| Title: | Data Generation with Poisson, Binary and Continuous Components |
|---|---|
| Description: | Generation of multiple count, binary and continuous variables simultaneously given the marginal characteristics and association structure. Throughout the package, the word 'Poisson' is used to imply count data under the assumption of Poisson distribution. The details of the method are explained in Amatya et al. (2015) <DOI:10.1080/00949655.2014.953534>. |
| Authors: | Gul Inan, Hakan Demirtas, Ran Gao |
| Maintainer: | Ran Gao <[email protected]> |
| License: | GPL-2 | GPL-3 |
| Version: | 1.3.3 |
| Built: | 2025-03-06 06:04:01 UTC |
| Source: | https://github.com/cran/PoisBinNonNor |
Provides R functions for generation of multiple count, binary and continuous variables simultaneously given the marginal characteristics and association structure. Continuous variables can be of any nonnormal shape allowed by the Fleishman polynomials, taking the normal distribution as a special case.
| Package: | PoisBinNonNor |
| Type: | Package |
| Version: | 1.3.3 |
| Date: | 2021-03-21 |
| License: | GPL-2 | GPL-3 |
The package consists of fourteen functions. The functions validation.bin, validation.corr, and
validation.skewness.kurtosis validate the specified quantities. correlation.limits returns the lower and upper bounds of pairwise correlations of
Poisson, binary and continuous variables. correlation.bound.check
validates pairwise correlation values.
intermediate.corr.PP, intermediate.corr.BB, intermediate.corr.CC,
intermediate.corr.PB, intermediate.corr.PC, and intermediate.corr.BC
compute intermediate correlation matrix for Poisson-Poisson combinations, binary-binary,
continuous-continuous, Poisson-binary, Poisson-continuous,
binary-continuous combinations, respectively. The function overall.corr.mat assembles
the final correlation matrix. The engine function gen.PoisBinNonNor
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 continuous variables should be placed.
Gul Inan, Hakan Demirtas, Ran Gao
Maintainer: Ran Gao <[email protected]>
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.
This function checks if there are range violations among correlation of Poisson-Poisson, Poisson-binary, Poisson-continuous, binary-binary, binary-continuous, and continuous-continuous combinations.
correlation.bound.check(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)correlation.bound.check(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)
n.P |
Number of Poisson variables. |
n.B |
Number of binary variables. |
n.C |
Number of continuous variables. |
lambda.vec |
Rate vector for Poisson variables. |
prop.vec |
Proportion vector for binary variables. |
coef.mat |
Matrix of coefficients produced from |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered column-wise. |
corr.mat |
Specified correlation matrix. |
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.
validation.corr, correlation.limits
## Not run: n.P<-1 n.B<-1 n.C<-1 lambda.vec<-c(1) prop.vec<-c(0.3) coef.mat<-matrix(c(-0.3137491,0.8263239,0.3137491,0.0227066),4,1,byrow=F) 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.C,lambda.vec,prop.vec,coef.mat,corr.vec=NULL, corr.mat) n.P<-2 n.B<-2 n.C<-2 lambda.vec<-c(1,2) prop.vec<-c(0.3,0.5) coef.mat<-matrix(c( -0.3137491, 0.0000000, 0.8263239, 1.0857433, 0.3137491, 0.0000000, 0.0227066, -0.0294495),4,2,byrow=F) corr.mat=matrix(0.8,6,6) diag(corr.mat)=1 correlation.bound.check(n.P,n.B,n.C,lambda.vec,prop.vec,coef.mat,corr.vec=NULL, corr.mat) ## End(Not run)## Not run: n.P<-1 n.B<-1 n.C<-1 lambda.vec<-c(1) prop.vec<-c(0.3) coef.mat<-matrix(c(-0.3137491,0.8263239,0.3137491,0.0227066),4,1,byrow=F) 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.C,lambda.vec,prop.vec,coef.mat,corr.vec=NULL, corr.mat) n.P<-2 n.B<-2 n.C<-2 lambda.vec<-c(1,2) prop.vec<-c(0.3,0.5) coef.mat<-matrix(c( -0.3137491, 0.0000000, 0.8263239, 1.0857433, 0.3137491, 0.0000000, 0.0227066, -0.0294495),4,2,byrow=F) corr.mat=matrix(0.8,6,6) diag(corr.mat)=1 correlation.bound.check(n.P,n.B,n.C,lambda.vec,prop.vec,coef.mat,corr.vec=NULL, corr.mat) ## End(Not run)
This function computes lower and upper limits for pairwise correlations of Poisson-Poisson, Poisson-binary, Poisson-continuous, binary-binary, binary-continuous, and continuous-continuous combinations.
