| Type: | Package |
| Title: | Simultaneous Generation of Count and Continuous Data |
| Version: | 1.6.3 |
| Date: | 2021-03-21 |
| Author: | Hakan Demirtas, Yaru Shi, Rawan Allozi, Ran Gao |
| Maintainer: | Ran Gao <rgao8@uic.edu> |
| Description: | Generation of count (assuming Poisson distribution) and continuous data (using Fleishman polynomials) simultaneously. The details of the method are explained in Demirtas et al. (2012) <doi:10.1002/sim.5362>. |
| License: | GPL-2 | GPL-3 |
| Depends: | BB, corpcor, MASS, Matrix |
| NeedsCompilation: | no |
| Packaged: | 2021-03-21 22:22:21 UTC; rangao |
| Repository: | CRAN |
| Date/Publication: | 2021-03-21 22:50:04 UTC |
Simultaneous generation of count and continuous data with Poisson and continuous marginals
Description
A package for simulating multivariate data with count and continuous variables with a pre-specified correlation matrix and marginal distributions. The count variables are assumed to have Poisson distribution, and continuous variables can take any shape that is allowed by the Fleishman polynomials. This mixed data generation scheme is a combination of the normal to anything principle for the count part, and multivariate continuous data generation mechanism via the Fleishman polynomials.
Details
| Package: | PoisNonNor |
| Type: | Package |
| Version: | 1.6.3 |
| Date: | 2021-03-21 |
| License: | GPL-2 | GPL-3 |
This package consists of eleven functions.
The functions bounds.corr.GSC.NN, bounds.corr.GSC.NNP, and bounds.corr.GSC.PP return the lower and upper bounds of the pairwise correlation of continuous-continuous, continuous-count, and count-count pairs, respectively. The function Validate.correlation validates the specified quantities to avoid obvious correlation matrix specification errors in regarding to the correlation matrix. The functions intercor.NN, intercor.NNP, and intercor.PP give the intermediate normal correlation matrix for continuous-continuous, continuous-count, and count-count combinations, respectively. The function intercor.all returns the final intermediate correlation matrix by combining the three parts of correlation together. The function Param.fleishman calculates the Fleishman coefficient. The engine function RNG.P.NN generates mixed data in accordance with the specified marginal and correlation matrix.
n1, n2, and n=n1+n2 stand for the number of count, continuous, and the total number of the variables, respectively. By design, the first n1 variables are count, and the last n2 variables are continuous in the generated data matrix.
Author(s)
Hakan Demirtas, Yaru Shi, Rawan Allozi, Ran Gao
Maintainer: Ran Gao <rgao8@uic.edu>
References
Amatya, A. and Demirtas, H. (2017). PoisNor: An R package for generation of multivariate data with Poisson and normal marginals. Communications in Statistics–Simulation and Computation, 46(3), 2241-2253.
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.
Vale, C.D. and Maurelli, V.A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48(3), 465-471.
Calculates the Fleishman coefficients
Description
This function calculates the four coefficients in the Fleishman system given skewness and kurtosis values.
Usage
Param.fleishman(rmat)
Arguments
rmat |
a n2x2 matrix that includes skewness and kurtosis values for each continuous variable, where the first and second columns represent skewness and kurtosis, respectively. |
Value
Returns a matrix of size n2x4 where rows and columns represent variables and coefficients, respectively.
References
Fleishman A.I. (1978). A method for simulating non-normal distributions. Psychometrika, 43(4), 521-532.
Examples
## Not run:
rmat = matrix(c(-0.5486,-0.2103, 0.3386, 0.9035, 1.0283, 0.9272), byrow=TRUE, ncol=2)
Param.fleishman(rmat)
## End(Not run)
Simultaneously generates count and continuous data
Description
This function simulates count and continuous data, where the count part is assumed to follow a multivariate Poisson distribution and the continuous part can take any shape allowed by the Fleishman polynomials. A correlation matrix and marginal features (rate parameter for the count variables, and skewness and kurtosis parameters for the continuous variables must be supplied by users).
Usage
RNG.P.NN(lamvec, cmat, rmat, norow, mean.vec, variance.vec)
RNG_P_NN(lamvec, cmat, rmat, norow, mean.vec, variance.vec) #Deprecated
Arguments
lamvec |
a vector of lambda values of length n1 |
cmat |
specified correlation matrix |
rmat |
a n2x2 matrix that includes skewness and kurtosis values for each continuous variable |
norow |
number of rows in the multivariate mixed data |
mean.vec |
mean vector for continuous variables of length n2 |
variance.vec |
variance vector for continuous variables of length n2 |
Value
Returns a data matrix of size norowx(n1+n2). By design, the first n1 variables are count, and the last n2 variables are continuous.
