Data Generation with Count, Binary, Ordinal and Normal Components

Description

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).

Details

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.

Author(s)

Hakan Demirtas, Yiran Hu, Rawan Allozi, Ran Gao

Maintainer: Ran Gao <rgao8@uic.edu>

References

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.

Finds the tetrachoric correlation based on user-specified correlation between binary variables.

Description

This function computes the tetrachoric correlation given the correlation for a pair of binary variables (phi coefficient).

Usage

corr.nn4bb(p1, p2, BB.cor)

Arguments

Value

A tetrachoric correlation coefficient.

References

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.

Examples

## Not run: 
corr.nn4bb(0.43, 0.7, 0.129)

## End(Not run)

Finds the biserial correlation given the correlation for a binary-normal pair.

Description

This function computes the biserial correlation given the specified correlation for a pair of binary and normal variables (point-biserial correlation).

Usage

corr.nn4bn(p, BN.cor)

Arguments

Value

A biserial correlation coefficient.

Examples

## Not run: 
corr.nn4bn(0.43, 0.12)

## End(Not run)

Finds polyserial correlation for given the correlation for an ordinal-normal pair.

Description

This function computes the polyserial correlation given the specified correlation for a pair of ordinal and normal variables (point-polyserial correlation).

Usage

corr.nn4on(p, ON.cor)

Arguments

Value

A tetrachoric correlation coefficient.

Examples

## Not run: 
corr.nn4on(c(0.33, 0.66), 0.22)

## End(Not run)

Finds the underlying bivariate normal correlation given the correlation for a count-binary or count-ordinal pair.

Description

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.

Usage

corr.nn4pbo(lam, p, PO.cor)

Arguments

Value

A tetrachoric correlation coefficient.

References

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.

Examples

## Not run: 
corr.nn4pbo(0.5, c(0.2, 0.5), 0.235)

## End(Not run)

Finds the underlying bivariate normal correlation given the correlation for a count-normal pair.

Description

This function computes the underlying bivariate normal correlation given the specified correlation for a pair of count and normal variables.

Usage

corr.nn4pn(lam, PN.cor)

Arguments

Value

Correlation of underlying bivariate normal data.

Examples

## Not run: 
corr.nn4pn(0.5, 0.32)

## End(Not run)

Finds the underlying bivariate normal correlation given the correlation for a pair of count variables.

Description

This function computes the underlying bivariate normal correlation given the specified correlation for a pair of count variables.

Usage

corr.nn4pp(lambda1, lambda2, PP.cor)

Arguments

Value

Correlation of underlying bivariate normal data.

References

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.

Examples

## Not run: 
corr.nn4pp(0.5, 2, 0.4)

## End(Not run)

Generates correlated data with multiple count, binary, ordinal and normal variables

Description

This function simulates a multivariate data set that is composed of count, binary, ordinal and normal variables with specified marginals and a correlation matrix.

Usage

genPBONdata(n, no_pois, no_bin, no_ord, no_norm, inter.mat, lamvec, prop_vec_bin,
 prop_vec_ord, nor.mean, nor.var)

Arguments

Value

Examples

## 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)

Calculates and assembles the intermediate correlation matrix entries for the multivariate normal data.

Description

This function computes and assembles the correlation entries for the intermediate multivariate normal data.

Usage

intermat(no_pois, no_bin, no_ord, no_norm, corr_mat, prop_vec_bin, prop_vec_ord,
 lam_vec, nor_mean, nor_var)

Arguments

Value

The intermediate correlation matrix that will be used later for multivariate normal data simulation.

References

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.

See Also

corr.nn4bb, corr.nn4bn, corr.nn4on, corr.nn4pbo, corr.nn4pn, corr.nn4pp, and validation.specs.

Examples

## 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)

Validates user-specified parameters

Description

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.

Usage

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) #deprecated

Arguments

Details

This function computes the lower and upper bounds for all possible pairs that involve count, binary, ordinal and normal variables.

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.

Examples

## 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)