| Title: | Data Generation with Poisson, Binary, Ordinal and Normal Components |
|---|---|
| Description: | Generation of multiple count, binary, ordinal and normal variables simultaneously given the marginal characteristics and association structure. The details of the method are explained in Demirtas et al. (2012) <DOI:10.1002/sim.5362>. |
| Authors: | Hakan Demirtas, Yiran Hu, Rawan Allozi, Ran Gao |
| Maintainer: | Ran Gao <[email protected]> |
| License: | GPL-2 | GPL-3 |
| Version: | 1.6.3 |
| Built: | 2024-11-11 07:07:54 UTC |
| Source: | CRAN |
Generation of multiple count, binary, ordinal and normal variables simultaneously given the marginal characteristics and association structure based on the methodologies proposed in Demirtas et al. (2012), Demirtas and Yavuz (2015), Amatya and Demirtas (2016), Demirtas and Hedeker (2016).
| Package: | PoisBinOrdNor |
| Type: | Package |
| Version: | 1.6.3 |
| Date: | 2021-03-21 |
| License: | GPL-2 | GPL-3 |
PoisBinOrdNor package consists of nine functions. The function validation.specs validates the specificed quantities to avoid obvious specification errors.
The functions corr.nn4bb, corr.nn4bn, corr.nn4on, corr.nn4pbo, corr.nn4pn, and corr.nn4pp
each computes the intermediate correlation coefficient for binary-binary combinations, binary-normal combinations, ordinal-normal combinations, count-binary/ordinal combinations,
count-normal and count-count combinations, respectively.
The function intermat assembles the intermediate correlation matrix for the multivariate data based on input from functions corr.nn4bb,
corr.nn4bn, corr.nn4on, corr.nn4pbo, corr.nn4pn and corr.nn4pp.
The engine function genPBONdata computes the final correlation matrix and generates mixed data in accordance with the specified marginal and correlational quantities.
Hakan Demirtas, Yiran Hu, Rawan Allozi, Ran Gao
Maintainer: Ran Gao <[email protected]>
Amatya, A. & 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. & 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. & 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. (2016). Computing the point-biserial correlation under any underlying continuous distribution. Communications in Statistics–Simulation and Computation, 45(8), 2744-2751.
Demirtas, H., Hedeker, D. & Mermelstein, R. J. (2012). Simulation of massive public health data by power polynomials. Statistics in Medicine, 31(27), 3337-3346.
Demirtas, H. & Yavuz, Y. (2015). Concurrent generation of ordinal and normal data. Journal of Biopharmaceutical Statistics, 25(4), 635-650.
Ferrari, P.A. and Barberio, A. (2012). Simulating ordinal data. Multivariate Behavioral Research, 47(4), 566-589.
Yahav, I. & Shmueli, G. (2012). On generating multivariate Poisson data in management science applications. Applied Stochastic Models in Business and Industry, 28(1), 91-102.
This function computes the tetrachoric correlation given the correlation for a pair of binary variables (phi coefficient).
corr.nn4bb(p1, p2, BB.cor)corr.nn4bb(p1, p2, BB.cor)
p1 |
Probability parameter for the first binary variable. |
p2 |
Probability parameter for the second binary variable. |
BB.cor |
Pre-specified correlation for a pair of binary variables. |
A tetrachoric correlation coefficient.
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.
## Not run: corr.nn4bb(0.43, 0.7, 0.129) ## End(Not run)## Not run: corr.nn4bb(0.43, 0.7, 0.129) ## End(Not run)
This function computes the biserial correlation given the specified correlation for a pair of binary and normal variables (point-biserial correlation).
corr.nn4bn(p, BN.cor)corr.nn4bn(p, BN.cor)
p |
Probability parameter for the binary variable. |
BN.cor |
Pre-specified correlation for a pair of binary and normal variables. |
A biserial correlation coefficient.
