specification problem is encountered. Otherwise, it returns an error message.
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.
n.NN<-3 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,8) validation.skewness.kurtosis(n.NN,skewness.vec,kurtosis.vec) ## Not run: n.NN<--1 skewness.vec=c(0) kurtosis.vec=c(-1.2) validation.skewness.kurtosis(n.NN,skewness.vec,kurtosis.vec) n.NN<-3 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,5) validation.skewness.kurtosis(3) n.NN<-3 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,5) validation.skewness.kurtosis(n.NN,skewness.vec) validation.skewness.kurtosis(n.NN,kurtosis.vec) n.NN<-0 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,8) validation.skewness.kurtosis(n.NN,skewness.vec,kurtosis.vec) n.NN<-2 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,8) validation.skewness.kurtosis(n.NN,skewness.vec,kurtosis.vec) n.NN<-2 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6) validation.skewness.kurtosis(n.NN,skewness.vec,kurtosis.vec) skewness.vec=c(2,3) kurtosis.vec=c(1,5) validation.skewness.kurtosis(n.NN,skewness.vec,kurtosis.vec) ## End(Not run)n.NN<-3 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,8) validation.skewness.kurtosis(n.NN,skewness.vec,kurtosis.vec) ## Not run: n.NN<--1 skewness.vec=c(0) kurtosis.vec=c(-1.2) validation.skewness.kurtosis(n.NN,skewness.vec,kurtosis.vec) n.NN<-3 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,5) validation.skewness.kurtosis(3) n.NN<-3 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,5) validation.skewness.kurtosis(n.NN,skewness.vec) validation.skewness.kurtosis(n.NN,kurtosis.vec) n.NN<-0 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,8) validation.skewness.kurtosis(n.NN,skewness.vec,kurtosis.vec) n.NN<-2 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,8) validation.skewness.kurtosis(n.NN,skewness.vec,kurtosis.vec) n.NN<-2 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6) validation.skewness.kurtosis(n.NN,skewness.vec,kurtosis.vec) skewness.vec=c(2,3) kurtosis.vec=c(1,5) validation.skewness.kurtosis(n.NN,skewness.vec,kurtosis.vec) ## End(Not run)