correlation.limits(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL)correlation.limits(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL)
n.P |
Number of Poisson variables. |
n.B |
Number of binary variables. |
n.C |
Number of continuous variables. |
lambda.vec |
Rate vector for Poisson variables. |
prop.vec |
Proportion 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 Poisson-Poisson, Poisson-binary, Poisson-continuous, binary-continuous, and continuous-continuous variables through the method suggested by Demirtas and Hedeker (2011).
The function returns a matrix of size (n.P + n.B + n.C)*(n.P + n.B + n.C), 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.
validation.corr, correlation.bound.check
## Not run: n.P<-3 n.B<-2 n.C<-3 lambda.vec<-c(1,2,3) prop.vec<-c(0.3,0.5) coef.mat<-matrix(c( -0.3137491, 0.0000000, 0.1004464, 0.8263239, 1.0857433, 1.1050196, 0.3137491, 0.0000000, -0.1004464, 0.0227066, -0.0294495, -0.0400078),4,3,byrow=F) #Correlation limits among Poisson variables correlation.limits(n.P,n.B=0,n.C=0,lambda.vec,prop.vec=NULL,coef.mat=NULL) #See also Cor.PP.Limit in R package PoisNor #Correlation limits among binary variables correlation.limits(n.P=0,n.B,n.C=0,lambda.vec=NULL,prop.vec,coef.mat=NULL) #See also correlation.limits in R package BinNonNor #Correlation limits among continuous variables correlation.limits(n.P=0,n.B=0,n.C,lambda.vec=NULL,prop.vec=NULL,coef.mat) #Correlation limits among Poisson and binary variables and within themselves. correlation.limits(n.P,n.B,n.C=0,lambda.vec,prop.vec,coef.mat=NULL) #Correlation limits among Poisson and continuous variables and within themselves. correlation.limits(n.P,n.B=0,n.C,lambda.vec,prop.vec=NULL,coef.mat) #Correlation limits among binary and continuous variables and within themselves. correlation.limits(n.P=0,n.B,n.C,lambda.vec=NULL,prop.vec,coef.mat) #Correlation limits among Poisson, binary, and continuous variables and within themselves. correlation.limits(n.P,n.B,n.C,lambda.vec,prop.vec,coef.mat) n.P<-2 lambda.vec=c(-1,1) correlation.limits(n.P,n.B=0,n.C=0,lambda.vec,prop.vec=NULL,coef.mat=NULL) ## End(Not run)## Not run: n.P<-3 n.B<-2 n.C<-3 lambda.vec<-c(1,2,3) prop.vec<-c(0.3,0.5) coef.mat<-matrix(c( -0.3137491, 0.0000000, 0.1004464, 0.8263239, 1.0857433, 1.1050196, 0.3137491, 0.0000000, -0.1004464, 0.0227066, -0.0294495, -0.0400078),4,3,byrow=F) #Correlation limits among Poisson variables correlation.limits(n.P,n.B=0,n.C=0,lambda.vec,prop.vec=NULL,coef.mat=NULL) #See also Cor.PP.Limit in R package PoisNor #Correlation limits among binary variables correlation.limits(n.P=0,n.B,n.C=0,lambda.vec=NULL,prop.vec,coef.mat=NULL) #See also correlation.limits in R package BinNonNor #Correlation limits among continuous variables correlation.limits(n.P=0,n.B=0,n.C,lambda.vec=NULL,prop.vec=NULL,coef.mat) #Correlation limits among Poisson and binary variables and within themselves. correlation.limits(n.P,n.B,n.C=0,lambda.vec,prop.vec,coef.mat=NULL) #Correlation limits among Poisson and continuous variables and within themselves. correlation.limits(n.P,n.B=0,n.C,lambda.vec,prop.vec=NULL,coef.mat) #Correlation limits among binary and continuous variables and within