## Not run: corr.nn4bn(0.43, 0.12) ## End(Not run)## Not run: corr.nn4bn(0.43, 0.12) ## End(Not run)
This function computes the polyserial correlation given the specified correlation for a pair of ordinal and normal variables (point-polyserial correlation).
corr.nn4on(p, ON.cor)corr.nn4on(p, ON.cor)
p |
A vector of probabilities for an ordinal variable. The i-th element of the pvec is the cumulative probability defining the marginal distribution of the ordinal variable. If the variable has k categories, the i-th element of p will contain k-1 probabilities. The k-th element is implicitly 1. |
ON.cor |
Pre-specified correlation for a pair of ordinal-normal variables. |
A tetrachoric correlation coefficient.
## Not run: corr.nn4on(c(0.33, 0.66), 0.22) ## End(Not run)## Not run: corr.nn4on(c(0.33, 0.66), 0.22) ## End(Not run)
This function computes the underlying bivariate normal correlation given the correlation for a pair of count and binary variables or a pair of count and ordinal variables.
corr.nn4pbo(lam, p, PO.cor)corr.nn4pbo(lam, p, PO.cor)
lam |
Rate parameter for the count variable. |
p |
A vector of probabilities for an ordinal variable. The i-th element of the pvec is the cumulative probability defining the marginal distribution of the ordinal variable. If the variable has k categories, the i-th element of p will contain k-1 probabilities. The k-th element is implicitly 1. |
PO.cor |
Pre-specified correlation for a pair of count and binary, or count and ordinal, variables. |
A tetrachoric correlation coefficient.
Amatya, A. & Demirtas, H. (2015). Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation, 85(15), 3129-3139.
Yahav, I. & Shmueli, G. (2012). On generating multivariate Poisson data in management science applications. Applied Stochastic Models in Business and Industry, 28(1), 91-102.
## Not run: corr.nn4pbo(0.5, c(0.2, 0.5), 0.235) ## End(Not run)## Not run: corr.nn4pbo(0.5, c(0.2, 0.5), 0.235) ## End(Not run)
This function computes the underlying bivariate normal correlation given the specified correlation for a pair of count and normal variables.
corr.nn4pn(lam, PN.cor)corr.nn4pn(lam, PN.cor)
lam |
Rate parameter for the count variable. |
PN.cor |
Pre-specified correlation for a pair of count and normal variables. |
Correlation of underlying bivariate normal data.
## Not run: corr.nn4pn(0.5, 0.32) ## End(Not run)## Not run: corr.nn4pn(0.5, 0.32) ## End(Not run)
This function computes the underlying bivariate normal correlation given the specified correlation for a pair of count variables.
corr.nn4pp(lambda1, lambda2, PP.cor)corr.nn4pp(lambda1, lambda2, PP.cor)
lambda1 |
Rate parameter for the first count variable. |
lambda2 |
Rate parameter for the second count variable. |
PP.cor |
Pre-specified correlation for a pair of count variables. |
Correlation of underlying bivariate normal data.
Amatya, A. & Demirtas, H. (2015). Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation, 85(15), 3129-3139.
## Not run: corr.nn4pp(0.5, 2, 0.4) ## End(Not run)## Not run: corr.nn4pp(0.5, 2, 0.4) ## End(Not run)
This function simulates a multivariate data set that is composed of count, binary, ordinal and normal variables with specified marginals and a correlation matrix.