References
Amatya, A. and Demirtas, H. (2017). PoisNor: An R package for generation of multivariate data with Poisson and normal marginals. Communications in Statistics–Simulation and Computation, 46(3), 2241-2253.
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 A.I. (1978). A method for simulating non-normal distributions. Psychometrika, 43(4), 521-532.
Vale, C.D. and Maurelli, V.A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48(3), 465-471.
Yahav, I. and 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:
lamvec = c(0.5,0.7,0.9)
cmat = matrix(c(
1.000, 0.352, 0.265, 0.342, 0.090, 0.141,
0.352, 1.000, 0.121, 0.297, -0.022, 0.177,
0.265, 0.121, 1.000, 0.294, -0.044, 0.129,
0.342, 0.297, 0.294, 1.000, 0.100, 0.354,
0.090, -0.022, -0.044, 0.100, 1.000, 0.386,
0.141, 0.177, 0.129, 0.354, 0.386, 1.000), nrow=6, byrow=TRUE)
rmat = matrix(c(-0.5486,-0.2103, 0.3386, 0.9035, 1.0283, 0.9272), byrow=TRUE, ncol=2)
norow=10e+5
mean.vec=c(1,0.5,100)
variance.vec=c(1,0.02777778,1000)
P_NN_data = RNG.P.NN(lamvec, cmat, rmat, norow, mean.vec, variance.vec)
## End(Not run)
Checks the validity of the specified correlation matrix
Description
The function checks the validity of pairwise correlations. Additionally, it checks positive definiteness, symmetry, and correctness of the dimensions.
Usage
Validate.correlation(cmat, pmat = NULL, lamvec = NULL)
Arguments
cmat |
a nxn matrix of specified correlations for the n-variate distribution. |
pmat |
a n2x4 matrix where each row includes the four coefficients (a,b,c,d) of the Fleishman's system. |
lamvec |
a vector of lambda values of length n1. |
Details
In addition to being positive definite and symmetric, the values of pairwise correlations in the target correlation matrix must also fall within the limits imposed by the marginal distributions in the system. The function ensures that the supplied correlation matrix is valid for simulation. If a violation occurs, an error message is displayed that identifies the violation. The function returns a logical value TRUE when no such violation occurs.
See Also
bounds.corr.GSC.PP, bounds.corr.GSC.NN, bounds.corr.GSC.NNP
Examples
## Not run:
pmat = matrix(c(
0.1148643, 1.0899150, -0.1148643, -0.0356926,
-0.0488138, 0.9203374, 0.0488138, 0.0251256,
-0.2107427, 1.0398224, 0.2107427, -0.0293247), nrow=3, byrow=TRUE)
lamvec = c(0.5,0.7,0.9)
cmat = matrix(c(
1.000, 0.352, 0.265, 0.342, 0.090, 0.141,
0.352, 1.000, 0.121, 0.297, -0.022, 0.177,
0.265, 0.121, 1.000, 0.294, -0.044, 0.129,
0.342, 0.297, 0.294, 1.000, 0.100, 0.354,
0.090, -0.022, -0.044, 0.100, 1.000, 0.386,
0.141, 0.177, 0.129, 0.354, 0.386, 1.000), nrow=6, byrow=TRUE)
Validate.correlation (cmat,pmat,lamvec)
## End(Not run)
Computes the approximate lower and upper bounds of the correlation matrix entries for the continuous pairs
Description
This function calculates the approximate lower and upper bounds for all continuous pairs by the method in Demirtas and Hedeker (2011).
Usage
bounds.corr.GSC.NN(pmat)
Arguments
pmat |
a n2x4 matrix where each row includes the four coefficients (a,b,c,d) of the Fleishman's system. |
Details
The approximate correlation bounds are computed via the 'Generate, Sort, and Correlate' (GSC) technique, proposed by Demirtas and Hedeker (2011).
Value
Returns a list with two components
min |
lower correlation bound matrix |
max |
upper correlation bound matrix |
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.