themselves. correlation.limits(n.P=0,n.B,n.C,lambda.vec=NULL,prop.vec,coef.mat) #Correlation limits among Poisson, binary, and continuous variables and within themselves. correlation.limits(n.P,n.B,n.C,lambda.vec,prop.vec,coef.mat) n.P<-2 lambda.vec=c(-1,1) correlation.limits(n.P,n.B=0,n.C=0,lambda.vec,prop.vec=NULL,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.C, skewness.vec = NULL, kurtosis.vec = NULL)fleishman.coef(n.C, skewness.vec = NULL, kurtosis.vec = NULL)
n.C |
Number of continuous variables. |
skewness.vec |
Skewness vector for continuous variables. |
kurtosis.vec |
Kurtosis vector for continuous 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 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.C<-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.C,skewness.vec,kurtosis.vec) n.C<-1 skewness.vec=c(0) kurtosis.vec=c(-1.2) coef.mat=fleishman.coef(n.C,skewness.vec,kurtosis.vec) n.C<-1 skewness.vec1=c(3) kurtosis.vec1=c(5) coef.mat=fleishman.coef(n.C,skewness.vec1,kurtosis.vec1) ## End(Not run)## Not run: #Consider four 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.C<-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.C,skewness.vec,kurtosis.vec) n.C<-1 skewness.vec=c(0) kurtosis.vec=c(-1.2) coef.mat=fleishman.coef(n.C,skewness.vec,kurtosis.vec) n.C<-1 skewness.vec1=c(3) kurtosis.vec1=c(5) coef.mat=fleishman.coef(n.C,skewness.vec1,kurtosis.vec1) ## End(Not run)
This function simulates a sample of size n from a set of multivariate Poisson, binary, and continuous data with pre-specified marginals and a correlation matrix.
gen.PoisBinNonNor(n, n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, mean.vec=NULL, variance.vec=NULL, coef.mat = NULL, final.corr.mat)gen.PoisBinNonNor(n, n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, mean.vec=NULL, variance.vec=NULL, coef.mat = NULL, final.corr.mat)
n |
Number of variates. |
n.P |
Number of Poisson variables. |
n.B |
Number of binary variables. |
n.C |
Number of continuous variables. |
lambda.vec |
Rate vector for Poisson variables. |
prop.vec |
Proportion vector for binary variables. |
mean.vec |
Mean vector of continuous variables. |
variance.vec |
Variance vector of continuous variables. |
coef.mat |
Matrix of coefficients produced from |
final.corr.mat |
Final correlation matrix produced from |
A matrix of size n*(n.P + n.B + n.C), of which the first n.P columns are Poisson variables, the next n.B columns are binary variables, and the last n.C columns are continuous variables.
## Not run: n=100000 n.P<-2 n.B<-2 n.C<-2 lambda.vec<-c(2,3) prop.vec<-c(0.3,0.5) mean.vec<-c(0,0) variance.vec<-c(1,1) coef.mat=matrix(rep(c(0,1,0,0), each=2),4,2,byrow=T) corr.mat=matrix(0.4,6,6) diag(corr.mat)=1 final.corr.mat=overall.corr.mat(n.P,n.B,n.C,lambda.vec,prop.vec, coef.mat,corr.vec=NULL,corr.mat) mymixdata=gen.PoisBinNonNor(n,n.P,n.B,n.C,lambda.vec,prop.vec, mean.vec,variance.vec,coef.mat,final.corr.mat) #Check marginals #apply(mymixdata,2,mean) #cor(mymixdata) n=100000 n.P<-2 n.B<-2 n.N<-2 lambda.vec<-c(2,3) prop.vec<-c(0.3,0.5) mean.vec=c(1,0.5) variance.vec=c(1,0.02777778) skewness.vec=c(2,0) kurtosis.vec=c(6,-0.5455) coef.mat=fleishman.coef(2,skewness.vec, kurtosis.vec) corr.mat=matrix(0.3,6,6) diag(corr.mat)=1 