genPBONdata(n, no_pois, no_bin, no_ord, no_norm, inter.mat, lamvec, prop_vec_bin, prop_vec_ord, nor.mean, nor.var)genPBONdata(n, no_pois, no_bin, no_ord, no_norm, inter.mat, lamvec, prop_vec_bin, prop_vec_ord, nor.mean, nor.var)
n |
Number of rows |
no_pois |
Number of count variables |
no_bin |
Number of binary variables |
no_ord |
Number of ordinal variables |
no_norm |
Number of normal variables |
inter.mat |
The intermediate correlation matrix obtained from function intermat |
lamvec |
A vector of marginal rates for the count variables |
prop_vec_bin |
A vector of probabilities for the binary variables |
prop_vec_ord |
A vector of probabilities for the ordinal variables. For each of the variable, the i-th element of the pvec is the cumulative probability defining the marginal distribution of the ordinal variable. If the variable has k categories, the i-th element of p will contain k-1 probabilities. The k-th element is implicitly 1. |
nor.mean |
A vector of means for the normal variables |
nor.var |
A vector of variances for the normal variables |
data |
A simulated data matrix of size nx(no_pois + no_bin + no_ord + no_norm), of which the first no_pois are count variables, followed by no_bin binary variables, no_ord ordinal variables, and lastly no_norm normal variables. |
n.rows |
Number of rows in the simulated data |
prob.bin |
A vector of probabilities for the binary variables |
prob.ord |
A vector of probabilities for the ordinal variables |
nor.mean |
A vector of means for the normal variables |
nor.var |
A vector of variances for the normal variables |
lamvec |
A vector of rate parameters for the count variables |
n.pois |
Number of count variables |
n.bin |
Number of binary variables |
n.ord |
Number of ordinal variables |
n.norm |
Number of normal variables |
final.corr |
The final correlation matrix for the simulated data |
## Not run: ss=10000 num_pois<-2 num_bin<-1 num_ord<-2 num_norm<-1 lamvec=sample(10,2) pbin=runif(1) pord=list(c(0.1, 0.9), c(0.2, 0.3, 0.5)) nor.mean=3.1 nor.var=0.85 M=c(-0.05, 0.26, 0.14, 0.09, 0.14, 0.12, 0.13, -0.02, 0.17, 0.29, -0.04, 0.19, 0.10, 0.35, 0.39) N=diag(6) N[lower.tri(N)]=M TV=N+t(N) diag(TV)<-1 intmat<-intermat(num_pois,num_bin,num_ord,num_norm,corr_mat=TV,pbin,pord,lamvec, nor.mean,nor.var) genPBONdata(ss,num_pois,num_bin,num_ord,num_norm,intmat,lamvec,pbin,pord,nor.mean,nor.var) ## End(Not run)## Not run: ss=10000 num_pois<-2 num_bin<-1 num_ord<-2 num_norm<-1 lamvec=sample(10,2) pbin=runif(1) pord=list(c(0.1, 0.9), c(0.2, 0.3, 0.5)) nor.mean=3.1 nor.var=0.85 M=c(-0.05, 0.26, 0.14, 0.09, 0.14, 0.12, 0.13, -0.02, 0.17, 0.29, -0.04, 0.19, 0.10, 0.35, 0.39) N=diag(6) N[lower.tri(N)]=M TV=N+t(N) diag(TV)<-1 intmat<-intermat(num_pois,num_bin,num_ord,num_norm,corr_mat=TV,pbin,pord,lamvec, nor.mean,nor.var) genPBONdata(ss,num_pois,num_bin,num_ord,num_norm,intmat,lamvec,pbin,pord,nor.mean,nor.var) ## End(Not run)
This function computes and assembles the correlation entries for the intermediate multivariate normal data.
intermat(no_pois, no_bin, no_ord, no_norm, corr_mat, prop_vec_bin, prop_vec_ord, lam_vec, nor_mean, nor_var)intermat(no_pois, no_bin, no_ord, no_norm, corr_mat, prop_vec_bin, prop_vec_ord, lam_vec, nor_mean, nor_var)
no_pois |
Number of the count variables. |
no_bin |
Number of the binary variables. |
no_ord |
Number of the ordinal variables. |
no_norm |
Number of the normal variables. |
corr_mat |
Pre-specified correlation matrix for the multivariate data. |
prop_vec_bin |
Vector of probabilities for the binary variables. |
prop_vec_ord |
Vector of probabilities for the ordinal variables. |
lam_vec |
Vector of rate parameters for the count variables. |
nor_mean |
Vector of means for the normal variables. |
nor_var |
Vector of variances for the normal variables. |
The intermediate correlation matrix that will be used later for multivariate normal data simulation.
Barberio, A. & Ferrari, P.A. (2015). GenOrd: Simulation of discrete random variables with given correlation matrix and marginal distributions. https://cran.r-project.org/web/packages/GenOrd/index.html.