See Also
bounds.corr.GSC.NNP, bounds.corr.GSC.PP
Examples
## Not run:
pmat = matrix(c(
0.1148643, 1.0899150, -0.1148643, -0.0356926,
-0.0488138, 0.9203374, 0.0488138, 0.0251256,
-0.2107427, 1.0398224, 0.2107427, -0.0293247), nrow=3, byrow=TRUE)
bounds.corr.GSC.NN (pmat)
## End(Not run)
Computes the approximate lower and upper bounds of the correlation matrix entries for the continuous-count pairs
Description
This function calculates the approximate lower and upper bounds for all continuous-count pairs by the method in Demirtas and Hedeker (2011).
Usage
bounds.corr.GSC.NNP(lamvec, pmat)
Arguments
lamvec |
a vector of lambda values of length n1. |
pmat |
a n2x4 matrix where each row includes the four coefficients (a,b,c,d) of the Fleishman's system. |
Details
The approximate correlation bounds are computed via the 'Generate, Sort, and Correlate' (GSC) technique, proposed by Demirtas and Hedeker (2011).
Value
Returns a list with two components, both are matrices of size n1xn2 where n1 and n2 are the number of count and continuous variables, respectively.
min |
lower correlation bound matrix |
max |
upper correlation bound matrix |
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.
See Also
bounds.corr.GSC.NN, bounds.corr.GSC.PP
Examples
## Not run:
pmat = matrix(c(
0.1148643, 1.0899150, -0.1148643, -0.0356926,
-0.0488138, 0.9203374, 0.0488138, 0.0251256,
-0.2107427, 1.0398224, 0.2107427, -0.0293247), nrow=3, byrow=TRUE)
lamvec = c(0.5,0.7,0.9)
bounds.corr.GSC.NNP(lamvec,pmat)
## End(Not run)
Computes the approximate lower and upper bounds of the correlation matrix entries for the count pairs
Description
This function calculates the approximate lower and upper bounds for all count pairs by the method in Demirtas and Hedeker (2011).
Usage
bounds.corr.GSC.PP(lamvec)
Arguments
lamvec |
a vector of lambda values of length n1. |
Details
The approximate correlation bounds are computed via the 'Generate, Sort, and Correlate' (GSC) technique, proposed by Demirtas and Hedeker (2011).
Value
Returns a list with two components, both are matrices of size n1xn1.
min |
lower correlation bound matrix |
max |
upper correlation bound matrix |
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.
See Also
bounds.corr.GSC.NNP, bounds.corr.GSC.PP
Examples
## Not run:
lamvec = c(0.5,0.7,0.9)
bounds.corr.GSC.PP(lamvec)
## End(Not run)
An auxiliary function that is called by Param.fleishman function
Description
This function sets up formulae that are needed at the subsequent stages.
Usage
fleishman.roots(p, r)
Arguments
p |
a vector of length three that contains the Fleishman coefficients. |
r |
a vector of length two that contains skewness and kurtosis values. |
References
Fleishman A.I. (1978). A method for simulating non-normal distributions. Psychometrika, 43(4), 521-532.
See Also
Computes the subset of the intermediate correlation matrix that is pertinent to the continuous pairs
Description
This function computes the submatrix of the intermediate correlation matrix of the multivariate normal distribution. It is relevant to the continuous part of the data.
Usage
intercor.NN(pmat, cmat)
Arguments
pmat |
a n2x4 matrix where each row includes the four coefficients (a,b,c,d) of the Fleishman's system. |
cmat |
a n2xn2 matrix of specified correlations for the continuous part. |
Details
Fleishman polynomials is a method to generate real-life non-normal distributions of variables by using their first four moments. It is based on the polynomial transformation, Y = a + bZ + cZ^2 + dZ^3, where Z follows a standard normal distribution and Y is standardized (zero mean and unit variance).
Normal-Normal correlation for a given continuous pair can be calculated by solving the following equation.
r_{Y_1Y_2} = r_{Z_1Z_2}(b_1b_2+3b_1d_2+3d_1b_2+9d_1d_2) + r_{Z_1Z_2}^2(2c_1c_2)+r_{Z_1Z_2}^3(6d_1d_2)
Value
Returns an intermediate matrix of size n2xn2
References
Yahav, I. and 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:
pmat = matrix(c(
0.1148643, 1.0899150, -0.1148643, -0.0356926,
-0.0488138, 0.9203374, 0.0488138, 0.0251256,
-0.2107427, 1.0398224, 0.2107427, -0.0293247), nrow=3, byrow=TRUE)
cmat = matrix(c(
1.000, 0.100, 0.354,
0.100, 1.000, 0.386,
0.354, 0.386, 1.000),nrow=3,byrow=TRUE)
intercor.NN(pmat,cmat)
## End(Not run)
Computes the subset of the intermediate correlation matrix that is pertinent to the count-continuous pairs
Description
This function computes the submatrix of the intermediate correlation matrix of the multivariate normal distribution. It is relevant to the count-continuous part of the data.