final.corr.mat=overall.corr.mat(n.P,n.B,n.N,lambda.vec,prop.vec, coef.mat,corr.vec=NULL,corr.mat) mymixdata=gen.PoisBinNonNor(n,n.P,n.B,n.N,lambda.vec,prop.vec, mean.vec, variance.vec,coef.mat,final.corr.mat) #Check marginals #apply(mymixdata,2,mean)[4:5] #apply(mymixdata,2,var)[4:5] #cor(mymixdata) ## End(Not run)## Not run: n=100000 n.P<-2 n.B<-2 n.C<-2 lambda.vec<-c(2,3) prop.vec<-c(0.3,0.5) mean.vec<-c(0,0) variance.vec<-c(1,1) coef.mat=matrix(rep(c(0,1,0,0), each=2),4,2,byrow=T) corr.mat=matrix(0.4,6,6) diag(corr.mat)=1 final.corr.mat=overall.corr.mat(n.P,n.B,n.C,lambda.vec,prop.vec, coef.mat,corr.vec=NULL,corr.mat) mymixdata=gen.PoisBinNonNor(n,n.P,n.B,n.C,lambda.vec,prop.vec, mean.vec,variance.vec,coef.mat,final.corr.mat) #Check marginals #apply(mymixdata,2,mean) #cor(mymixdata) n=100000 n.P<-2 n.B<-2 n.N<-2 lambda.vec<-c(2,3) prop.vec<-c(0.3,0.5) mean.vec=c(1,0.5) variance.vec=c(1,0.02777778) skewness.vec=c(2,0) kurtosis.vec=c(6,-0.5455) coef.mat=fleishman.coef(2,skewness.vec, kurtosis.vec) corr.mat=matrix(0.3,6,6) diag(corr.mat)=1 final.corr.mat=overall.corr.mat(n.P,n.B,n.N,lambda.vec,prop.vec, coef.mat,corr.vec=NULL,corr.mat) mymixdata=gen.PoisBinNonNor(n,n.P,n.B,n.N,lambda.vec,prop.vec, mean.vec, variance.vec,coef.mat,final.corr.mat) #Check marginals #apply(mymixdata,2,mean)[4:5] #apply(mymixdata,2,var)[4:5] #cor(mymixdata) ## End(Not run)
Computes an intermediate normal correlation matrix for binary variables before dichotomization given the specified correlation matrix.
intermediate.corr.BB(n.P, n.B, n.C, prop.vec, corr.vec = NULL, corr.mat = NULL)intermediate.corr.BB(n.P, n.B, n.C, prop.vec, corr.vec = NULL, corr.mat = NULL)
n.P |
Number of Poisson variables. |
n.B |
Number of binary variables. |
n.C |
Number of continuous variables. |
prop.vec |
Proportion vector for binary variables. |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered column-wise. |
corr.mat |
Specified correlation matrix. |
A correlation matrix of size n.B*n.B.
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.
intermediate.corr.PB, intermediate.corr.BC
## Not run: n.P<-2 n.B<-2 n.C<-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) intmatBB=intermediate.corr.BB(n.P,n.B,n.C,prop.vec,corr.vec=NULL,corr.mat) intmatBB ## End(Not run)## Not run: n.P<-2 n.B<-2 n.C<-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) intmatBB=intermediate.corr.BB(n.P,n.B,n.C,prop.vec,corr.vec=NULL,corr.mat) intmatBB ## End(Not run)
This function computes the intermediate correlation matrix for binary-continuous combinations as formulated in Demirtas et al. (2012).
intermediate.corr.BC(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)intermediate.corr.BC(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)
n.P |
Number of Poisson variables. |
n.B |
Number of binary variables. |
n.C |
Number of continuous variables. |
lambda.vec |
Rate vector for Poisson variables. |
prop.vec |
Proportion vector for binary variables. |
coef.mat |
Matrix of coefficients produced from |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered column-wise. |
corr.mat |
Specified correlation matrix. |
A correlation matrix of size n.B*n.C.