Demirtas, H. & Hedeker, D. (2011). A practical way for computing approximate lower and upper correlation bounds. American Statistician, 65(2), 104-109.
Demirtas, H. & Hedeker, D. (2016). Computing the point-biserial correlation under any underlying continuous distribution. Communications in Statistics–Simulation and Computation, 45(8), 2744-2751.
Ferrari, P.A. and Barberio, A. (2012). Simulating ordinal data. Multivariate Behavioral Research, 47(4), 566-589.
corr.nn4bb, corr.nn4bn, corr.nn4on, corr.nn4pbo,
corr.nn4pn, corr.nn4pp, and validation.specs.
## Not run: num_pois<-2 num_bin<-1 num_ord<-2 num_norm<-1 lamvec=sample(10,2) pbin=runif(1) pord=list(c(0.3, 0.7), c(0.2, 0.3, 0.5)) nor.mean=3.1 nor.var=0.85 M= c(-0.05, 0.26, 0.14, 0.09, 0.14, 0.12, 0.13, -0.02, 0.17, 0.29, -0.04, 0.19, 0.10, 0.35, 0.39) N=diag(6) N[lower.tri(N)]=M TV=N+t(N) diag(TV)<-1 intmat<- intermat(num_pois,num_bin,num_ord,num_norm,corr_mat=TV,pbin,pord,lamvec,nor.mean,nor.var) ## End(Not run)## Not run: num_pois<-2 num_bin<-1 num_ord<-2 num_norm<-1 lamvec=sample(10,2) pbin=runif(1) pord=list(c(0.3, 0.7), c(0.2, 0.3, 0.5)) nor.mean=3.1 nor.var=0.85 M= c(-0.05, 0.26, 0.14, 0.09, 0.14, 0.12, 0.13, -0.02, 0.17, 0.29, -0.04, 0.19, 0.10, 0.35, 0.39) N=diag(6) N[lower.tri(N)]=M TV=N+t(N) diag(TV)<-1 intmat<- intermat(num_pois,num_bin,num_ord,num_norm,corr_mat=TV,pbin,pord,lamvec,nor.mean,nor.var) ## End(Not run)
This function checks the validity of user specified parameters including rate parameters for count variables, proportion parameters for binary and ordinary variables, mean and variance parameters for normal data, as well as the validity of entries in the correlation matrix. This function also computes the lower and upper limits for each pairwise correlation based on the marginal probabilities for range violation checks.
validation.specs(no.pois, no.bin, no.ord, no.norm, corr.mat, prop.vec.bin, prop.vec.ord, lamvec, nor.mean, nor.var) validation_specs(no.pois, no.bin, no.ord, no.norm, corr.mat, prop.vec.bin, prop.vec.ord, lamvec, nor.mean, nor.var) #deprecatedvalidation.specs(no.pois, no.bin, no.ord, no.norm, corr.mat, prop.vec.bin, prop.vec.ord, lamvec, nor.mean, nor.var) validation_specs(no.pois, no.bin, no.ord, no.norm, corr.mat, prop.vec.bin, prop.vec.ord, lamvec, nor.mean, nor.var) #deprecated
no.pois |
Number of count variables. |
no.bin |
Number of binary variables. |
no.ord |
Number of ordinal variables. |
no.norm |
Number of normal variables. |
corr.mat |
User specified correlation matrix for the multivariate data. |
prop.vec.bin |
Vector of probabilities corresponding to each of the binary variables. |
prop.vec.ord |
Vector of probabilities corresponding to each of the ordinal variables. For each of the ordinal variable, the i-th element of the probability vector is the cumulative probability defining the marginal distribution of the ordinal variable. If the variable has k categories, the i-th element of p will contain k-1 probabilities. The k-th element is implicitly 1. |
lamvec |
Vector of rate parameters for the count variables. |
nor.mean |
Vector of means for the normal variables. |
nor.var |
Vector of variances for the normal variables. |
This function computes the lower and upper bounds for all possible pairs that involve count, binary, ordinal and normal variables.
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.