Usage
intercor.NNP(lamvec, cmat, pmat)
Arguments
lamvec |
a vector of lambda values of length n1. |
cmat |
a (n1+n2)x(n1+n2) matrix of specified correlations. |
pmat |
a n2x4 matrix where each row includes the four coefficients (a,b,c,d) of the Fleishman's system. |
Details
Calculations are done by combining the methods described in Demirtas, Hedeker and Mermelstein (2012) and Amatya and Demirtas (2017).
Value
Returns an intermediate correlation matrix of size n1 x n2
References
Amatya, A. and Demirtas, H. (2017). PoisNor: An R package for generation of multivariate data with Poisson and normal marginals. Communications in Statistics–Simulation and Computation, 46(3), 2241-2253.
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:
pmat = matrix(c(
0.1148643, 1.0899150, -0.1148643, -0.0356926,
-0.0488138, 0.9203374, 0.0488138, 0.0251256,
-0.2107427, 1.0398224, 0.2107427, -0.0293247), nrow=3, byrow=TRUE)
lamvec = c(0.5,0.7,0.9)
cmat = matrix(c(
0.342, 0.090, 0.141,
0.297, -0.022, 0.177,
0.294, -0.044, 0.129), nrow=3, byrow=TRUE)
intercor.NNP(lamvec, cmat, pmat)
## End(Not run)
Computes the subset of the intermediate correlation matrix that is pertinent to the count pairs
Description
This function computes the submatrix of the intermediate correlation matrix of the multivariate normal distribution. It is relevant to the count part of the data.
Usage
intercor.PP(lamvec, cmat)
Arguments
lamvec |
a vector of lambda values of length n1. |
cmat |
a n1xn1 matrix of specified correlations. |
Details
Calculations are done by combining the methods described in Yahav and Shumeli (2012) and Amatya and Demirtas (2017).
Value
Returns an intermediate matrix of size n1xn1.
References
Amatya, A. and Demirtas, H. (2017). PoisNor: An R package for generation of multivariate data with Poisson and normal marginals. Communications in Statistics–Simulation and Computation, 46(3), 2241-2253.
Yahav, I. and 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:
lamvec = c(0.5,0.7,0.9)
cmat = matrix(c(
1.000, 0.352, 0.265,
0.352, 1.000, 0.121,
0.265, 0.121, 1.000), nrow=3, byrow=TRUE)
intercor.PP(lamvec, cmat)
## End(Not run)
Computes the intermediate correlation matrix
Description
This function computes the intermediate correlation matrix of the multivariate normal distribution that provides a basis for subsequent tranformations.
Usage
intercor.all(cmat, pmat, lamvec)
Arguments
cmat |
a (n1+n2)x(n1+n2) matrix of specified correlations. |
pmat |
a n2x4 matrix where each row includes the four coefficients (a,b,c,d) of the Fleishman's system. |
lamvec |
a vector of lambda values of length n1. |
Details
This function assembles all three submatrices that are pertinent to all continuous-continuous, count-count, and count-continuous pairs.
Value
Returns an intermediate matrix of size (n1+n2)x(n1+n2).
See Also
intercor.NN, intercor.NNP, intercor.PP
Examples
## Not run:
pmat = matrix(c(
0.1148643, 1.0899150, -0.1148643, -0.0356926,
-0.0488138, 0.9203374, 0.0488138, 0.0251256,
-0.2107427, 1.0398224, 0.2107427, -0.0293247), nrow=3, byrow=TRUE)
lamvec = c(0.5,0.7,0.9)
cmat = matrix(c(
1.000, 0.352, 0.265, 0.342, 0.090, 0.141,
0.352, 1.000, 0.121, 0.297, -0.022, 0.177,
0.265, 0.121, 1.000, 0.294, -0.044, 0.129,
0.342, 0.297, 0.294, 1.000, 0.100, 0.354,
0.090, -0.022, -0.044, 0.100, 1.000, 0.386,
0.141, 0.177, 0.129, 0.354, 0.386, 1.000), nrow=6, byrow=TRUE)
intercor.all(cmat,pmat,lamvec)
## End(Not run)