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.
intermediate.corr.BB, intermediate.corr.CC
## Not run: n.B<-2 n.C<-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) 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) intmatBC=intermediate.corr.BC(n.P=0,n.B,n.C,lambda.vec=NULL,prop.vec,coef.mat, corr.vec=NULL,corr.mat) intmatBC n.B<-1 n.C<-1 prop.vec=0.6 coef.mat=matrix(c(-0.31375,0.82632,0.31375,0.02271),4,1) corr.vec=NULL corr.mat=matrix(c(1,-0.3,-0.3,1),2,2) intmatBC=intermediate.corr.BC(n.P=0,n.B,n.C,lambda.vec=NULL,prop.vec,coef.mat, corr.vec=NULL,corr.mat) intmatBC ## End(Not run)## Not run: n.B<-2 n.C<-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) 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) intmatBC=intermediate.corr.BC(n.P=0,n.B,n.C,lambda.vec=NULL,prop.vec,coef.mat, corr.vec=NULL,corr.mat) intmatBC n.B<-1 n.C<-1 prop.vec=0.6 coef.mat=matrix(c(-0.31375,0.82632,0.31375,0.02271),4,1) corr.vec=NULL corr.mat=matrix(c(1,-0.3,-0.3,1),2,2) intmatBC=intermediate.corr.BC(n.P=0,n.B,n.C,lambda.vec=NULL,prop.vec,coef.mat, corr.vec=NULL,corr.mat) intmatBC ## End(Not run)
This function computes the intermediate correlation matrix for continuous-continuous combinations as formulated in Demirtas et al. (2012).
intermediate.corr.CC(n.P, n.B, n.C, coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)intermediate.corr.CC(n.P, n.B, n.C, coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)
n.P |
Number of Poisson variables. |
n.B |
Number of binary variables. |
n.C |
Number of continuous variables. |
coef.mat |
Matrix of coefficients produced from |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered column-wise. |
corr.mat |
Specified correlation matrix. |
A correlation matrix of size n.C*n.C.
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.
intermediate.corr.PC, intermediate.corr.BC
## Not run: n.P=2 n.C=4 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) 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) intmatCC=intermediate.corr.CC(n.P,n.B=0,n.C,coef.mat,corr.vec=NULL,corr.mat) intmatCC ## End(Not run)## Not run: n.P=2 n.C=4 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) 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) intmatCC=intermediate.corr.CC(n.P,n.B=0,n.C,coef.mat,corr.vec=NULL,corr.mat) intmatCC ## End(Not run)
This function computes the pairwise entries of the intermediate normal correlation matrix for all Poisson-binary combinations given the specified correlation matrix as formulated in Amatya and Demirtas (2015).
intermediate.corr.PB(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)intermediate.corr.PB(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)
n.P |
Number of Poisson variables. |
n.B |
Number of binary variables. |
n.C |
Number of continuous variables. |
lambda.vec |
Rate vector for Poisson variables. |
prop.vec |
Proportion vector for binary variables. |
coef.mat |
Matrix of coefficients produced from |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered column-wise. |
corr.mat |
Specified correlation matrix. |
A matrix of n.P*n.B.
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.
intermediate.corr.PP, intermediate.corr.BB
## Not run: n.P<-2 n.B<-1 lambda.vec<-c(2,3) prop.vec<-c(0.3) corr.mat=matrix(c(1,0.2,0.1,0.2,1,0.5,0.1,0.5,1),3,3) intmatPB=intermediate.corr.PB(n.P,n.B,n.C=0,lambda.vec,prop.vec,coef.mat=NULL, corr.vec=NULL,corr.mat) intmatPB ## End(Not run)## Not run: n.P<-2 n.B<-1 lambda.vec<-c(2,3) prop.vec<-c(0.3) corr.mat=matrix(c(1,0.2,0.1,0.2,1,0.5,0.1,0.5,1),3,3) intmatPB=intermediate.corr.PB(n.P,n.B,n.C=0,lambda.vec,prop.vec,coef.mat=NULL, corr.vec=NULL,corr.mat) intmatPB ## End(Not run)
This function computes the pairwise entries of the intermediate normal correlation matrix for all Poisson-continuous combinations given the specified correlation matrix as formulated in Amatya and Demirtas (2015).
intermediate.corr.PC(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)intermediate.corr.PC(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)
n.P |
Number of Poisson variables. |
n.B |
Number of binary variables. |
n.C |
Number of continuous variables. |
lambda.vec |
Rate vector for Poisson variables. |
prop.vec |
Proportion vector for binary variables. |
coef.mat |
Matrix of coefficients produced from |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered column-wise. |
corr.mat |
Specified correlation matrix. |
A correlation matrix of size n.P*n.C.