## Not run: num_pois<-1 num_bin<-1 num_ord<-1 num_norm<-1 lambda<-c(1) pbin<-c(0.3) pord<-list(c(0.3,0.6)) normean<-15 norvar<-7 corr.mat=matrix(c(1,0.2,0.1,0.3, 0.2,1,0.5,0.4, 0.1,0.5,1, 0.7, 0.3, 0.4, 0.7, 1),4,4) validation.specs(num_pois, num_bin, num_ord, num_norm, corr.mat, pbin, pord, lambda, normean,norvar) num_pois<-2 num_bin<-2 num_ord<-2 num_norm<-0 lambda<-c(1,2) pbin<-c(0.3,0.5) pord<-list(c(0.3,0.6),c(0.5,0.6)) corr.mat=matrix(0.64,6,6) diag(corr.mat)=1 validation.specs(num_pois, num_bin, num_ord, num_norm, corr.mat, pbin, pord, lambda, nor.mean=NULL, nor.var=NULL) # An example with an invalid target correlation matrix (bound violation). num_pois<-1 num_bin<-2 num_ord<-2 num_norm<-1 lamvec=c(1) pbin=c(0.3, 0.7) pord=list(c(0.2, 0.5), c(0.4, 0.7, 0.8)) nor.mean=2.1 nor.var=0.75 M=c(-0.35, 0.26, 0.34, 0.09, 0.14, 0.12, 0.30, -0.02, 0.17, 0.29, -0.04, 0.19, 0.10, 0.35, 0.39) N=diag(6) N[lower.tri(N)]=M TV=N+t(N) diag(TV)<-1 validation.specs(num_pois, num_bin, num_ord, num_norm, corr.mat=TV, pbin, pord, lamvec, normean, norvar) # An example with a non-positive definite correlation matrix. pbin=c(0.3, 0.7) TV1=TV TV1[3,2]=TV[2,3]=5 validation.specs(num_pois, num_bin, num_ord, num_norm, corr.mat=TV1, pbin, pord, lamvec, normean, norvar) ## End(Not run)## Not run: num_pois<-1 num_bin<-1 num_ord<-1 num_norm<-1 lambda<-c(1) pbin<-c(0.3) pord<-list(c(0.3,0.6)) normean<-15 norvar<-7 corr.mat=matrix(c(1,0.2,0.1,0.3, 0.2,1,0.5,0.4, 0.1,0.5,1, 0.7, 0.3, 0.4, 0.7, 1),4,4) validation.specs(num_pois, num_bin, num_ord, num_norm, corr.mat, pbin, pord, lambda, normean,norvar) num_pois<-2 num_bin<-2 num_ord<-2 num_norm<-0 lambda<-c(1,2) pbin<-c(0.3,0.5) pord<-list(c(0.3,0.6),c(0.5,0.6)) corr.mat=matrix(0.64,6,6) diag(corr.mat)=1 validation.specs(num_pois, num_bin, num_ord, num_norm, corr.mat, pbin, pord, lambda, nor.mean=NULL, nor.var=NULL) # An example with an invalid target correlation matrix (bound violation). num_pois<-1 num_bin<-2 num_ord<-2 num_norm<-1 lamvec=c(1) pbin=c(0.3, 0.7) pord=list(c(0.2, 0.5), c(0.4, 0.7, 0.8)) nor.mean=2.1 nor.var=0.75 M=c(-0.35, 0.26, 0.34, 0.09, 0.14, 0.12, 0.30, -0.02, 0.17, 0.29, -0.04, 0.19, 0.10, 0.35, 0.39) N=diag(6) N[lower.tri(N)]=M TV=N+t(N) diag(TV)<-1 validation.specs(num_pois, num_bin, num_ord, num_norm, corr.mat=TV, pbin, pord, lamvec, normean, norvar) # An example with a non-positive definite correlation matrix. pbin=c(0.3, 0.7) TV1=TV TV1[3,2]=TV[2,3]=5 validation.specs(num_pois, num_bin, num_ord, num_norm, corr.mat=TV1, pbin, pord, lamvec, normean, norvar) ## End(Not run)