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.
intermediate.corr.PP, intermediate.corr.CC
## Not run: n.P=2 n.C=4 lambda.vec=c(2,3) coef.mat=matrix(rep(c(0,1,0,0),each=4),4,byrow=TRUE) 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) intmatPC=intermediate.corr.PC(n.P,n.B=0,n.C,lambda.vec,prop.vec=NULL, coef.mat,corr.vec=NULL,corr.mat) intmatPC #See also cmat.star in R package PoisNor #cmat.star(no.pois=2,no.norm=4,corMat=corr.mat,lamvec=lambda.vec) ## End(Not run)## Not run: n.P=2 n.C=4 lambda.vec=c(2,3) coef.mat=matrix(rep(c(0,1,0,0),each=4),4,byrow=TRUE) 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) intmatPC=intermediate.corr.PC(n.P,n.B=0,n.C,lambda.vec,prop.vec=NULL, coef.mat,corr.vec=NULL,corr.mat) intmatPC #See also cmat.star in R package PoisNor #cmat.star(no.pois=2,no.norm=4,corMat=corr.mat,lamvec=lambda.vec) ## End(Not run)
This function computes the intermediate normal correlation matrix for Poisson-Poisson combinations before inverse cdf matching as formulated in Amatya and Demirtas (2015).
intermediate.corr.PP(n.P, n.B, n.C, lambda.vec, corr.vec = NULL, corr.mat = NULL)intermediate.corr.PP(n.P, n.B, n.C, lambda.vec, corr.vec = NULL, corr.mat = NULL)
n.P |
Number of Poisson variables. |
n.B |
Number of binary variables. |
n.C |
Number of continuous variables. |
lambda.vec |
Rate vector for Poisson variables |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered column-wise. |
corr.mat |
Specified correlation matrix. |
A correlation matrix of size n.P*n.P.
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.
intermediate.corr.PB, intermediate.corr.PC
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,n.B=0,n.C=0,lambda.vec,corr.vec=NULL,corr.mat) intmatPP ## 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)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,n.B=0,n.C=0,lambda.vec,corr.vec=NULL,corr.mat) intmatPP ## 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)
This function computes the final correlation matrix by combining pairwise intermediate correlation matrix entries for Poisson-Poisson, Poisson-binary, Poisson-continuous, binary-binary, binary-continuous, and continuous-continuous combinations. If the resulting correlation matrix is not positive definite, a nearest positive matrix will be used.
overall.corr.mat(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)overall.corr.mat(n.P, n.B, n.C, lambda.vec = NULL, prop.vec = NULL, coef.mat = NULL, corr.vec = NULL, corr.mat = NULL)
n.P |
Number of Poisson variables. |
n.B |
Number of binary variables. |
n.C |
Number of continuous variables. |
lambda.vec |
Rate vector for Poisson variables. |
prop.vec |
Proportion vector for binary variables. |
coef.mat |
Matrix of coefficients produced from |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered column-wise. |
corr.mat |
Specified correlation matrix. |
A correlation matrix of size (n.P+N.B+n.C)*(n.P+N.B+n.C).
intermediate.corr.PP, intermediate.corr.BB, intermediate.corr.CC,
intermediate.corr.PB, intermediate.corr.PC, intermediate.corr.BC
## Not run: n.P<-1 n.B<-1 n.C<-1 lambda.vec<-c(1) prop.vec<-c(0.3) coef.mat<-matrix(c(0,1,0,0),4,1) 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.C,lambda.vec,prop.vec,coef.mat, corr.vec=NULL,corr.mat) finalmat ## End(Not run)## Not run: n.P<-1 n.B<-1 n.C<-1 lambda.vec<-c(1) prop.vec<-c(0.3) coef.mat<-matrix(c(0,1,0,0),4,1) 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.C,lambda.vec,prop.vec,coef.mat, corr.vec=NULL,corr.mat) finalmat ## End(Not run)
Checks whether the marginal specification of the binary part is valid and consistent.
validation.bin(n.B, prop.vec = NULL)validation.bin(n.B, prop.vec = NULL)
n.B |
Number of binary variables. |
prop.vec |
Proportion vector for binary variables. |
The function returns TRUE if no specification problem is encountered. Otherwise, it returns an error message.
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)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)
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.P, n.B, n.C, corr.vec = NULL, corr.mat = NULL)validation.corr(n.P, n.B, n.C, corr.vec = NULL, corr.mat = NULL)
n.P |
Number of Poisson variables. |
n.B |
Number of binary variables. |
n.C |
Number of continuous variables. |
corr.vec |
Vector of elements below the diagonal of correlation matrix ordered column-wise. |
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.P<-1 n.B<-1 n.C<-1 corr.vec=c(0.2,0.1,0.5) validation.corr(n.P,n.B,n.C,corr.vec,corr.mat=NULL) n.P<-2 n.B<-2 n.C<-2 corr.mat=matrix(0.5,6,6) diag(corr.mat)=1 validation.corr(n.P,n.B,n.C,corr.vec=NULL,corr.mat) ## Not run: n.P<-2 n.B<-2 n.C<-1 corr.mat=matrix(0.5,6,6) diag(corr.mat)=1 validation.corr(n.P,n.B,n.C,corr.vec=NULL,corr.mat) n.P<-2 n.B<-2 n.C<-2 corr.mat=matrix(0.5,6,6) corr.mat[1,2]=0.4 diag(corr.mat)=1 validation.corr(n.P,n.B,n.C,corr.vec=NULL,corr.mat) ## End(Not run)n.P<-1 n.B<-1 n.C<-1 corr.vec=c(0.2,0.1,0.5) validation.corr(n.P,n.B,n.C,corr.vec,corr.mat=NULL) n.P<-2 n.B<-2 n.C<-2 corr.mat=matrix(0.5,6,6) diag(corr.mat)=1 validation.corr(n.P,n.B,n.C,corr.vec=NULL,corr.mat) ## Not run: n.P<-2 n.B<-2 n.C<-1 corr.mat=matrix(0.5,6,6) diag(corr.mat)=1 validation.corr(n.P,n.B,n.C,corr.vec=NULL,corr.mat) n.P<-2 n.B<-2 n.C<-2 corr.mat=matrix(0.5,6,6) corr.mat[1,2]=0.4 diag(corr.mat)=1 validation.corr(n.P,n.B,n.C,corr.vec=NULL,corr.mat) ## End(Not run)
Checks whether the marginal specification of the continuous part is valid and consistent.
validation.skewness.kurtosis(n.C, skewness.vec = NULL, kurtosis.vec = NULL)validation.skewness.kurtosis(n.C, skewness.vec = NULL, kurtosis.vec = NULL)
n.C |
Number of continuous variables. |
skewness.vec |
Skewness vector for continuous variables. |
kurtosis.vec |
Kurtosis vector for continuous 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.C<-3 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,8) validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec) ## Not run: n.C<--1 skewness.vec=c(0) kurtosis.vec=c(-1.2) validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec) n.C<-3 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,5) validation.skewness.kurtosis(3) n.C<-3 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,5) validation.skewness.kurtosis(n.C,skewness.vec) validation.skewness.kurtosis(n.C,kurtosis.vec) n.C<-0 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,8) validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec) n.C<-2 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,8) validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec) n.C<-2 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6) validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec) skewness.vec=c(2,3) kurtosis.vec=c(1,5) validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec) ## End(Not run)n.C<-3 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,8) validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec) ## Not run: n.C<--1 skewness.vec=c(0) kurtosis.vec=c(-1.2) validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec) n.C<-3 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,5) validation.skewness.kurtosis(3) n.C<-3 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,5) validation.skewness.kurtosis(n.C,skewness.vec) validation.skewness.kurtosis(n.C,kurtosis.vec) n.C<-0 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,8) validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec) n.C<-2 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6,8) validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec) n.C<-2 skewness.vec=c(0,2,3) kurtosis.vec=c(-1.2,6) validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec) skewness.vec=c(2,3) kurtosis.vec=c(1,5) validation.skewness.kurtosis(n.C,skewness.vec,kurtosis.vec) ## End(Not run)